Playing more than 60 cards

[laxkiddan]

What are your opinions on playing more than 60 cards? Im talking about 61-70, nothing ridiculous. Is it that much of a mtg sin?

[Brushwagg]

I use to play 61 in pre-VV Survival but really nothing else.

[GGoober]

Pretty much. Every card above 60 IS going to affect the chances of you drawing every other card. However, if that 61st card means a lot more to what the deck could achieve, it could possibly be worth it. I have tables/percentages all worked out for these and it's up to you to decide if 0.3-2% mean anything/significant. The truth is the analysis is much more complicated than just the value of 0.3-2%. I personally play 61 cards in control lists running 23 or more lands, otherwise I stick strictly with 60 cards if my decks tend not to involve the late-game.

I know some people play with 61 card lists as well, and do alright. Don't let people that tell you it's absolutely right/wrong catch you off guard. You need to do your own maths, playtest hundreds of games, both with 60 cards and with 61 cards to see how it pans out. I don't think many people have done this, but fall back on statistical results to make the decision for themselves, which tends to be 'playing a deck with more than 60 cards is wrong'. The problem with statistics/numbers is that they can always be twisted or intepreted to tell a story, so just be careful on what you're telling yourself or what others are telling you.

[.dk]

I'm on the same page as metalwalker. i've recently been running some control lists with a lot of card draw at 61 cards. i can never seem to decide on what the last card to cut is, so i started playing at 61. I didn't do the hundred game comparison, but my experience at least with the decks that i've been playing recently have been positive. Just remember that there is no one "right" answer - just because an approach is unconventional doesn't make it wrong. unless mounds of ridicule that you're an idiot distract you into playing poorly... then maybe it's wrong. ;)

[sco0ter]

It is maybe worth it in toolbox decks. Imagine you have little toolbox with Kuldotha Forgemaster. (4 Robot targets).
Then you squeeze in your 61st card, which is the 5th robot (e.g. Blightsteel Colossus).

Having the option to put Blightsteel Colossus onto the battlefield and just win against some decks or in some situations is probably worth more, than the tiny risk of drawing Blightsteel Colossus instead of a land, which then maybe cost you the game.
Or take Platinum Angel. I had many situations, where I would have wanted to search for it, because he would win me the game, since my oppoent can't deal with it, or buys me enough time, to win next turn.
Drawing 0.2% less Forgemasters (I didnt do the math) seems so marginal compared to the option to search for a game winning card.

[Cthuloo]

There is a very good discussion on the same subject here: http://www.mtgthesource.com/forums/showthread.php?15820-61-or-more-cards-in-toolbox-decks&highlight=61+cards

[codegeass]

I currently play a 61 card UB merfolk deck. I have topped once out of the three times I have played it since the rebuild I did, In a 25+ tourney at GYGO. I love it And I and have no intention of changing it anytime soon.

Bob helps get the job done even in merfolk!

[Gui]

This is probability. If your deck is a pile of optimal things, like Zoo and Zoo's creatures, and if they are all the same even if your deck has 61 cards, it all comes up to the chances of hitting a specific creature.

For example, if you don't care about always opening a Nacatl first turn, but you manabase needs a slightly higher count, you could add a land, making it a 61 cards deck, without diluting your core deck.

But, if you think your deck will be way better when you open with a card than it is when it open with another, than 60 is the best you can do for it (example, as above: If you really want to open a Nacatl/Vial T1, Show and Tell...)

TBH, the probabilities decrease so little, that in the end, 61 and 60 are pretty much the same, but for the added card, which gains a lot in chance of drawing.

So, bottom line, it isn't stupid, unless you want to maximize your chances of having specific cards over all the other cards.

[Julian23]

I wonder what's the reasoning for running 61 cards in a deck that's built on redundancy like the Ub Merfolk mentioned above. Except maybe for smoothing out the manabase.

However, I'm currently running 61 cards in Lands which is super tutor-heavy with Tolaria West and Intuition.

[bruizar]

There is a lot of conflicting Magic theory.

60-15-vision-theory
This theory holds that any deck should run 60 cards in the maindeck and 15 in the sideboard. Anything else is sub-optimal. Cut chaff until you reach 60 cards or you suck.

Replacement-fallacy-theory
Theory 2 claims that the thinning of your deck through cards such as fetch land, stoneforge mystic, Squadron Hawk, Gitaxian Probe and Street Wraithis nigh meaningless, . The replacement fallacy implies that cards such as Fetch should be used solely for color-fixing and brainstorming, not for deck thinning.

If you put these conflicting theories together, you can see the problem.

According to theory 1, a 61 card deck is strictly worse than 60, yet, according to theory 2, running a deck smaller than 60 cards has a negligible effect on top decks. This means that either running more than 60 cards doesn't affect your decks statistics in any meaningful way, or that fetch dramatically increases your chances of reaching certain desired cards. Feel free to pick which ever argument you like most.

[GGoober]

This is probability. If your deck is a pile of optimal things, like Zoo and Zoo's creatures, and if they are all the same even if your deck has 61 cards, it all comes up to the chances of hitting a specific creature.

For example, if you don't care about always opening a Nacatl first turn, but you manabase needs a slightly higher count, you could add a land, making it a 61 cards deck, without diluting your core deck.

But, if you think your deck will be way better when you open with a card than it is when it open with another, than 60 is the best you can do for it (example, as above: If you really want to open a Nacatl/Vial T1, Show and Tell...)

TBH, the probabilities decrease so little, that in the end, 61 and 60 are pretty much the same, but for the added card, which gains a lot in chance of drawing.

So, bottom line, it isn't stupid, unless you want to maximize your chances of having specific cards over all the other cards.

This is a good summary. Essentially, you should never play more than 60 cards for reasons that every card you add is worsening the chances to draw every other card. If you argue that the 61st slot is worth drawing, the first thing to do is to check if you can cut any other card to trim down to 60 cards.

This is most definitely true for decks that are based on optimal card selection or redundancy e.g. Tempo Thresh, Zoo, Combo, where the impact of drawing every card is huge, and you don't want to risk losing games because of a suboptimal deck. In decks like control/tutorbox/flex-slots, you can afford some 0.3-2% variation in draws by having the flexibility offsetting the statistical disadvantage.

[codegeass]

I wonder what's the reasoning for running 61 cards in a deck that's built on redundancy like the Ub Merfolk mentioned above. Except maybe for smoothing out the manabase.

However, I'm currently running 61 cards in Lands which is super tutor-heavy with Tolaria West and Intuition.

Yeah I understand it's not very efficient choice. It just I have a weak spot in my heart for jitte!
But I currently have had no problems with the deck. But if I start to see problems with the card redundancy I will remove it immediately!!

[Julian23]

To be fair, in order to actually recognize a difference you'd have to keep track of your drawings over several hundreds of games. Nobody does that.

[Richard Cheese]

To be fair, in order to actually recognize a difference you'd have to keep track of your drawings over several hundreds of games. Nobody does that.

Or you could just simulate it, although that would assume that shuffling is random when it really isn't all that random. Still much easier than actually playing hundreds of games and recording the data.

I would like to see all the tables/percentages, and would be even more interested on how those numbers are affected by decks that have draw engines like Jace/Brainstorm, or don't use the conventional draw mechanic like Dredge and Lands.

[Tammit67]

To be fair, in order to actually recognize a difference you'd have to keep track of your drawings over several hundreds of games. Nobody does that.

But there is a difference. You increase your variance.


There is a lot of conflicting Magic theory.

60-15-vision-theory
This theory holds that any deck should run 60 cards in the maindeck and 15 in the sideboard. Anything else is sub-optimal. Cut chaff until you reach 60 cards or you suck.

Replacement-fallacy-theory
Theory 2 claims that the thinning of your deck through cards such as fetch land, stoneforge mystic, Squadron Hawk, Gitaxian Probe and Street Wraithis nigh meaningless, . The replacement fallacy implies that cards such as Fetch should be used solely for color-fixing and brainstorming, not for deck thinning.

If you put these conflicting theories together, you can see the problem.

According to theory 1, a 61 card deck is strictly worse than 60, yet, according to theory 2, running a deck smaller than 60 cards has a negligible effect on top decks. This means that either running more than 60 cards doesn't affect your decks statistics in any meaningful way, or that fetch dramatically increases your chances of reaching certain desired cards. Feel free to pick which ever argument you like most.
Uh... what? Running fetchlands in goblins gives you on average 1 more goblin of off ringleader than previously. I get the feeling you made up Replacement fallacy on the spot. Is it not the general concensus that thinning your deck has an actual effect?
It isn't about what people like the most, it isn't an opinion that variance is introduced/reduced. The only thing up to interpretation is how significant it is. It is clear to see why the differene between 56 and 60 is larger than 64 and 60.

[Gui]

Or you could just simulate it, although that would assume that shuffling is random when it really isn't all that random. Still much easier than actually playing hundreds of games and recording the data.

I would like to see all the tables/percentages, and would be even more interested on how those numbers are affected by decks that have draw engines like Jace/Brainstorm, or don't use the conventional draw mechanic like Dredge and Lands.

I have these tables @ excel and the difference is usually less than 0.5%, or say, once every 200 games, you'll miss the other card. xD

[Julian23]

Uh... what? Running fetchlands in goblins gives you on average 1 more goblin of off ringleader than previously.

This might be the biggest overestimation of Fetchlands I have ever seen. Sorry. The general consus is that the "thinning" provided by Fetchlands is so little that you'll hardly ever note the difference and it's usually never worth the point of life you have to pay for it if you can't utilize the shuffling in another way (e.g. Brainstorm).
/edit: this is very likely true after casting several Ringleaders + using even more Fetchlands, way late into the game. Way deeper than almost all of you games go.

I know there used to be a pretty big article on SCG from like 5 years ago that was running all the numbers on this and came to the exact same conclusion. If someone feels like, please go check the archives, would be really worth it.


Or you could just simulate it, although that would assume that shuffling is random when it really isn't all that random. Still much easier than actually playing hundreds of games and recording the data..

I know. What I was trying to do was to tell him in a polite way, that his personal experience isn't of actual relevance ;-) .

[Einherjer]

I do it like this... I build an 60 card deck...when i got too much cards(which i dont) i play less, and some decks.. im just playing more..wheres the problem...actually i dont see any. Just do what you want.

[Koby]

I remember seeing a value that states the difference, accumulated over many turns and multiple activations, that a 2% difference in card quality will become apparent when using 8 fetchlands in your deck.

2% is a large value, equating to 1.2 cards in a 60 card deck.

[Julian23]

I think our discussion can't really reach a statistical backboned conclusion unless someone runes the numbers with specific scenarios in mind, e.g. the Goblin Ringleader example.

But, based on what we assume right now (like the 8 fetchland activations equaling about 1 card) over the course of a very long game....isn't paying almost half your life total for drawing a single more spell in the lategame really worth it? Again, totally depends on the kind of deck you're running. And your matchup. And the metagame in general.

What I want to show people is, that there is no actual 100% always correct way to decide this.

[Star|Scream]

This might be the biggest overestimation of Fetchlands I have ever seen. Sorry. The general consus is that the "thinning" provided by Fetchlands is so little that you'll hardly ever note the difference and it's usually never worth the point of life you have to pay for it if you can't utilize the shuffling in another way (e.g. Brainstorm).
/edit: this is very likely true after casting several Ringleaders + using even more Fetchlands, way late into the game. Way deeper than almost all of you games go.

I know there used to be a pretty big article on SCG from like 5 years ago that was running all the numbers on this and came to the exact same conclusion. If someone feels like, please go check the archives, would be really worth it.
.

What bruizar is saying though, is it seems that while this seems to be the general "consensus," it is also agreed that you must play 60 cards maximum in order to have the most optimal deck. These two ideas (appear to) conflict with each other.

Either the 1 card difference is so significant that it's definitely worth the few life to thin out your deck OR the difference is so "negligible" that if you want to run a 61st card, go for it.

[Mr. Safety]

My take on 61 card decks:

I think in combo decks where you have an absurd number of tutors (TES, ANT) 61 cards makes a negligable difference. If your deck has the potential to rip through up to 50%+ of itself in a game (like with Aggro Loam, Dredge, TES, ANT, Elves Combo) then 61 cards also seems to make a negligable difference, and the extra card can be a tutor target/metagame choice.

If you're playing a stream-lined list like Zoo, Team America, CounterTop, Gobbos, Fish...I would say stick
to 60. Consistency is key when you only have a handful of library manipulations/draw spells.

[Richard Cheese]

This might be the biggest overestimation of Fetchlands I have ever seen. Sorry. The general consus is that the "thinning" provided by Fetchlands is so little that you'll hardly ever note the difference and it's usually never worth the point of life you have to pay for it if you can't utilize the shuffling in another way (e.g. Brainstorm).
/edit: this is very likely true after casting several Ringleaders + using even more Fetchlands, way late into the game. Way deeper than almost all of you games go.

I know there used to be a pretty big article on SCG from like 5 years ago that was running all the numbers on this and came to the exact same conclusion. If someone feels like, please go check the archives, would be really worth it.


I found this, but it comes to the conclusion that multiple fetches does give you a statistically higher chance of drawing a non-land spell:
http://www.starcitygames.com/php/news/print.php?Article=15815 (http://www.starcitygames.com/php/news/print.php?Article=15815)

Then there's this post, where the guy claims that fetching doesn't improve your draws, but basically proves the opposite by showing that by fetching 4 times, you're 5% less likely to draw a land.
http://forums.mtgsalvation.com/showthread.php?t=201619

I think that's pretty relevant for most decks. There's this misconception in the Legacy community that if you get to turn 5-6, someone is winning or has already won. I guess with a format full of turn 1-4 combo, that's somewhat true, but plenty of decks have a good mid-late game, and can force it to go long enough where fetching starts to matter.

[Tammit67]

I think our discussion can't really reach a statistical backboned conclusion unless someone runes the numbers with specific scenarios in mind, e.g. the Goblin Ringleader example.

But, based on what we assume right now (like the 8 fetchland activations equaling about 1 card) over the course of a very long game....isn't paying almost half your life total for drawing a single more spell in the lategame really worth it? Again, totally depends on the kind of deck you're running. And your matchup. And the metagame in general.

What I want to show people is, that there is no actual 100% always correct way to decide this.

Play to win.

If you want me to do a Statistical test on it, I will. My thought is to determine the amount of spells in the next x cards after y fetch activations, evaluated at specified turns. I'm working towards being an Actuary, so it would be good practice.

[Nihil Credo]

Play to win.

If you want me to do a Statistical test on it, I will. My thought is to determine the amount of spells in the next x cards after y fetch activations, evaluated at specified turns. I'm working towards being an Actuary, so it would be good practice.
Suit yourself, but it's been done already:

http://magic.tcgplayer.com/db/article.asp?ID=3096

[Tammit67]

I find it strange that he decided to do repeated sampling (and without seeing the algorithm itself, called it a Monte Carlo).

I'd like to explore the potential advantage of fetchlands in hitting better off of the usual cards that see multiple cards from the deck, effects such as brainstorm/Ancestral visions/Standstill/Sylvan Library/Top and Ringleader/FoF. I won't have to use a sampling method, and can instead calculate using the Hypergeometric which is more commonly understood.

I'm not convinced his trials conclusions are well thought out enough. A deck that runs the above cards sees much more of its library than a deck not doing so, and these spells might accelerate the time before he calculated a player will actually feel the effects.

[.dk]

I found this, but it comes to the conclusion that multiple fetches does give you a statistically higher chance of drawing a non-land spell:
http://www.starcitygames.com/php/news/print.php?Article=15815 (http://www.starcitygames.com/php/news/print.php?Article=15815)

Then there's this post, where the guy claims that fetching doesn't improve your draws, but basically proves the opposite by showing that by fetching 4 times, you're 5% less likely to draw a land.
http://forums.mtgsalvation.com/showthread.php?t=201619

I think that's pretty relevant for most decks. There's this misconception in the Legacy community that if you get to turn 5-6, someone is winning or has already won. I guess with a format full of turn 1-4 combo, that's somewhat true, but plenty of decks have a good mid-late game, and can force it to go long enough where fetching starts to matter.

Yes, I don't think anyone would argue the mathematics... the question is whether or not it is worth the life you pay by cracking your fetch lands. 5% is measurable, but is it worth the 4 life you mention?

[.nemesis]

My take on 61 card decks:

I think in combo decks where you have an absurd number of tutors (TES, ANT) 61 cards makes a negligable difference. If your deck has the potential to rip through up to 50%+ of itself in a game (like with Aggro Loam, Dredge, TES, ANT, Elves Combo) then 61 cards also seems to make a negligable difference, and the extra card can be a tutor target/metagame choice.

In most combo decks, you want to gather very specific cards or cards of a certain subset. Like, when running ANT, you want to somehow put mana sources worth 5-7 mana and a business spell together. ANT runs 12 to 16 cantrips just to find these specific pieces, so digging through an extra card in your library can reduce your ability to "find what you need" by a relevant amount. It won't be much, statistically speaking, but the principle is pretty clear: If you want to cantrip into some specific cards in your library, you never go above 60 cards, because each card above 60 makes it harder to achieve your goal of putting said cards together.

(BTW: Neither TES nor ANT run an absurd amount of tutors. Infernal Tutor pretty much sucks when you need a 1-of answer. Burning Wish does this job, but 4 cards out of 60 hardly qualifies as an absurd amount. Currently, there is only two "Tier 1 tutors" in the format that see play - Merchant Scroll and Enlightened Tutor. And in their respective decks, running 61 cards might just be fine.)

On the other Hand, in a deck as redundant as Zoo or Merfolk, it won't really matter if you're running 60 or 61 cards, because most of the cards do essentially the same. I can't really imagine a card you would want as a 61st card in those decks though. Most likely some miser's 1-of.

Personally, I go above 60 cards if my mana/spell ratio doesn't feel right. When I need that 1 extra land but can't find anything to remove from my 60, it's card number 61. Sure, this may be wrong but honestly I don't care. As long as it works for me I'm fine.

[honestabe]

This has been discussed before by top-level pros, and i think their general consensus was that given the correct circumstances, it can be right (I remember one deck from GP Atlanta popping up) but a vast majority of the time, it is strictly worse to run 60 cards. There is also something to be said about running 61 if you don't know what to cut, because you don't want to cut the wrong card and be screwed.

[Tammit67]

but a vast majority of the time, it is strictly worse to run 60 cards. There is also something to be said about running 61 if you don't know what to cut, because you don't want to cut the wrong card and be screwed.

Strictly worse?

[mcfarland]

Strictly worse?


"it is strictly worse to run (more than) 60 cards," I'm assuming.

[Uncoordinated]

In reference to fetchlands and deck thinning: http://magic.tcgplayer.com/db/print.asp?ID=3096

As for running 61 cards, I think it's totally fine - if you're not playing at the top of the top. I'm sure everyone would agree even a top tier list running 61 cards isn't fully optimized. That's not to say a finely tuned and innovative metagame deck couldn't place high even with 61 cards, but I don't see it happening very often. Above-mentioned theoretical deck piloted by the same person minus a land probably wouldn't even end up showing much of a difference throughout the course of a tournament.

I can definitely see the benefits of a 61st card in control decks or maybe even decks that toolbox quite a bit for silver bullets ( GSZ, E. Tutor ), etc. I generally find it pretty easy to shave down to 3 of a certain card. My lists are always pretty scattered looking.

[NesretepNoj]

I would say, that running 61 cards is never correct in a statistical sense. I you were allowed to run 59 cards, would you then still insist on running 60 or even 61?

However, with regard to deck building, it can be argued, that running 61 i correct if you don't know what to cut. In any given tournament, if you compare two similar decks (one running 60 cards, the other 61), in which one of them did cut "the correct" card, the one with 60 cards will be the better deck.

[alderon666]

Taking this from non-math point of view. Everytime I'm playing TES reach my combo turn, and I know I have to go off the next turn or I'll lose, I always crack that last fetch in order to remove a land from the deck. Statistics show that I increased my chance of drawing a non-land card by 0.001234125 and probably just wasted 1 life point without knowing I needed to (sometimes +1 life when Ad Nauseing means drawing a lot of cards). But real life is not an average of a million games. I effectively removed a card of my deck, that I'm not drawing for sure.

61 cards is an excuse for adding some card you don't need because you don't know what to take out.

[Gui]

61 cards is an excuse for adding some card you don't need because you don't know what to take out.

Yet it's a good one. When you add a card like this, you reduce the chance of every card in the deck equaly. and can drastically increase the chance of a type of card. It's a fair trade, and not stupid.

I wouldn't recomend 61 card decks as starting list, but when you already have a finished 60 cards list in which you want to increase somethins a little, but without reducing something too much, 61 card decks are an option.

UNLESS you want to start with Mountain->Lackey go every game, in which case you should aim as much as possible for 60 cards.

[alderon666]

Yet it's a good one. When you add a card like this, you reduce the chance of every card in the deck equaly. and can drastically increase the chance of a type of card. It's a fair trade, and not stupid.

I wouldn't recomend 61 card decks as starting list, but when you already have a finished 60 cards list in which you want to increase somethins a little, but without reducing something too much, 61 card decks are an option.

UNLESS you want to start with Mountain->Lackey go every game, in which case you should aim as much as possible for 60 cards.

If it's so good why not just for 62 then? After all, the difference is SO tiny. When do you draw the line of X cards above 60 hurt my chances of drawing my good cards too much? I draw that line at 0.

[Cthuloo]

If it's so good why not just for 62 then? After all, the difference is SO tiny. When do you draw the line of X cards above 60 hurt my chances of drawing my good cards too much? I draw that line at 0.

It's hard to have precise extimations, but I guess that playskill and pairings have a much larger impact than playing with 61 cards. E.G., playing with 1 more card decreases the probability of seeing a 4-of in your opening hand by 0.6%, this means it will be relevant in one out of 167 matches. You also will have to be pretty damn sure about the right card to cut, since the margin is so small. Since you also don't know with 100% certainty what the metagame will be, it is very well possible that you can choose the wrong card to cut, resulting in a much bigger negative effect than the positive one coming from reducing the variance. Anyways, I guess any discussion is almost pointless, since we can't produce a reasonable simple model to evaluate precisely.

[Gui]

If it's so good why not just for 62 then? After all, the difference is SO tiny. When do you draw the line of X cards above 60 hurt my chances of drawing my good cards too much? I draw that line at 0.

Just stating, it's not as stupid as you think. Even 62 gives less than 1% less chance of drawing determined card at starting seven. I Think going with "60 is the perfect number" is just ignoring math. You know it's the best chance to draw determined card, but instead of ruining the chance of drawing another in favor of a third, if you add the 61st instead, you don't ruin all the chances.

I draw the line as close as possible to 0, for most of my decks have 60 cards, but I'm not hard-headed enough to ignore the fact that, if needed, I can play a 61 cards deck and mantain the good balance of my previous 60 cards deck while adding the business I think it lacks.
Note that I'm not defending "Play 61 cards as much as possible". I try to build 60 cards decks as well, it's the best starting point.

Besides all that, adding a Land as 61st card works wonders sometimes, to greedy manabases that wish to have a slightly higher land count, but no an entire land.

But really, if you don't have reasons to play 61 cards, than try as hard as you can to build 60 cards decks.


EDIT: I fully agree with Cthuloo's post, above /\

[alderon666]

Just stating, it's not as stupid as you think. Even 62 gives less than 1% less chance of drawing determined card at starting seven. I Think going with "60 is the perfect number" is just ignoring math. You know it's the best chance to draw determined card, but instead of ruining the chance of drawing another in favor of a third, if you add the 61st instead, you don't ruin all the chances.

I draw the line as close as possible to 0, for most of my decks have 60 cards, but I'm not hard-headed enough to ignore the fact that, if needed, I can play a 61 cards deck and mantain the good balance of my previous 60 cards deck while adding the business I think it lacks.
Note that I'm not defending "Play 61 cards as much as possible". I try to build 60 cards decks as well, it's the best starting point.

Besides all that, adding a Land as 61st card works wonders sometimes, to greedy manabases that wish to have a slightly higher land count, but no an entire land.

But really, if you don't have reasons to play 61 cards, than try as hard as you can to build 60 cards decks.


EDIT: I fully agree with Cthuloo's post, above /\

Yeah, but those numbers are open to interpretation. While a simulation ran a million times or statistics calculation show that the impact is very low, a tournment only has 6/7/8 rounds. Drawing that 61st removal card you added instead of a Mental Misstep against Storm is going to lose you the game, no matter how slim the chances are.

What I'm saying is, adding a card increases the variance. And while in a large sample the difference could not matter, the randomness added in small samples could make a big difference.

[Gui]

Yeah, but those numbers are open to interpretation. While a simulation ran a million times or statistics calculation show that the impact is very low, a tournment only has 6/7/8 rounds. Drawing that 61st removal card you added instead of a Mental Misstep against Storm is going to lose you the game, no matter how slim the chances are.

What I'm saying is, adding a card increases the variance. And while in a large sample the difference could not matter, the randomness added in small samples could make a big difference.

This makes no sense. The same randomness can win you games that you otherwise wouldn't. It'll all about % chances.

Edit: And in this case, adding a card that fights best against the metagame means drawing that card will increase your chances, not the opposite. Besides, the chances of drawing the card are better, but the chances of not drawing any of the other cards are just slightly decreased.

[Cthuloo]

I agree with Gui.

@alderon: In your example, adding a removal spell will decrease the probability of seeing a Misstep in the fist 10 cards by 0.7%, but (assuming e.g. that you moved up from 3 to 4 removal spells) it has increased the probability of drawing a removal by almost 10%, which can be a huge boost if the fields turns out to be more aggro than combo. The point is: if you have perfect knowledge of the field and perfect practice with the deck, then obviously 60 cards is the best configuration. If you don't (which is always the case), going up to 61 can be a more conservative, yet acceptable move.

[Mr. Safety]

(BTW: Neither TES nor ANT run an absurd amount of tutors. Infernal Tutor pretty much sucks when you need a 1-of answer. Burning Wish does this job, but 4 cards out of 60 hardly qualifies as an absurd amount. Currently, there is only two "Tier 1 tutors" in the format that see play - Merchant Scroll and Enlightened Tutor. And in their respective decks, running 61 cards might just be fine.)

I was counting Ad Nauseum as a tutor, along with Infernal Tutor and Burning Wish. That totals up to a minimum of 6, probably closer to 7-8. I shouldn't have said 'tutor'...I should have said 'library manipulation' spells. What I'm saying is it has a lot of ways to find the cards it needs. I misworded it; many apologies. Taking into account Brainstorm and Ponder, I would say that totals up to 'absurd' in my opinion, lol.

EDIT: the TES list in the TES primer actually plays 17 tutors/library manipulation spells...I think that's an absurd amount, lol. Maybe the list has changed slightly, but I don't think by much. Someone with more familiarity would be able to answer that better than I.

[alderon666]

Good players tend to avoid high variance decks, so they capitalize on their play skill and outplay their opponents.

Dredge is a fine example of a high variance deck. The deck is extremely powerful and can even fight hate decently. But the deck has so many dead draws that the variance is ridiculous. You can literally draw several 7 card hands and a lot of the will be unplayable or slowed down to a crawl by a single MM or FoW. On the other hand, there's a decent amount of hands that can basicaly win turn 2 fighting though a Crypt .


I agree with Gui.

@alderon: In your example, adding a removal spell will decrease the probability of seeing a Misstep in the fist 10 cards by 0.7%, but (assuming e.g. that you moved up from 3 to 4 removal spells) it has increased the probability of drawing a removal by almost 10%, which can be a huge boost if the fields turns out to be more aggro than combo. The point is: if you have perfect knowledge of the field and perfect practice with the deck, then obviously 60 cards is the best configuration. If you don't (which is always the case), going up to 61 can be a more conservative, yet acceptable move.

Then the correct thing to do is to remove some card that's bad against aggro and replace it with the extra removal spell. That way you tune your deck to be slightly better against aggro without altering the chances to draw land, creatures, etc.

[.dk]

Then the correct thing to do is to remove some card that's bad against aggro and replace it with the extra removal spell. That way you tune your deck to be slightly better against aggro without altering the chances to draw land, creatures, etc.

I think you just agreed with him... Given perfect knowledge of the meta, then 60 cards is ideal. His point was that if you don't have perfect knowledge, running 61 may be an acceptable trade.

So maybe the lesson here is to get the best knowledge of the meta as possible, and stop worrying about how many cards you run?

[Gui]

Then the correct thing to do is to remove some card that's bad against aggro and replace it with the extra removal spell. That way you tune your deck to be slightly better against aggro without altering the chances to draw land, creatures, etc.

This is true, but only if you know exactly what to cut, and is 100% certain you won't miss that card. If you cut something good against control to add the removal, and face a lot of aggro, the change made sence. But if you do that and end up facing controls, you risked yourself more than I would have by playing a 61-cards deck, and yet my 61-cards deck is almost as suited as yours against aggro. It's impossible to predict exactly against what you will play.

We are not saying "always play 61-cards deck, they are awesome!", but rather saying it is not as impactant as some people judges it to be. And we are actually providing numbers that prove this by showing the difference is barely sensible. But if you have the chance to playtest endlessly against every deck and decide precisely what to cut, that's the best move.

[Koby]

I believe a prime example of the 61st card syndrome is demonstrated by old Landstill - a deck that typically wants 23.5 lands. 23 oftentimes feel too few, and 24 feels too many. Adding the 24th land as the 61st card was a way to balance out the mana/cost ratio in the deck while still providing an additional mana source.

I also remember Jamie Wakefield (of Secret Force fame) always started his deck contruction with 26 lands, 62 cards. Is this correct? probably not. But it does lend some evidence on building better mana bases that are otherwise tricky to get right in decks that require a certain number of lands by a certain turn.

I don't think the above model is fit for Legacy deck construction. Cantrips and fetchland also skew this old theory.

[Shimi]

The only reason to play 61 cards deck is:

A)It's some lucky number or anything stupid like that.

B)You are testing some silverbullets and would like to see what to cut to make you deck a 60 card deck.

C)You are running something like lands + engine + tutors + 1of tutor targets that REALLY can't be cut.(eg. lands decks).

[SpikeyMikey]

This has been discussed before by top-level pros, and i think their general consensus was that given the correct circumstances, it can be right (I remember one deck from GP Atlanta popping up) but a vast majority of the time, it is strictly worse to run 60 cards. There is also something to be said about running 61 if you don't know what to cut, because you don't want to cut the wrong card and be screwed.

Top level pros are generally the last people I want to get deck construction advice from. Very few of them have the first clue what they're doing. What it boils down to is that while we like to pretend that Magic functions like an art, it really is a science. It's just a far more complex version of poker. But in Poker, calculating odds is much easier. You can talk about playing to outs in Magic, but the math is too difficult to do in your head. In hold 'em, you know if you've got AK suited you're ~33.3% against KK. It's far more difficult to, on the fly, calculate your chance of drawing both a land and a removal spell in the next 3 draws in order to stay in the game.

I almost never play decks with more than 60 cards (although I regularly play 41 in limited and occasionally 42 or 43) but that doesn't mean that I feel that 60 is always the correct choice. Deckbuilding, in my opinion, is primarily about ratios. The Bant deck I ran for the first 6 months of this year ran 4 Swords to Plowshares and 1 Path to Exile (although for the last 2 months or so while the format has been slower due to Mental Misstep, Path has become Engineered Explosives). People think of the singleton Path as strange, but it's not a singleton, it's the 5th Swords to Plowshares. It's the difference between being able to remove a creature 50% of the time by turn 3 (average between play and draw) and 59% of the time. By the same principle, if I've got a deck where I want to both maximize my chance of drawing Tarmogoyfs and Knights of the Reliquary but I also want to run 19 blue spells to help ensure I have enough to pitch to Force of Will, it may be necessary for me to run 61 or 62 cards. Cutting a Tarmogoyf or Knight for a junk blue spell, even a filtering blue spell like Ponder or Preordain is not an option. It's going to significantly reduce the number of whatever it was I cut that I draw because when I draw the Ponder instead of Knight, I'm looking at a (very slightly less than)4/(15-18)ish chance of finding a Knight with it (depending on how many cards are left in my library). I could run out the hypergeometric distribution, but let's just say that 75% of the time, that Ponder won't find me Knight. So instead of a 50% chance of having that Knight I need, I now have a 40% chance. That's pretty significant, you're talking once every 4-5 matches or about twice in a major tournament. And that's just for the first Knight, the odds are exponentially worse when you talk about finding a second one (having 2 left vs. 3 left).

[alderon666]

I think you just agreed with him... Given perfect knowledge of the meta, then 60 cards is ideal. His point was that if you don't have perfect knowledge, running 61 may be an acceptable trade.

So maybe the lesson here is to get the best knowledge of the meta as possible, and stop worrying about how many cards you run?



61 cards is an excuse for adding some card you don't need because you don't know what to take out.

Because quoting yourself is cool.
If you don't the meta well you should just tune the deck to play more versatile cards instead of just adding more of X or Y.


Playing 61 cards because you need half a land could probably be achieve in some other way. Like playing more cantrips or even playing less fetchlands (to increase your chance of drawing land cards, LOL).

[Hanni]

This thread needs more Jack Elgin.

[TheInfamousBearAssassin]

Well that's always true.

I kind of feel like I hashed this before. While I concede that there's the possibility that 61 cards is the correct number for mathematical reasons (or even 62), I think the math behind that is going to be so complex that it is pretty much certain that you're wrong for thinking so. And certainly it's the wrong default.

61 is fine if you're not sure what to cut the day of a tournament. I would otherwise much rather run 63 cards than 61 as doing the former will legitimately enrage some people (like running 8th Edition basic lands), and that makes people make mistakes.

But short of trying to psych people out (which I would only recommend in a highly redundant deck), stick to 60.

[Kuma]

Playing more than 60 cards is wrong:

1: The cards in your deck can be ranked in order of overall power from 1 to 60. This is hard to do in practice, but we all know that some cards in our deck are better than others.

2: Running a 61st card decreases your chances of drawing the 60 cards more powerful than your worst card. It's only a small amount, but why willingly sacrifice any chance of drawing your best cards, especially when there's a card in the list that's weaker than all the other cards that you don't have to run? You need to figure out which card this is and cut it.

Therefore, playing more than 60 cards is wrong.

[Julian23]

@Kuma:

I disagree with your first assumption. Therefor I disagree with your conclusion.

[.dk]

@alderon666 yep, that's a fair point. if you can find more versatile cards to play in your 60 without sacrificing much, then that would be better. I think the only point here is that it isn't ALWAYS wrong to run more than 60. If you can't find a more versatile solution without sacrificing too much, and you don't know the field, then perhaps it could be better to run 61.

@Kuma isn't your first point dependent on what your matched against? Again, I think this comes down to meta-game knowledge. If you knew exactly what you'd be playing every time, then yes, you could rank your cards from 1-75 (don't forget your other 15). However, some of those might be relatively weak against some portion of the field, which would change their ranking.

i'm going to stick to my last post and claim that this really comes down to understanding the meta-game. If you know the meta-game like the back of your hand, you should be able to narrow it down to 60.

[Gui]

Playing more than 60 cards is wrong:

1: The cards in your deck can be ranked in order of overall power from 1 to 60. This is hard to do in practice, but we all know that some cards in our deck are better than others.

They can, but then you are taking into account the % of decks played in the metagame.

Let's say, just for the sake of argument, that you can predict 100% of your metagame and this wouldn't require NOAA Super Computers and complex models to be done.

Then you'd have to calculate the % of the time each card wins against each given possible matchup in the field in order to determine which is better, using a weighted mean.

This, without taking into consideration the interaction of that card with the rest of your deck, and the interaction of that card with varied build from different decks. Only then you'd have, precisely, the power level of each card on your deck, and could order then from 1 to 60.

Then you'd have to take out the least powerful card you found, add yours, and do the whole process again, and see if your % winning against the field is now better.

Well, if you really can do all that, suit yourself. I'd rather take almost the same risk by adding the 61st card instead.


No, really, noone knows exactly the % of matchups and the % of time each of his cards wins, the stupid thing is not playing 61 cards, the stupid thing is claiming that you know that much, enough to dismiss 61 card decks all the time.

And just to reinforce, I'm not saying 61 cards should be the starting point to build a deck, just saying that given a few situations, you can as well play 61 cards. Unless of course you have NASA super computers and 300 IQ.

[SpikeyMikey]

Playing more than 60 cards is wrong:

1: The cards in your deck can be ranked in order of overall power from 1 to 60. This is hard to do in practice, but we all know that some cards in our deck are better than others.

2: Running a 61st card decreases your chances of drawing the 60 cards more powerful than your worst card. It's only a small amount, but why willingly sacrifice any chance of drawing your best cards, especially when there's a card in the list that's weaker than all the other cards that you don't have to run? You need to figure out which card this is and cut it.

Therefore, playing more than 60 cards is wrong.

This is the common logic behind the idea that 60 cards is a hard and fast "rule". It's a theory that dates back to the late 90's and has held on as firmly as the card counting rule of "card advantage" (card played is -1CA, card drawn is +1). It is also absolutely and unequivocally wrong. Outside of the ratio argument that I gave above, you can use two general scenarios to show the fallacy of this theory.

Let's follow the chain to its logical conclusion. If card 61 is better than card 62, and card 60 is better than 61 and 59 is better than 60, we would be forced to conclude that the best deck would be a single card, as card 1 is obviously superior to card 2. Obviously, this is impossible due to the mechanics of M:tG (you'd deck, you wouldn't actually be able to cast this card, etc.). Even if we remove decking from the equation, a 13-14 card version of a current deck wouldn't be competitive (if it were legal). There's not enough room to boil Counterbalance down to 14 cards. You're looking at 5 lands (5.13 lands would be equivalent to 22 lands in a 60 card deck) and 9 spells. You want to fit Sensei's Divining Top, Counterbalance, Swords to Plowshares, Force of Will and Tarmogoyf into the deck at a minimum. You need a minimum 4 blue cards to support Force of Will (17 blue cards in a 60 card deck is equivalent to 3.96 in a 14 card deck) so you'll have to have at least 2 more. We've got 2 cards beyond that to play with. And you have little to no redundancy, so if something doesn't resolve or if it's removed, you're fucked.

The other way to show the fallacy of your theory is to discuss deckbuilding with a removal of the 4-of rule. If there were no limits on how many copies you could run of a given card, would you go to a single unique spell? Probably not. You need more than one effect. Tarmogoyf might be how you win the game, but 22 lands and 38 Tarmogoyfs will get the everloving snot kicked out of it by half the decks in Legacy. Your opponent plays a single Wild Nacatl and proceeds to beat you to death with it. We had a similar discussion in IBA's "Tour de Force" thread. The idea was that a 0 mana hard counter with no drawback would be the best card in the format, hands down. But you couldn't run a 60 Tour de Force deck. At a minimum, you'd have to have at least 1 win condition. Say a Mishra's Factory. And the way to beat that deck would be to run at least 1 Wasteland. So the way to beat that is to run say Crucible of Worlds and more Factories. And the way to beat that is to run Krosan Grips. And eventually, you follow this chain of "in order to beat this..." and you find out that you're not actually running all that many Tour de Forces. Maybe you can fit 8-10. Maybe not even that many. Any way you slice it, the format has grown a bit more complex from 20 Lotus, 20 Channel and 20 Fireball.

There are plenty of cards in plenty of decks that are phenomenally powerful and necessary for the function of the deck that you don't even run 4 copies of. When's the last time you saw a Natural Order deck run 4 Natural Orders? It's the focus of the whole goddamn deck and they play 3. Everyone plays 3. Because it's all about ratios and percentages. You don't want multiple NO's clogging up your hand. And you don't need to resolve more than 1. It's easily the most powerful card in the deck. No other card gives you 10 unblockable, untargetable power worth of creature for 4 mana. A pair of Tarmos may give you 10 power, but they'll be blockable and Plowable. And yet, despite being the most poweful card in the deck, you don't even run the maximum legally allowable.

And as a further exercise, let's discuss Brainstorm. Brainstorm has been called, by more talking heads than I can count, the best card in Legacy. But Brainstorm's power has a directly proportional relationship with the number of unique cards in a deck. For instance, if your deck is nothing but Relentless Rats, some U/B lands and Brainstorm, you're not getting much out of it. As the number of unique cards in the deck rises, the value of Brainstorm increases. Brainstorm is not the only card that acts this way. Any sort of filter effect becomes stronger the more unique cards the deck has. Creatures like Knight of the Reliquary gain a lot of EV from running tutorable lands even though those lands are suboptimal in a non-KotR situation (because they can't reliably be found without KotR and can't be run as 4-ofs). Think Karakas, Maze of Ith or Volrath's Stronghold. Maybe I decide that Volrath's Stronghold is the weakest card in my Rock deck and I cut it. But in doing so, I make my 4 KotR's worse. And maybe that loss is greater than what I'd lose cutting a Tarmogoyf. But cutting a Tarmogoyf makes my Volrath's Stronghold weaker. In an era with so many filtering and tutoring effects, cutting cards does not necessarily make a deck stronger. And you can't just cut the filtering effects, assuming that the deck will be stronger for simply playing more "good" spells and not running filler filter spells. Take Nassif's 2008 Counterbalance deck and pull Brainstorm and Ponder from it. See how playable it is.

[Julian23]

Thanks Mikey for pointing out what I might have been to lazy to present. Especially that 38 goyf 22 lands example really showcases how you can't just argue that Card 60 will/should always be better than card #61.

[Kuma]

@Kuma:

I disagree with your first assumption. Therefor I disagree with your conclusion.

Care to elaborate?


@Kuma isn't your first point dependent on what your matched against? Again, I think this comes down to meta-game knowledge. If you knew exactly what you'd be playing every time, then yes, you could rank your cards from 1-75 (don't forget your other 15). However, some of those might be relatively weak against some portion of the field, which would change their ranking.

Well yes, the weakest card in your deck is obviously match dependent. You should have enough metagame knowledge to know what the overall weakest card in your deck is, or you have another problem entirely.

When I say rank the cards in your main deck from 1-60, I mean in terms of overall usefulness against your likely opponents. If you're running a 61 card toolbox deck, there's probably one card in your main deck that is good in fewer and less common matchups than the rest. That card needs to be in your sideboard or out of the 75.


i'm going to stick to my last post and claim that this really comes down to understanding the meta-game. If you know the meta-game like the back of your hand, you should be able to narrow it down to 60.

Exactly, and if you don't know the metagame you have a bigger problem than the 61st card. Why not learn the metagame and solve both problems?


They can, but then you are taking into account the % of decks played in the metagame.

Obviously.



Let's say, just for the sake of argument, that you can predict 100% of your metagame and this wouldn't require NOAA Super Computers and complex models to be done.

Then you'd have to calculate the % of the time each card wins against each given possible matchup in the field in order to determine which is better, using a weighted mean.

This, without taking into consideration the interaction of that card with the rest of your deck, and the interaction of that card with varied build from different decks. Only then you'd have, precisely, the power level of each card on your deck, and could order then from 1 to 60.

etc...

I'm not saying that we can be absolutely certain what the worst overall card in our deck is, but if you know your metagame and have played with the deck significantly, you should have a pretty good idea of what that card is.

If you can't trust your judgment to know what the weakest card in your deck is, how can you trust your judgment to know that the 61st card you've added is correct?


And just to reinforce, I'm... just saying that given a few situations, you can as well play 61 cards. Unless of course you have NASA super computers and 300 IQ.

The 61st card reduces the chances of drawing your other 60 cards. That is a mathematical fact. If that 61st card is really better than the other 60 cards, it's not the 61st card, it's the 1st.


Let's follow the chain to its logical conclusion. If card 61 is better than card 62, and card 60 is better than 61 and 59 is better than 60, we would be forced to conclude that the best deck would be a single card, as card 1 is obviously superior to card 2. Obviously, this is impossible due to the mechanics of M:tG (you'd deck, you wouldn't actually be able to cast this card, etc.).

Except that since we can't take our decks below 60 cards, the fact that the idea breaks down below eight cards isn't relevant. We aren't discussing theoretical 59 card or smaller decks, we're arguing 60 vs. 61.


Even if we remove decking from the equation, a 13-14 card version of a current deck wouldn't be competitive (if it were legal).

I think combo would be pretty ridiculous if you could run 13-14 cards. The odds of you having your combo plus protection would be much higher than is acceptable for Legacy power levels.

A few years back, my friends and I played 15-card singleton with everything legal as a thought exercise. The best two decks in that format were Stax and Storm. Stax was good, because it didn't have to worry about consistency at all and won pretty much every game it went first. Storm was good because you put your whole deck in your hand and just won. I can comfortably say that at least that Stax deck would be ridiculous even in Vintage.



The other way to show the fallacy of your theory is to discuss deckbuilding with a removal of the 4-of rule. If there were no limits on how many copies you could run of a given card, would you go to a single unique spell? Probably not. You need more than one effect.

Oh, I don't know. I'll bet Burn would love to be 22 Mountains and 38 Lightning Bolts. It would be better if there were some Fireblasts in there, sure, but it would be ridiculous with just Bolt.


Tarmogoyf might be how you win the game, but 22 lands and 38 Tarmogoyfs will get the everloving snot kicked out of it by half the decks in Legacy. Your opponent plays a single Wild Nacatl and proceeds to beat you to death with it. We had a similar discussion in IBA's "Tour de Force" thread. The idea was that a 0 mana hard counter with no drawback would be the best card in the format, hands down. But you couldn't run a 60 Tour de Force deck. At a minimum, you'd have to have at least 1 win condition. Say a Mishra's Factory. And the way to beat that deck would be to run at least 1 Wasteland. So the way to beat that is to run say Crucible of Worlds and more Factories. And the way to beat that is to run Krosan Grips. And eventually, you follow this chain of "in order to beat this..." and you find out that you're not actually running all that many Tour de Forces. Maybe you can fit 8-10. Maybe not even that many. Any way you slice it, the format has grown a bit more complex from 20 Lotus, 20 Channel and 20 Fireball.

Okay, I'll concede the point that if there were no four-card limit in Magic, decks would not usually have lands plus multiple copies of one card. That said, the only way this is relevant to the discussion of 60 vs. 61 is if 60 wasn't enough to have everything you need to have a functioning deck, and 61 was. I don't think a single deck in Magic fits that criteria.

I'm the guy saying 61 is never correct. All you guys need is one counterexample of a Legacy deck where 61 is obviously better than 60.

You can't find one? Then, in the absence of solid evidence, shouldn't we go with what we know to be mathematically true, that running 61 cards hurts our chances of drawing our most powerful cards, no matter what they are?


There are plenty of cards in plenty of decks that are phenomenally powerful and necessary for the function of the deck that you don't even run 4 copies of. When's the last time you saw a Natural Order deck run 4 Natural Orders? It's the focus of the whole goddamn deck and they play 3. Everyone plays 3.

You might want to check out the NO RUG thread.


Because it's all about ratios and percentages.

Maybe 61 cards gets you the perfect set of percentages. If someone, in defense of some 61 card list could give me the perfect percentages, or at least what they think the perfect percentages are, and showed me how it's impossible to get those percentages at 60 cards, I'd concede the point.

But that's never what happens when somebody suggests a 61 card deck. It's always vague arguments about how you can't prove 60 is better than 61. Or that they don't know what to cut. Or how they aren't sure what the metagame will be so they want to cover their bases. Or the worst of them all, that it just doesn't matter, despite that being demonstrably, mathematically false. Every percent is crucial in tournament Magic. If you don't believe that, you probably don't have the mindset to be a truly great Magic player.


And as a further exercise, let's discuss Brainstorm. Brainstorm has been called, by more talking heads than I can count, the best card in Legacy. But Brainstorm's power has a directly proportional relationship with the number of unique cards in a deck.

To a point, yes. I'd argue that Brainstorm is better in Legacy than EDH, because it's more likely to get you the card/cards you need.


Creatures like Knight of the Reliquary gain a lot of EV from running tutorable lands even though those lands are suboptimal in a non-KotR situation (because they can't reliably be found without KotR and can't be run as 4-ofs). Think Karakas, Maze of Ith or Volrath's Stronghold.

Once again, this is only true to a point. Running too many singletons will lead to bad draws when you get useless singletons in your hand instead of relevant cards.

Even if Knight of the Reliquary gains EV from running more singleton tutor targets, not only are you less likely to draw a Knight of the Reliquary for each card over 60, you're more likely to draw a useless silver bullet than a useful card. You said yourself that you need a variety of cards in a deck to win. How does running cards that are marginal in a large number of matchups help you get relevant cards?


Maybe I decide that Volrath's Stronghold is the weakest card in my Rock deck and I cut it. But in doing so, I make my 4 KotR's worse. And maybe that loss is greater than what I'd lose cutting a Tarmogoyf. But cutting a Tarmogoyf makes my Volrath's Stronghold weaker. In an era with so many filtering and tutoring effects, cutting cards does not necessarily make a deck stronger. And you can't just cut the filtering effects, assuming that the deck will be stronger for simply playing more "good" spells and not running filler filter spells. Take Nassif's 2008 Counterbalance deck and pull Brainstorm and Ponder from it. See how playable it is.

If you've played your Rock deck enough, you should have a good idea of what the worst overall card in your deck is, despite its synergy with other cards in the deck.

I repeat, if you can't trust your judgment to know what the weakest card in your deck is, how can you trust your judgment to know that running the 61st card is correct?

[.dk]

Well yes, the weakest card in your deck is obviously match dependent. You should have enough metagame knowledge to know what the overall weakest card in your deck is, or you have another problem entirely.

When I say rank the cards in your main deck from 1-60, I mean in terms of overall usefulness against your likely opponents. If you're running a 61 card toolbox deck, there's probably one card in your main deck that is good in fewer and less common matchups than the rest. That card needs to be in your sideboard or out of the 75.



Exactly, and if you don't know the metagame you have a bigger problem than the 61st card. Why not learn the metagame and solve both problems?


I think we're agreeing, but strangely coming to different conclusions. I guess I'm saying that the more perfect your knowledge is, the easier it is to make an optimal 60. Since one can never have perfect knowledge, it is conceivable that bringing 76 with you may be the right choice sometimes for reasons already mentioned (marginally reduce the chance of drawing most of your types of cards, and greatly increase the chance of drawing 1 other one).

[Gui]

If you can't trust your judgment to know what the weakest card in your deck is, how can you trust your judgment to know that running the 61st card is correct?

Exactly, but, mathematically, I'm taking less risks adding the 61st than cutting what I believe to be the worth 60th, exactly because the effect of adding the 61st increases almost the same as if it was the 60th, but the reduction of each card in the deck is marginal, technically non-sensible, 1 out of 150 games difference.



I think we're agreeing, but strangely coming to different conclusions. I guess I'm saying that the more perfect your knowledge is, the easier it is to make an optimal 60. Since one can never have perfect knowledge, it is conceivable that bringing 76 with you may be the right choice sometimes for reasons already mentioned (marginally reduce the chance of drawing most of your types of cards, and greatly increase the chance of drawing 1 other one).

I second this opinion.

[Koby]

I'm the guy saying 61 is never correct. All you guys need is one counterexample of a Legacy deck where 61 is obviously better than 60.

You can't find one? Then, in the absence of solid evidence, shouldn't we go with what we know to be mathematically true, that running 61 cards hurts our chances of drawing our most powerful cards, no matter what they are?


I will boldly go on record that such no such proof exists. This is a NP versus P type dilemma. We can't even say that Deck A (60 cards) vs Deck B (60 cards) is objectively better, when the difference between them is only 1 card, using mathematics. Therefore, it is just as unlikely to prove that 60 vs 61 cards is objectively superior using mathematics. The problem therein lies that we can model a scenario, but cannot prove its validity. On the flip side, there are many who claim that 60 is objectively better by limiting variance.

There are too many variables involved to find such converging, hard numbers. With elements in deck design such as fetchland, cantrips, tutors, and colored mana sources (i.e., Volcanic Island vs Tundra), any single element can be ordered such that the desired result is non-deterministic.

As for examples, I submit 24 land / 61 card Landstill as an example of a deck that uses 61st card. The case of a deck with 24/60 is too high for mana ratio, and 23/60 is too low. This holds true even for modern Jace lists that require 4 mana by turn 4.

Taking that into practice - odds for drawing 4 lands by turn 4:

On the play:(sample = 10)
24/60 - P (X >= 4) = 63.2%
24/61 - P (X >= 4) = 61.4%
23/60 - P (X >= 4) = 58.6%

On the draw: (sample = 11)
24/60 - P (X >= 4) = 72.6%
24/61 - P (X >= 4) = 70.9%
23/60 - P (X >= 4) = 68.3%

Thus, on the play, there is 4.6% difference between 23 to 24 lands.
On the draw, there is a difference of 4.3%.

Playing an extra land from the 23/60 model provides better consistency in hitting the 4th land by the 4th turn. This assumes no card drawing and fetching obviously.

[Julian23]

I'm the guy saying 61 is never correct. All you guys need is one counterexample of a Legacy deck where 61 is obviously better than 60.

You can't find one? Then, in the absence of solid evidence, shouldn't we go with what we know to be mathematically true, that running 61 cards hurts our chances of drawing our most powerful cards, no matter what they are?

That's the main point we are argueing about: there are no cards in your deck that are "better" than others.

[TheInfamousBearAssassin]

That's the main point we are argueing about: there are no cards in your deck that are "better" than others.


Of course there are.

Question: Would the people who are saying it is sometimes correct to run 61 cards say that it is sometimes correct to run 62 cards? And if that, then 63 cards?

Is there some deck where it is correct, mathematically, to run 63 cards?

[Tao]

This has been debated often enough in the many years since tournament magic exists.

Everyone who plays 61 or more cards makes his deck inferior (you could theorize a format in which decking matters so playing more cards is relevant but this is certainly not true for the current Legacy format)
Everyone who argues that it improves or doesn't weaken his deck to play 61 or more cards has no clue what he is talking about. Just because something is hard to prove mathematically it doesn't mean you can't use common sense.

[Gui]

Question: Would the people who are saying it is sometimes correct to run 61 cards say that it is sometimes correct to run 62 cards? And if that, then 63 cards?

I would say so, but this would be a circunstance so hard to find that I won't advocate anyone to do so.

Believe me when I say I do my math in order to determine which cards to run, I actually use an excel table with varying deck size, hand size, number of copies and amount of copies drawn, and the % chances converted to amount of games (I have some friends that can tell you this is true), and then, besides that, I use a java simulation software to the harder cases (such as, the last time I used it, I was trying to see how often would discarding one or two dredgers with Firestorm and dredging would find me another dredger so that I could keep going without another discard outlet).

Besides, it's not really a common situation we are advocating the run of a 61st card. It's narrow, specific, in which you have a tunned deck and want to add power to it in one direction, but don't really know what to cut, for metagame reasons. If you keep adding cards like that, say the 62nd, 63rd, then you are compromising your core deck more than if you took a card you are not sure if you should. So I'd only advocate for the 61st, in extreme cases ( in which you already played a sharp 61 cards deck) you could add the 62nd.

We are saying that, in the end, it comes up to wether or not you believe to have this tunned deck, and if you are really not sure about which card to take out. These advocating you can always cut a card are right about the chance on hitting good cards, but are taking a risk of scratching more the deck that it was needed in case they don't know precisely what to cut.


In theory, almost no deck should have 61 cards, but for a really finely built tune within its ratios that couldn't be done with 60.
But in practice, no, we never are that omniscient. I seriously doubt anyone is even close to work that much with the ratios.

[Julian23]

Of course there are.

Uhm, no. See the 38 goyf 22 lands example. You can't rank your cards in a vacuum. It all depends on the circumstance which is the main reason people run different cards or sometimes decks without any 4 offs. And that's the reason why 61 can be +EV.

[Kuma]

Exactly, but, mathematically, I'm taking less risks adding the 61st than cutting what I believe to be the worth 60th, exactly because the effect of adding the 61st increases almost the same as if it was the 60th, but the reduction of each card in the deck is marginal, technically non-sensible, 1 out of 150 games difference.

As a competitive Magic player, let me thank you in advance for giving me an extra 1 in 150 chance of beating you should I ever be seated across from you.


I will boldly go on record that such no such proof exists. This is a NP versus P type dilemma. We can't even say that Deck A (60 cards) vs Deck B (60 cards) is objectively better, when the difference between them is only 1 card, using mathematics. Therefore, it is just as unlikely to prove that 60 vs 61 cards is objectively superior using mathematics.

Are you telling me that you don't even have a vague idea of the relative power level of the cards in your deck? Are you disputing that adding a 61st card decreases the chances of drawing the other 60?

If not, how did I not just prove mathematically that 60 is better than 61?


The problem therein lies that we can model a scenario, but cannot prove its validity. On the flip side, there are many who claim that 60 is objectively better by limiting variance.

Look, the number of possible 61 card Magic decks is probably greater than the number of particles in the universe. Given that, it's incredibly likely that there's some combination of 61 cards that no matter what you cut you're hurting the deck's win percentages.

That said, what the hell makes any of you unique snowflakes of unique specialness think your 61 card deck fits that criteria? I'll freely admit that we can't prove that there is no combination of 61 cards that can't be improved by cutting one card, if you'll admit that we also can't prove the reverse. My point is that in the absence of proof, shouldn't we just use what we know? Some cards in any deck are better than others. Anyone disputing that doesn't know their deck or doesn't understand Magic. We also know that adding a 61st card decreases your chances of drawing the other 60. This is a mathematical fact, and no one in the thread has disputed this.

Why not err on the side of increasing your chances of drawing your most powerful cards?


As for examples, I submit 24 land / 61 card Landstill as an example of a deck that uses 61st card. The case of a deck with 24/60 is too high for mana ratio, and 23/60 is too low. This holds true even for modern Jace lists that require 4 mana by turn 4.

Taking that into practice - odds for drawing 4 lands by turn 4:

On the play:(sample = 10)
24/60 - P (X >= 4) = 63.2%
24/61 - P (X >= 4) = 61.4%
23/60 - P (X >= 4) = 58.6%

On the draw: (sample = 11)
24/60 - P (X >= 4) = 72.6%
24/61 - P (X >= 4) = 70.9%
23/60 - P (X >= 4) = 68.3%

Thus, on the play, there is 4.6% difference between 23 to 24 lands.
On the draw, there is a difference of 4.3%.

Playing an extra land from the 23/60 model provides better consistency in hitting the 4th land by the 4th turn. This assumes no card drawing and fetching obviously.

Your argument is that 61 cards can be better than 60 because drawing more than four lands in Landstill is fine 614 games out of 1000, but if it creeps up to 632 out of 1000 that's too much?

Come on.

Since you've obviously played a ton of games of Magic to come to this conclusion, let me ask you this. How many games have you lost because you drew the card you needed a turn to late? How many of those games would you have won if you were running 60 cards? I'm pretty sure the answer is greater than zero.


That's the main point we are argueing about: there are no cards in your deck that are "better" than others.

Oh, good Lord.

I don't think I've ever had an easier argument to disprove. Let's look at this NO RUG decklist:

Creatures
2 Grim Lavamancer
4 Noble Hierarch
4 Tarmogoyf

Instants
4 Brainstorm
3 Daze
4 Force of Will
4 Lightning Bolt
3 Mental Misstep

Legendary Creatures
1 Progenitus
3 Vendilion Clique

Sorceries
3 Green Sun's Zenith
4 Natural Order
2 Ponder

Basic Lands
1 Island

Lands
4 Misty Rainforest
1 Scalding Tarn
1 Taiga
3 Tropical Island
3 Volcanic Island
4 Wooded Foothills

Land Creatures
2 Dryad Arbor

Since all the cards in this deck are "equally good" according to you, would I be correct in saying that if I cut a Brainstorm for another Ponder that the deck wouldn't lose or gain any power? According to you, Brainstorm and Ponder are equally good in this list. Once again, this means that Natural Order and Progenitus are equally good cards in this deck. If I cut three Natural Orders for three Progenituses, the deck is still just as good, right?


Uhm, no. See the 38 goyf 22 lands example. You can't rank your cards in a vacuum. It all depends on the circumstance which is the main reason people run different cards or sometimes decks without any 4 offs. And that's the reason why 61 can be +EV.

Who's ranking their cards in a vacuum?

You rank your cards in the context of how they perform in general, and how good they are against your expected metagame?

Also, the 38 goyf 22 lands example isn't anywhere close to reality and therefore has no relevance to this discussion.

[TheDarkshineKnight]

As a mathematician, let me just say that reading this topic physically painful for me.

Also, I've got two short comments to add:

1. Adding a 61st card is ALMOST ALWAYS a bad idea as it decreases your chance of drawing what you want and/or need by an amount that is not insignificant.

2. I am open to the possibility that a deck can be so finely tuned that the only possible improvement is, in fact, adding a 61st card. While I cannot provide evidence of this being true as I know of no such examples, I find it much more likely that such an example exists than not. Out of an, for all intents and purposes, infinite number of 60 card decks, probability dictates that at least one of these decks could be improved only by adding a 61st card.

[Koby]

Your argument is that 61 cards can be better than 60 because drawing more than four lands in Landstill is fine 614 games out of 1000, but if it creeps up to 632 out of 1000 that's too much?

Come on.

Since you've obviously played a ton of games of Magic to come to this conclusion, let me ask you this. How many games have you lost because you drew the card you needed a turn to late? How many of those games would you have won if you were running 60 cards? I'm pretty sure the answer is greater than zero.


No, my argument is that to improve a deck's consistency in drawing just enough lands. Hence, adding the 24th land as the 61st card. I would never add a non-land as the 61st, because there is always room for improving and making the curve tighter.

Like you said, I only need to show one example of a deck using 61 card and I have. The probabilities calculated demonstrated not a soft-factor for determining the utility of the 61st card, but rather, the middle ground between the 23rd and 24th land in the deck. Hence, there is efficiency in adding the 61st card, and disproving your theory that "60 is better than 61 in every instance".

The idea that the 24th land is the 61st card in Landstill is an old topic, and if you wish, I will dredge up the post.

[Julian23]

As a mathematician, let me just say that reading this topic physically painful for me.

Also, I've got two short comments to add:

1. Adding a 61st card is ALMOST ALWAYS a bad idea as it decreases your chance of drawing what you want and/or need by an amount that is not insignificant.

2. I am open to the possibility that a deck can be so finely tuned that the only possible improvement is, in fact, adding a 61st card. While I cannot provide evidence of this being true as I know of no such examples, I find it much more likely that such an example exists than not. Out of an, for all intents and purposes, infinite number of 60 card decks, probability dictates that at least one of these decks could be improved only by adding a 61st card.

That's the kind of open-mindedness I've been looking for throughout this thread. Especially the second paragraph.

[Tacosnape]

The first thing to note is that the difference isn't all that big, ever. Don't ever discount an opponent because they're playing 61 cards.

That said, having more than 60 cards in a deck is never a good idea. The difference can be miniscule, and I believe that a 61 card deck is quite capable of winning a major event, but that deck could be better at 60 cards.

Here are the two exceptions to this rule that can warrant running over 60 cards:

1. You have to have a strong reason to believe that the number of cards in your library could be relevant. This is less prominent in Legacy, given how many decks run fetchlands and card draw, than it is in something like Sealed, where you might run 42 in a highly defensive deck to ensure you can just outlast a deck with 40. This theory also applies to something like a Battle of Wits deck.

2. If the difference between a 61 card list and a 60 card list is only the one card, if the card cut is the wrong card for a given deck and/or metagame, the 61 card list can be stronger. This means that while hypothetically 60 card decks are always the perfect number, a 61 can be stronger if you make the wrong decision as to what the last card to cut is. So if you don't know what the right card to cut is, you could in theory run 61 and at least not be running the worst possible deck. You just won't be running the best, either.

It's also worth noting that any time you have a card where you'd run more than four of if you could in your deck, you shouldn't run more than 60 because you're essentially lowering your ratio of your most powerful cards to a less than 1/15 occurrence.

[Julian23]

I don't think I've ever had an easier argument to disprove.

Since all the cards in this deck are "equally good" according to you, would I be correct in saying that if I cut a Brainstorm for another Ponder that the deck wouldn't lose or gain any power? According to you, Brainstorm and Ponder are equally good in this list. Once again, this means that Natural Order and Progenitus are equally good cards in this deck. If I cut three Natural Orders for three Progenituses, the deck is still just as good, right?


You still don't get it. You assume my argument is "Power level (NO) = Power level (Progenitus". That's bullshit and doesn't accomplish anything in this discussion. On the same level of polemic I could assume that your argument is "Power level (NO) > Power level (Progenitus)" therefor if there was a card that was a functional reprint of NO, people should cut a Progeniuts for it. Again, argueing this way would be pointless as well.

See what TheDarkshineKnight said for what's basically the conclusion:



1. Adding a 61st card is ALMOST ALWAYS a bad idea as it decreases your chance of drawing what you want and/or need by an amount that is not insignificant.

2. I am open to the possibility that a deck can be so finely tuned that the only possible improvement is, in fact, adding a 61st card. While I cannot provide evidence of this being true as I know of no such examples, I find it much more likely that such an example exists than not. Out of an, for all intents and purposes, infinite number of 60 card decks, probability dictates that at least one of these decks could be improved only by adding a 61st card.

Amen.

[Kuma]

As a mathematician, let me just say that reading this topic physically painful for me.

As an aspiring Statistician, let me say I feel your pain.


No, my argument is that to improve a deck's consistency in drawing just enough lands. Hence, adding the 24th land as the 61st card. I would never add a non-land as the 61st, because there is always room for improving and making the curve tighter.

Like you said, I only need to show one example of a deck using 61 card and I have. The probabilities calculated demonstrated not a soft-factor for determining the utility of the 61st card, but rather, the middle ground between the 23rd and 24th land in the deck. Hence, there is efficiency in adding the 61st card, and disproving your theory that "60 is better than 61 in every instance".

Okay, let's say I concede the point that you can't get the "perfect" mana ratio without playing 61 cards. I'll ignore the fact you haven't given any evidence that 61.4% and 70.9% are the perfect ratios. There's so much more to Magic than drawing the right number of lands and spells. Your perfect mana ratio comes at the cost of a 61st card. In a non-zero number of games, that 61st card is what you're going to draw instead of a Jace, the Mind Sculptor, Wrath of God, Brainstorm, or whatever the hell bombs Landstill runs these days. You will lose games because of this. Is this trade-off worth it? That's what I was looking for.

When I said give me the percentages I was talking about more than just lands. I was talking about doing some kind of cost benefit analysis between how many games you lose because you drew what you needed a turn to late and how many games you win because you drew just the right amount of lands.

I'm no Landstill expert, but I assume under ideal circumstances you will have drawn four lands by your fourth turn. In order to convince me that 61 cards is correct, you will have to find the number of lands that maximizes this occurrence without drawing too many lands, say more than seven or eight. You will then have to show that running 61 cards gets you closer to this number than 60. Following that, you'll have to demonstrate that the number of additional games you drew four lands by turn four is greater than the number of games where you'll lose from drawing your 24th land instead of a card that would have won you the game.

That's mathematically doable, at least the first part. Don't get me wrong, I'm very glad you did what you did mathematically. At least you're trying to quantify when the 61st card is correct, which is more than I can say for the other people arguing your position. But your work is far from complete :)


You still don't get it. You assume my argument is "Power level (NO) = Power level (Progenitus". That's bullshit and doesn't accomplish anything in this discussion. On the same level of polemic I could assume that your argument is "Power level (NO) > Power level (Progenitus)" therefor if there was a card that was a functional reprint of NO, people should cut a Progeniuts for it. Again, argueing this way would be pointless as well.

Then you tell me how I'm supposed to interpret the statement, "there are no cards in your deck that are 'better' than others." I'd much rather debate you on what you actually mean than my seemingly poor interpretation.


See what TheDarkshineKnight said for what's basically the conclusion:


I am open to the possibility that a deck can be so finely tuned that the only possible improvement is, in fact, adding a 61st card. While I cannot provide evidence of this being true as I know of no such examples, I find it much more likely that such an example exists than not. Out of an, for all intents and purposes, infinite number of 60 card decks, probability dictates that at least one of these decks could be improved only by adding a 61st card.

I already addressed this idea, and I agree with it. I'll post what I said again.


Look, the number of possible 61 card Magic decks is probably greater than the number of particles in the universe. Given that, it's incredibly likely that there's some combination of 61 cards that no matter what you cut you're hurting the deck's win percentages.

That said, what the hell makes any of you unique snowflakes of unique specialness think your 61 card deck fits that criteria? I'll freely admit that we can't prove that there is no combination of 61 cards that can't be improved by cutting one card, if you'll admit that we also can't prove the reverse. My point is that in the absence of proof, shouldn't we just use what we know? Some cards in any deck are better than others. Anyone disputing that doesn't know their deck or doesn't understand Magic. We also know that adding a 61st card decreases your chances of drawing the other 60. This is a mathematical fact, and no one in the thread has disputed this.

Why not err on the side of increasing your chances of drawing your most powerful cards?

[Tammit67]

As an aspiring Statistician, let me say I feel your pain.


In all seriousness, how many here are involved in mathematics? Every time a thread like this comes up, it seems everyone is a Statistician, similar to how everyone on MWS is a level 3 judge. There is a difference between having a probabilities course and having had worked with random processes at the college level

[Kuma]

In all seriousness, how many here are involved in mathematics? Every time a thread like this comes up, it seems everyone is a Statistician, similar to how everyone on MWS is a level 3 judge. There is a difference between having a probabilities course and having had worked with random processes at the college level

I have a Bachelors of Science in Statistics and I'm almost two-thirds of the way through my Masters Degree in Statistics.

[Tacosnape]

Even if you require 61 cards to have the statistical perfect mana ratio in a given build of Landstill, which is almost impossible to prove because the number of land you want to hit by a certain turn actually varies on factors you can't predict, such as your opponent's deck, how many Wastelands he drops, etc, you're also lowering the ratio that you draw your draw spells like Standstill and Brainstorm. Which means the marginal difference you would get by having the perfect ratio at 61 cards is somewhere between mostly negated by and overshadowed by the fact that running less cards means you get marginally superior library/hand manipulation.

[Koby]

I have a Bachelors of Science in Statistics and I'm almost two-thirds of the way through my Masters Degree in Statistics.

Cool! I value your input in building good models to test out the ideas in this thread. To expand on what you asked above:

Assumption: Playing first
23/60 P(X=4) - 27.3%
24/61 P(X=4) - 27.4%
24/60 P(X=4) - 27.5%

23/60 P(X<4) - 41.4%
24/61 P(X<4) - 38.6%
24/60 P(X<4) - 36.8%

Not much change from getting to exactly 4 lands on turn 4. Dramatic shifts in reducing the amount of hands that "don't get there". Clearly playing 24/60 decreases those odds, but at tension with flooding more often than 24/61.

As for the question "What happens when you draw the 24th land instead of that non-land in 24/61?" I defer to the status of Late Game, where such a deck is much more heavily favored, and the marginal utility of drawing another land pretty much won't matter as much as the strengths of the cards in the deck (i.e., Jace TMS, Elspeth, recursion, etc). Unless you mean the unique 24th land drawn in place of another spell in the course of the game. This is not the issue at hand, as adding the 24th land is to improve the consistency of mana in the deck, not for a specific effect the 24th land adds to the deck.

Again, for clarity, these calculations assume no filtering nor fetching whatsoever. I'm not sure how to model such scenarios (nor program them into Monte Carlo simulator).

[Gui]

As a competitive Magic player, let me thank you in advance for giving me an extra 1 in 150 chance of beating you should I ever be seated across from you.

Interesting... Based on the fact that every competitive player I see just happen to play some of the tier decks available, and based on the fact that whenever I'm adding the 61st card, this is a metagame decision, chances are that I'm beating you with the card, not losing.

You threat the added card as if it was a darksteel relic, when in fact the 61st card could as well be a Tarmogoyf.

[Kuma]

Even if you require 61 cards to have the statistical perfect mana ratio in a given build of Landstill, which is almost impossible to prove because the number of land you want to hit by a certain turn actually varies on factors you can't predict, such as your opponent's deck, how many Wastelands he drops, etc, you're also lowering the ratio that you draw your draw spells like Standstill and Brainstorm. Which means the marginal difference you would get by having the perfect ratio at 61 cards is somewhere between mostly negated by and overshadowed by the fact that running less cards means you get marginally superior library/hand manipulation.

This is a very good point, and I'm glad you thought of it. In any deck with Brainstorm, running 61 cards seems absolutely wrong.


Cool! I value your input in building good models to test out the ideas in this thread.

There are a lot of ways we could go about this, and each one of them will rely on some assumptions we know to be false. I'm going to try to build an Excel spreadsheet that can answer these questions. Look for it later today.



As for the question "What happens when you draw the 24th land instead of that non-land in 24/61?" Unless you mean the unique 24th land drawn in place of another spell in the course of the game. This is not the issue at hand, as adding the 24th land is to improve the consistency of mana in the deck, not for a specific effect the 24th land adds to the deck.

I meant the unique 24th land drawn in place of a spell over the course of the game. I understand that has nothing to do with mana ratios, but it does have something to do with winning. You will lose games against Goblins, for example, because you topdeck that 24th land instead of the Wrath of God underneath it. You need to weigh situations like these against what you gain from improved mana consistency. This is the cost of your 61st card.


Again, for clarity, these calculations assume no filtering nor fetching whatsoever.

Those will be some of the flawed assumptions in whatever I come up with. There's not an easy way to account for that without making a complicated simulation.

[Gui]

The first thing to note is that the difference isn't all that big, ever. Don't ever discount an opponent because they're playing 61 cards.

That said, having more than 60 cards in a deck is never a good idea. The difference can be miniscule, and I believe that a 61 card deck is quite capable of winning a major event, but that deck could be better at 60 cards.

It's probably unfair to quote TacosGoyf thoughts since he happens to be right more often than not, but this sums up the cause to me.

If the two above stated thoughts are true, and they have been proved to be, since 61 card decks put valid results more often than Kuma would be willing to acknowledge, and in hand of high level pro players as well (hell, even Patrick Chapin, author of the "61 Cards - Magic Russian Roulette (http://www.starcitygames.com/magic/standard/12478_61_Cards_Magic_Russian_Roulette.html)" article, plays 61 cards decks once in a while (http://www.thecouncil.es/tcdecks/deck.php?id=5834&iddeck=42276)), we can say it's valid enough to play 61 cards (even if highly discouraged).

[Tammit67]

It's probably unfair to quote TacosGoyf thoughts since he happens to be right more often than not, but this sums up the cause to me.

If the two above stated thoughts are true, and they have been proved to be, since 61 card decks put valid results more often than Kuma would be willing to acknowledge, and in hand of high level pro players as well (hell, even Patrick Chapin, author of the "61 Cards - Magic Russian Roulette (http://www.starcitygames.com/magic/standard/12478_61_Cards_Magic_Russian_Roulette.html)" article, plays 61 cards decks once in a while (http://www.thecouncil.es/tcdecks/deck.php?id=5834&iddeck=42276)), we can say it's valid enough to play 61 cards (even if highly discouraged).

If you are going to use Logic, you cannot commit appeal to authority fallacy. Just because a High level player has done it does not make it optimal

[Kuma]

@ruckus

I finished a spreadsheet for your Landstill example. Unfortunatly, you can't change the number of desired lands and the fundamental turn without also altering the formulas, but it does cast some light on the issue. I'd need SAS, or similarly powerful software to make anything better than my spreadsheet. I'll email it to anyone who's interested. If anyone could host the file, that would be awesome too.

Interestingly enough, the ideal combination for getting exactly four lands by turn four without mana flood or screw is 24/60.

If you want more than two lands but less than seven by turn four, the best ratio is 25/60, with an 82.741% chance of that happening.

61 cards was not ideal for either situation. The best ratios for 61 cards were 25/61 and 26/61 respectively.


If the two above stated thoughts are true, and they have been proved to be, since 61 card decks put valid results more often than Kuma would be willing to acknowledge,

Whoa, whoa, whoa.

I never said a 61-card deck can't win a major event. I never said 61-card decks were terrible. What I'm saying is that 61-card decks are always sub-optimal and playing a sub-optimal deck is wrong.


and in hand of high level pro players as well (hell, even Patrick Chapin, author of the "61 Cards - Magic Russian Roulette (http://www.starcitygames.com/magic/standard/12478_61_Cards_Magic_Russian_Roulette.html)" plays 61 cards decks once in a while (http://www.thecouncil.es/tcdecks/deck.php?id=5834&iddeck=42276)), we can say it's valid enough to play 61 cards (even if highly discouraged).

First of all, nothing in that link says that's Patrick Chapin's deck. I'll give you the benefit of the doubt and say it is. Patrick Chapin, the author of "61 Cards - Magic Russian Roulette" played a 61-card deck in a large event.

So what? Did you even read the article you linked?


Playing 61 cards is a sin. One may not see why it is so bad without careful examination, but it is. Bad, that is.


2) My mana ration requires 25.5 land if I were 60, so I'm playing 25 in a 61 (or 62).

You are rationalizing the terrible. (You want to draw those Natural Orders, right?) I'll admit I've been guilty of this before, but it is wrong.

Congrats, you've demonstrated that you don't understand the "Tu quoque" fallacy.

[ajfennewald]

@ruckus


Whoa, whoa, whoa.

I never said a 61-card deck can't win a major event. I never said 61-card decks were terrible. What I'm saying is that 61-card decks are always sub-optimal and playing a sub-optimal deck is wrong.




It is almost impossible that there exist no scenario where a 61 card deck is better than a 60 card deck. I agree that finding those corner cases is not something people can probably actually do in practice.

[Cthuloo]

@Kuma: what I will be interested to, is to see if there's any combination of #lands and #turn for which 61 is better than 60, and if so, which is the range where this is valid. It would be interesting to do the same for 59 cards. It shouldn't be that hard to do, if you don't have the time, tomorrow I should be able to write a small code to analyze the parameter space. By the way, in the thread I linked in the first page, there was an analysis by Maverick(?) concerning an hypothetical x bolts + y mountains deck, and in the end, IIRC, it appeared that one of the versions playing 61 cards had a faster win rate than any of the ones playing 60. I will have to re-read the thread and find this result.

It would be nice to try and discuss the matter on a more solid ground, so any data is very valuable.


@the article by Chapin: with all due respect to the man (and he deserves a lot), I don't think this is one of his best pieces. Plus, of course, appealing to authority is never a good way to improve a discussion.

EDIT (forgot this piece)


I never said a 61-card deck can't win a major event. I never said 61-card decks were terrible. What I'm saying is that 61-card decks are always sub-optimal and playing a sub-optimal deck is wrong.

If I'm not mistaken, Gui's point (and mine, too) was that the difference is negligible, and is overshadowed by many other factors.

[Gui]

Whoa, whoa, whoa.

I never said a 61-card deck can't win a major event. I never said 61-card decks were terrible. What I'm saying is that 61-card decks are always sub-optimal and playing a sub-optimal deck is wrong.

Ok, so we agree that 61 card decks can be played to win? Even major tourneys? That's good enough for me.

Patrick Chapin's deck: http://sales.starcitygames.com//deckdatabase/displaydeck.php?DeckID=37452

[Kuma]

@Kuma: what I will be interested to, is to see if there's any combination of #lands and #turn for which 61 is better than 60, and if so, which is the range where this is valid. It would be interesting to do the same for 59 cards. It shouldn't be that hard to do, if you don't have the time, tomorrow I should be able to write a small code to analyze the parameter space.

Yeah, that's way beyond my ability to do with Excel quickly. I'm very interested in what you find.


By the way, in the thread I linked in the first page, there was an analysis by Maverick(?) concerning an hypothetical x bolts + y mountains deck, and in the end, IIRC, it appeared that one of the versions playing 61 cards had a faster win rate than any of the ones playing 60. I will have to re-read the thread and find this result.

I might accept that as proof if you could run as many Lightning Bolts as you wanted in Legacy. X bolts + Y Mountains isn't a deck. 38 Tarmogoyf + 22 lands isn't a deck. As such, any example involving either doesn't refute the statement that playing 61 cards in a deck is always sub-optimal. I mean, 60 Forests + 1 Thrun, the Last Troll is a stronger deck than 60 Forests, but those are only decks in the strictest and most pointless sense of the word.


If I'm not mistaken, Gui's point (and mine, too) was that the difference is negligible, and is overshadowed by many other factors.

How much does the 61st card have to hurt you before it's no longer negligible? One game in 50? 500? 5000? I'd say none of those numbers is negligible and there's no reason to give away even a fraction of a percentage point of winning percentage, especially when it's as easy as identifying the weakest card in your deck.

Is getting to from 61 to 60 the most important thing you can do to improve your winning percentage? No, but if you're at all familiar with your deck it should take you about five seconds to do so. I can tell you what the weakest card in any Legacy deck I play is. If Wizards made the minimum deck size 59 tomorrow, I know what I'd cut from each of my decks. It's good to do this thought exercise because when new cards come out, it's helpful to know what you should cut from your list. You can spend your time trying out new cards instead of figuring out what to cut for them.

@everyone who wants a copy of my spreadsheet

I need you guys to PM me with an email address.

[Koby]

@Kuma
You've piqued my interest enough to pursue building a calculator. How would we represent, or evaluate the following set of probabilities:

between 'X1' and 'X2' lands in 'Y' turns for a deck of Size 'N' with 'L' lands.

For instance:
4 Turns (samples = 10)
60 cards
24 lands

yields:


X=? 3 4 5 6 7
P(X=?) 22.4% 27.5% 21.3% 10.5% 3.3%
P(x<=?) 36.8% 64.3% 85.5% 96.0% 99.3%
P(X>?) 63.2% 35.7% 14.5% 4.0% 0.7%

[SpikeyMikey]

I might accept that as proof if you could run as many Lightning Bolts as you wanted in Legacy. X bolts + Y Mountains isn't a deck. 38 Tarmogoyf + 22 lands isn't a deck. As such, any example involving either doesn't refute the statement that playing 61 cards in a deck is always sub-optimal. I mean, 60 Forests + 1 Thrun, the Last Troll is a stronger deck than 60 Forests, but those are only decks in the strictest and most pointless sense of the word.

But by virtue of their simplicity, they are easier to dissect than actual decklists and in any case, reducto ad absurdum is a valid logical argument, which is why I made the point in the first place. You stated that a 60 card deck is unequivocally better than a 61 card deck because there is a definite hierarchy of value among the cards in a deck and removing the lower value cards increases the deck's EV by increasing the average power level of each draw. My statement is that a deck is not a rigid hierarchy of card values. You can't assign a scale of 0-100 and rank cards in power along that scale because each card's value shifts based on the other cards in the deck. That's the point of the 38 Tarmogoyf 22 land example. Tarmogoyf may be the strongest card in deck "y" but the strength of your deck decreases as you increase the number of Tarmos at the expense of other cards. Why? Because there is a proper ratio of various effects (creature removal, artifact/enchantment removal, card selection, counterspells, discard, mana disruption, win conditions, whatever) at which point your deck operates at maximum efficiency. When you move outside of that window, the power level of the deck suffers in direct proportion to the distance from ideal that you end up at. As you reduce the number of cards in your deck, you decrease variance, which is benefitial. But what you are proposing is that the decrease in variance ALWAYS leads to an equal to or greater increase in power than the decrease in power you wind up with from improper ratios. And you don't offer any proof of this. That's the first problem, because infinitives are so often wrong that any use of an infinitive clause becomes suspect.

If your deck contains 10 (9 4-of's and 24 of the same basic land) unique cards, Brainstorm doesn't really give you much in the way of increased card selection. If it contains 60 (highlander!) unique cards, Brainstorm gives you the maximum amount of increased selection possible (i.e., 3 cards) 100% of the time. Between those two extremes, you get a range of power levels dependent on exactly what Brainstorm drew you. If your hand is Tarmogoyf, Vendillion Clique, Tundra and Brainstorm and you cast Brainstorm drawing Tarmogoyf, Vendillion Clique and Tundra, you haven't improved your hand as much as if you drew Force of Will, Swords to Plowshares and Tropical Island. The more diverse your deck is, the better Brainstorm is. Its power level is directly proportional to the number of unique cards in your deck.

However, this is not the same as saying that the EV of the deck is increased by running a highlander deck. While Brainstorm's power level goes up proportional to the number of unique cards, the overall power level of the deck will most likely go down, moreso than the added value of a better Brainstorm can compensate for. It's a complicated equation and we don't even have numbers to work with, because any defined value of power level you could give a card outside of its relationship to every other card has to be arbitrary. Is Ancestral Recall twice as good as Brainstorm? Three times as good? Half as good? Go ahead, come up with a logical method to quantify that. You can't. But even if you could, you'd still have to adjust that value up or down based on the rest of the contents of the deck. So when you say:


Is getting to from 61 to 60 the most important thing you can do to improve your winning percentage? No, but if you're at all familiar with your deck it should take you about five seconds to do so. I can tell you what the weakest card in any Legacy deck I play is. If Wizards made the minimum deck size 59 tomorrow, I know what I'd cut from each of my decks. It's good to do this thought exercise because when new cards come out, it's helpful to know what you should cut from your list. You can spend your time trying out new cards instead of figuring out what to cut for them.

I call bullshit. Because in order for you to be able to confidently say "~this~ is the worst card in my deck" you have to know not only the expected field (since what you're facing has a major effect on the power level of cards in your deck) but also how removing "x" for "y" is going to affect the value of every other card in your deck; that is, how it affects the ratios and how it affects the individual power level of each card. And that's not possible without knowing what card "y" is. There are somewhere between 11,000 and 12,000 unique cards. The number of possible permutations of card combinations within a 60 card deck (even accounting for the removal of nonsensical combinations like cards you can't cast with a given land base or decks with obviously wrong ratios) is so astronomically high that I don't think we need to bother assigning a number to it. We both know it's a number far higher than either of us could count to if we lived to be 1,000 years old. For you to say that it takes you about 5 seconds to correctly pick the most efficient 60 card combination from those trillions of billions of combinations and from there identify the weakest of those 60 is such an audacious load of bullshit that I don't even have words to describe it. Politicians and advertising agencies ought to be studying at your feet.

[Kuma]

But by virtue of their simplicity, they are easier to dissect than actual decklists and in any case, reducto ad absurdum is a valid logical argument, which is why I made the point in the first place.

Fine. Let me better define my argument so it only holds true for:

61 card piles that are legal Magic decks. Maybe 61 cards is optimal if you get rid of the four-card limit, but my statement only applies to legal Magic decks.

61 card piles that you would take to a Legacy tournament. We can be loose about this requirement, but my statement doesn't apply to anything like 300 Forests.dec or 60 Forests + 1 Thrun, the Last Troll.dec, etc.

In order for reductio ad absurdum to apply you have to follow my implications to an absurd conclusion. Your "absurd conclusion" is outside the realm of my implications, therefore this particular application of reductio ad absurdum does not disprove my claim.


You stated that a 60 card deck is unequivocally better than a 61 card deck because there is a definite hierarchy of value among the cards in a deck and removing the lower value cards increases the deck's EV by increasing the average power level of each draw. My statement is that a deck is not a rigid hierarchy of card values. You can't assign a scale of 0-100 and rank cards in power along that scale because each card's value shifts based on the other cards in the deck.

Let's be clear. I'm not saying we can absolutely, certainly, 100% come up with this exact hierarchy based on our limited understanding. I'm saying that it exists, even when you take into account synergies and value shifts with other cards in the deck and your expected metagame. Based on our experiences with the deck, we have a good idea of what that hierarchy is, at least when it comes to weaker cards. There are cards you more frequently sideboard out than others, cards you aren't happy to draw as often as others, etc. These cards are likely weaker than the other cards in your deck even when you take synergies and value shifts into account. Cutting one of these cards from a 61 card deck will almost certainly lead to an improvement in winning percentage.

If you don't trust your ability to evaluate cards, why are you playing this game?


That's the point of the 38 Tarmogoyf 22 land example. Tarmogoyf may be the strongest card in deck "y" but the strength of your deck decreases as you increase the number of Tarmos at the expense of other cards. Why? Because there is a proper ratio of various effects (creature removal, artifact/enchantment removal, card selection, counterspells, discard, mana disruption, win conditions, whatever) at which point your deck operates at maximum efficiency.

Let me clarify once again. When I say strongest card or weakest card, I'm talking about an individual slot such as "the fourth Tarmogoyf" or "the third Ponder." I'm not talking about all the copies of a card, although it's entirely possible that the four weakest cards in a 64 card deck could be copies one through four of card X.


When you move outside of that window, the power level of the deck suffers in direct proportion to the distance from ideal that you end up at. As you reduce the number of cards in your deck, you decrease variance, which is benefitial. But what you are proposing is that the decrease in variance ALWAYS leads to an equal to or greater increase in power than the decrease in power you wind up with from improper ratios. And you don't offer any proof of this. That's the first problem, because infinitives are so often wrong that any use of an infinitive clause becomes suspect.

I don't claim to be able to prove that 60 cards is always better than 61. Part of my argument is that decreasing deck size reduces variance, which by your admission is beneficial. We can't be sure if a 61st card increases power more so than the increase in variance reduces it. Therefore, we should err on the side of reduced variance, because the only thing we can be certain about is that, all other things equal, reduced variance is good.


So when you say:


Is getting to from 61 to 60 the most important thing you can do to improve your winning percentage? No, but if you're at all familiar with your deck it should take you about five seconds to do so. I can tell you what the weakest card in any Legacy deck I play is. If Wizards made the minimum deck size 59 tomorrow, I know what I'd cut from each of my decks. It's good to do this thought exercise because when new cards come out, it's helpful to know what you should cut from your list. You can spend your time trying out new cards instead of figuring out what to cut for them.


I call bullshit. Because in order for you to be able to confidently say "~this~ is the worst card in my deck" you have to know not only the expected field (since what you're facing has a major effect on the power level of cards in your deck) but also how removing "x" for "y" is going to affect the value of every other card in your deck; that is, how it affects the ratios and how it affects the individual power level of each card. And that's not possible without knowing what card "y" is. There are somewhere between 11,000 and 12,000 unique cards. The number of possible permutations of card combinations within a 60 card deck (even accounting for the removal of nonsensical combinations like cards you can't cast with a given land base or decks with obviously wrong ratios) is so astronomically high that I don't think we need to bother assigning a number to it. We both know it's a number far higher than either of us could count to if we lived to be 1,000 years old.

I don't think it's ridiculous to say, after a significant amount of experience, that I "know" (DISCLAIMER: "know" means "am as sure as I can be." I can't believe I actually have to spell that out.) what the weakest card in my deck is. That doesn't mean that I am certain mathematically what the best replacement card for it would be, but chances are I can think of something that is likely better than that weakest card.

Do you really think like this when you build a deck? How do you decide what to cut from your deck to try something new? How do you decide whether to play 60 or 61 cards? You use your best judgment based on your experience with the deck, and hopefully what you know about mathematics.


For you to say that it takes you about 5 seconds to correctly pick the most efficient 60 card combination from those trillions of billions of combinations and from there identify the weakest of those 60 is such an audacious load of bullshit that I don't even have words to describe it. Politicians and advertising agencies ought to be studying at your feet.

That's not what I said. I said that in a 60 card combination in which I am sufficiently experienced (which I'll note takes waaay more than five seconds) It takes me about five seconds to actually make the decision about what is the weakest card currently in the deck. I have never claimed to know for certain what the optimal 60 card combination is for Magic. All I have said is that, based on what we know about mathematics, it is always better to err on the side of 60 cards and if you're experienced with a deck you should be able to make a reasonable stab at cutting the weakest card fairly easily.

[Cthuloo]

By the way, I run the code (and have a bunch of numbers, if you're interested). What I wanted to see is what's the combination of lands+spells (and therefore total cards) that maximizes the probability to see a number of lands inside some range on some turn. Since the code takes some time to run, I limited the analysis to the intervals 2-3/4/5/6/7, 3-4/5/6/7, 4-5/6/7 and 5-6/7 lands, on turn 3 or four and for decks of 59,60 and 61 cards. There is never a case where 60 or 61 decks perform better than 59 cards decks (although some numbers are very close, to the fifth digit). This is very interesting, from a theoretical point of view: apparently, the "correct lands/spell ratio" is not a valid argument. I included no fetching/filtering, though, I could try to implement them someway tomorrow. I'm not quite sure if they should impact the tendency of the results in any way, though.


I don't think it's ridiculous to say, after a significant amount of experience, that I "know" (DISCLAIMER: "know" means "am as sure as I can be." I can't believe I actually have to spell that out.) what the weakest card in my deck is.

The "am as sure as I can be" part is IMHO the focal point of the discussion. We're talking about fractions of a %, are you sure you really know your deck that much? Almost all of the tier decks have some "flexible" slots, that are filled with different cards by different people. If it was that easy to identify the weakest cards and find a better replacement, the lists will all look almost the same.

@ the reductio ad absurdum argument: it's pretty clear that we are not capable of correctly modeling a true legacy deck, but maybe it's possible to learn something from simplified and easier to handle models (see the land/spell ratio argument).