61 or more cards in toolbox decks

[sco0ter]

As a Survival player I often can't decide, which cards to cut in order to have a 60-card-deck eventually.

At some point, I wondered, is it actually a wise desicion to cut down to 60 cards?

I made following assumption:

If I play a 60 card deck, the probabilities of having at least one Survival in the opening hand is about 39,95%.

If I play a 61 card deck, the probabilities of having at least one Survival in the opening hand is about 39,40%.

If I play a 62 card deck, the probabilities of having at least one Survival in the opening hand is about 38,87%.

So by adding 2 cards to the deck the probability of having the important enchantment in your opening hand only decreases by about 1,08%. A value which usually makes no difference in practice.

I wonder if this little value is worth the inclusion of more silver bullets, which are usually only good in certain matchups, but can decide games. Cards like Faerie Macabre, Goblin Sharpshooter or even Spore Frog.

This question could be asked for any toolbox deck, of course.

[Phoenix Ignition]

Toolbox decks die to too much toolboxing. 1% making "no difference in practice" is not correct, but that aside, your assumption is that you don't draw the toolbox cards in your opener.

Toolbox decks die to consistancy issues, and you need to limit yourself to how many silver bullets you run or you will end up hitting the wrong ones at the wrong times (like your opening hand, forcing you to pretty much only draw 6 cards). It happens for every toolbox deck. I would run less than 5 silver bullet cards in any toolbox deck, because it really isn't worth drawing that shit in your opening hand.

[AngryTroll]

Jamie Wakefield used to play an odd number of cards in his decks-something like 65 or 66 to get the land/total card ratio to be what he wanted. Of course, he also played big fat green stuff, so he didn't have Ponder and Brainstorm to smooth his draws.

So if you can make a deck consistant enough, you can run more than 60 cards. Doing that in a format like Legacy is very hard to do, however, becuase the power level of some cards is so much higher than others that you want to see those particular cards in every game.

Still....I waffle between 60 and 61 cards in Survival. If that one extra card wins you more games than you lose from decreased efficiency, than it's probably worth it, but that's extremely hard to quantify. Plus, even in this case, you are almost certainly better off cutting something from the mainboard and getting to run your extra toolbox card and still playing a 60 card deck.

[Tinefol]

Exception would be a wish deck, and these do occupy valuable sideboard space too. No, don't run more than 60 cards, ever, it doesn't matter if you run toolbox, or not.

Because it's sin

[Goaswerfraiejen]

Toolbox decks die to consistancy issues, and you need to limit yourself to how many silver bullets you run or you will end up hitting the wrong ones at the wrong times (like your opening hand, forcing you to pretty much only draw 6 cards). It happens for every toolbox deck. I would run less than 5 silver bullet cards in any toolbox deck, because it really isn't worth drawing that shit in your opening hand.

That's very true, and it's a fact clearly reflected in most Gifts-based decks, which opt for far too many bullets in an effort to power up Gifts Ungiven. With that said, however, I'm in favour of going up to 61 cards in a deck with a toolbox-type engine (e.g. Survival, Intuition) if the toolbox options are a relatively small number of cards and/or complement one another closely enough to be considered multiples of that card. One example of the latter scenario would be to use Shriekmaw as a fifth piece of removal. Taking this case, let's say that Shriekmaw was card #61, and the rest of the deck is very tight. Shriekmaw provides a little versatility for your removal (since it's also a beater, and a Bridge-remover), and it also complements your Survival engine (easily fetched removal) and, in addition, it plays into your deck's other mechanics (Genesis, Volrath's Stronghold, etc.). In a case like that, I'd say that the 61st card gives more than a fair account of itself.

Otherwise, I'd probably be against it.

[crow_mw]

It has been addressed in the article linked above, though without giving any solid proof - adding more cards also decreases your chances of drawing Anger, Squee and the likes. That being said, however, I don't believe there are enough cards which power level compensates for lower chance to draw Goyfs and Survivals...

[Shugyosha]

So by adding 2 cards to the deck the probability of having the important enchantment in your opening hand only decreases by about 1,08%. A value which usually makes no difference in practice.

You are forgetting that there are other 4 ofs you want to draw on a regular basis. The reduced chance to draw removal, Goyf, Survival or other cards in other 61+ card decks will accumulate.

[Illissius]

I'm not actually sure about this whole 60 cards thing. It seems a bit like the whole efficient markets hypothesis in economics. (Yeah, I just lost 95% of people right there). It seems very elegant and appealing and you can do a good job of explaining away all the potential complications and objections so that it stays valid. But just because it's elegant and appealing doesn't mean it's actually true in 100% of cases.

I mean, the core thesis is that some of your cards are better than others, and you want the highest possible odds of drawing these cards. This is very solid, and most of the time it's probably right. But the theory doesn't actually make any kind of attempt to try and quantify this difference in quality, how much of advantage you're expected to gain, and how and why it actually outweighs all the potential advantages from having more than 60 cards (toolbox cards, land-mana ratio, cards-that-do-one-thing-to-cards-that-do-another-thing ratio, whatever). I mean, maybe there's some cases where it doesn't. Maybe a deck doesn't have such a big difference in power level between its cards. Maybe the power level difference multiplied by the marginal decrease in probability of drawing them from adding another card or two to the deck isn't actually all that significant relative to other considerations. Maybe the fact that cards aren't actually uniformly powerful across matchups and you can't know for certain what matchups you'll face actually matters. But how are we to know? The theory doesn't say. It just assumes.

[freakish777]

This is very solid, and most of the time it's probably right. But the theory doesn't actually make any kind of attempt to try and quantify this difference in quality, how much of advantage you're expected to gain, and how and why it actually outweighs all the potential advantages from having more than 60 cards

Unfortunately the theory here isn't something that can readily be quantified until Wizards opens up MagicOnline to allow Bots to play games (and then allows you to have access to the statistics of the games played by your Bot, and you're able to run a large enough number of Bots to get a sufficient data set).

I'm going to attempt to provide a method for actually quantifying the quality, it's just that in practice, you would never do it without a lot of computers doing a bunch of work for you.

Let's simplify the equation and say it's Time Spiral Block Constructed instead (in which Patrick Chapin proposed a 66 card Mystical Teachings deck, I don't know if he played it or not, but the reasoning was "you don't actually want to draw Teachings as often as you do with a 60 card deck, otherwise your hand gets stuffed up with cards you can't cast, and you're just tutoring for a bunch of silver bullets anyways, plus the mana being mixed correctly).

If Wizards did open up statistics of games and decks for MagicOnline (you pay a small subscription fee, you get all the data on decks, pairings, results, etc, pretty handy information for the pros, and if they aren't mining this data already to learn how to design better cards in the future, they're retards...), you could query the data for things like:

(first let's set A = "All Decks playing card X", B = "All Decks playing card Y", etc)

1. Percentage of A (how popular is this card).
2. Percentage of matches won by A compared to B, C, etc (how good is this card, where B, C, etc covers all cards in the format).

If you have a lot of data sets from Tournaments, you eventually get some values that estimate "the reality of the situation."

The formula would be something like (this is probably far too simplistic, but it's an attempt):

Card X's Value in the Metagame = Sum (how good is this card against X[i] * how popular is X[i]) (for all cards in the metagame, if you could normalize to 1 that would be even better).

Deck A's Value in the metagame = Sum(value of all cards in A)/Number of all cards in A = "percentage chance your deck has to win against an unknown opponent"


With a quantification of value, you shouldn't even have to do the statistics for probability of drawing X or drawing Y, you'd just say:

Well my Big Game Hunter has total value 0.35 and my 77 card Survival deck (62 main 15 board) has value 0.50, and it would go up if I removed Big Game Hunter...







So SCG will no doubt collect a lot of decklists for their 5k Series. They will also have a lot of data about pairings and results as well. Really, I would like to see SCG do a couple things (since Wizards is slow about doing things, being a large corporation):

1) Allow players to sign up for events electronically (payment, AND deck reg, filling out a web form with your deck reg on it before the event I'm sure would save a whole lot of time on their end manually keying in data later, it also speeds up tournament start time since there's less people to collect money from).

2) Lease the data gained (as opposed to giving select people access to it, it's nice seeing Steve Menendian write articles using your data, and I'm glad someone gets access to it, but why limit it to one person?) I'm sure there's a lot of really interesting things to be mined out of the data...

3) Once you implement #2, tell Wizards to get their fucking act together with MagicOnline data mining.

[Maveric78f]

Imagine that exhume, entomb and reanimate have so many clone cards (like armageddon being cloned by ravages of war) that you can decide put them in your deck in a lot of copies.

Imagine you're building a mono black deck with no disruption (just the above mentionned cards plus the reanimation targets. In this case you'll definitely want to play a deck with more than 60 cards in order to avoid drawing the reanimation targets.

Another default of decks with more than 60 cards is that it weakens the sb.

[grahf]

I think it matters more in draft, where you have very little card draw or deck manipulation. There, drawing land when you need some business, any business, will conclusively kill you. And the percentages of drawing what you want will be more greatly reduced by playing extra cards as you're starting with fewer cards to begin with. And also, one can make more conclusive judgments about "this card is less good than these other cards."

[Kuma]

At some point, I wondered, is it actually a wise desicion to cut down to 60 cards?

Yes. This is Deckbuilding 101.

If I play a 60 card deck, the probabilities of having at least one Survival in the opening hand is about 39,95%.

If I play a 61 card deck, the probabilities of having at least one Survival in the opening hand is about 39,40%.

If I play a 62 card deck, the probabilities of having at least one Survival in the opening hand is about 38,87%.

Why would you want to reduce your chances of drawing Survival at all? It's the engine that makes the deck work. Not only does running extra cards decrease your chances of drawing Survival, it decreases your chances of drawing everything else. Need a land? The 61st card reduces your chances of getting it. Need removal? Unless your 61st card was a Vindicate, or something, it's hurting your odds of getting it.

So by adding 2 cards to the deck the probability of having the important enchantment in your opening hand only decreases by about 1,08%. A value which usually makes no difference in practice.

The average tournament has 9-10 rounds counting Top 8, meaning an unnecessary loss every 10 or 11 tournaments, just for not being disciplined. This doesn't even count the damage from brining down the mean average or drawing that worst card actually directly lowering your percentages. Playing with a 61st card is like playing Russian Roulette. Every match you spin the chamber and have a one in one hundred chance of getting a loss... just because you couldn't cut that last card.

Those may not be the worst odds in the world, but would you play Russian Roulette with a 100-chamber gun in real life? Remember, there is no gain (unless your deck falls under one of the exceptions I'll list, but even then most people just pretend their deck is an exception to rationalize their sin).

Now imagine playing this one in one hundred Russian Roulette over and over. Every match you play, you take another spin and pull the trigger. It will catch up to you. You cannot beat math.

I wonder if this little value is worth the inclusion of more silver bullets, which are usually only good in certain matchups, but can decide games. Cards like Faerie Macabre, Goblin Sharpshooter or even Spore Frog.

When you take all the relative strengths of all the cards in your deck and take the mean average, you arrive at an imaginary line dividing cards that increase your chances of winning in general (Ancestral Recall) and cards that decrease your chances of winning compared to if you drew something else in your deck (Swords to Plowshares). This does not mean Swords to Plowshares is bad or should be cut. What it means is that Ancestral Recall is better in your deck in this metagame, and it is a better draw than Swords to Plowshares in general.

This mean average is how strong your deck is. It reflects the sum total of all contributions towards winning of all the cards in your deck. While it is an abstract idea, we can work with it...

If you add a 61st card to your deck, you are clearly bringing down the mean average. The 61st card cannot possibly be as good as the average. The 60th card is not as good as the average. Most likely, the 40th card isn't as good as the average. The 61st card may help you win games sometimes, but it will contribute to losses more (compared to the other 60) as a whole. Otherwise, it is not your 61st card, another card is and you should cut that one.

Imagine that exhume, entomb and reanimate have so many clone cards (like armageddon being cloned by ravages of war) that you can decide put them in your deck in a lot of copies.

Imagine you're building a mono black deck with no disruption (just the above mentionned cards plus the reanimation targets.

Why would you build that deck? It would be awful.

In this case you'll definitely want to play a deck with more than 60 cards in order to avoid drawing the reanimation targets.

No, no, no.

Not only will the extra cards you run likely be weaker versions of cards in the 60, you're going to hurt your chances of getting enough land. This doesn't even work as a theoretical.

It's not like drawing your reanimation targets is a huge problem in reanimator anyway. It's only a problem if you draw all of them, or you're not running any discard outlets, i.e. Putrid Imp or Cabal Therapy.

@everyone advocating running more than 60 cards:

60 card decks are the established norm for Magic. If you think 61 is somehow better, you need to provide a list of cards that is not improved by cutting it down to 60, and all the necessary proof required.

Read the Patrick Chapin article linked earlier in the thread. He addresses the issue very well and says it all better than I can.

[from Cairo]

That's very true, and it's a fact clearly reflected in most Gifts-based decks, which opt for far too many bullets in an effort to power up Gifts Ungiven. With that said, however, I'm in favour of going up to 61 cards in a deck with a toolbox-type engine (e.g. Survival, Intuition) if the toolbox options are a relatively small number of cards and/or complement one another closely enough to be considered multiples of that card. One example of the latter scenario would be to use Shriekmaw as a fifth piece of removal. Taking this case, let's say that Shriekmaw was card #61, and the rest of the deck is very tight. Shriekmaw provides a little versatility for your removal (since it's also a beater, and a Bridge-remover), and it also complements your Survival engine (easily fetched removal) and, in addition, it plays into your deck's other mechanics (Genesis, Volrath's Stronghold, etc.). In a case like that, I'd say that the 61st card gives more than a fair account of itself.

Otherwise, I'd probably be against it.

I follow your point and the way you defended it has merit. In your example I'd agree that Shriekmaw does fit well with the other components of the deck and is a worthy inclusion.

But I think it's wrong to look at 1 card as the "61st," in a 61 card deck every card is the 61st. While Shriekmaw may be absolutely defensible, there are 60 other cards that need to be pulling that weight as well.

In some cases cutting a card that is almost always seen as an x4 down to an x3 could make sense if you're running other spells that fill a similar role. Or maybe one's decided that 21 land and 39 spells is leaving them short on land when trying to curve out, and they attempt to solve this by adding the extra "61st" card of a 22nd land to smooth the mana base. Something like this could be addressed through a different angle by replacing some fetchlands with permanent mana sources, so that the deck is less likely to be thinning land drops and will draw into it's 21 land more frequently. Or by cutting a couple clunkier spells and the 22nd land for a couple cantrips, I mean it would all depend on the deck, but there's alot of options to consider when trying to optimize.

[Goaswerfraiejen]

But I think it's wrong to look at 1 card as the "61st," in a 61 card deck every card is the 61st. While Shriekmaw may be absolutely defensible, there are 60 other cards that need to be pulling that weight as well.

Touché. That's why I felt the need to specify, for the sake of our thought-experiment, that the rest of the deck was also very tight. But I guess that's dangerously close to begging the question.

Ultimately, as you say, it's something that will have to be determined on a case-by-case basis. The specific scenario I pointed to is not one that I can easily see occurring outside of a deck with a Survival or Intuition engine, however, so that might narrow the list down some. Although, come to think of it, it might also work for Lands.dec.

[Rico Suave]

You can't beat math. 61 cards will lose you games, and matches, if you play over a long period of time (and honestly it's not even *that* long for it to come up).

But I think it's wrong to look at 1 card as the "61st," in a 61 card deck every card is the 61st.

No.

There is *always* a weakest card in the deck, just like there is always a strongest card in the deck. It may be difficult for us to decide which is the weakest, but it is there. Even if a number of cards end up being metagame decisions, there is still a weakest card.

[FieryBalrog]

That's not necessarily true. Especially in decks that aim to cover different situations, the "weakest card" is not always the same.

Honestly the rigid 60 card limit is more like received wisdom than any actually theoretically solid knowledge. There just isn't enough objective data to make it conclusive. Not to mention many pros do run at least 61 card decks at times. If cutting from 61 to 60 means lower your land count to an unacceptable degree, or cutting a 4-of to a 3-of (which has a much bigger impact on the odds of drawing that card than cutting from 61 to 60 has on drawing any card), then I can see going for a 61 card deck.

[undone]

You can't beat math. 61 cards will lose you games, and matches, if you play over a long period of time (and honestly it's not even *that* long for it to come up).

No.

There is *always* a weakest card in the deck, just like there is always a strongest card in the deck. It may be difficult for us to decide which is the weakest, but it is there. Even if a number of cards end up being metagame decisions, there is still a weakest card.

Thats is not true. If the weakest card in matchup A exists, and the weakest card in matchup B exists but the torny will consist of something like 30% deck A and 30% deck B with 40 % other and the card your deciding has similar functions in the other matchups than going to a 61st card is not a terrible idea its simply a minimaly risky one. Silver bullets are awsome when they are relivant, the thing is silver bullets are MUCH MUCH more broken when you have brainstorm and can play something like enlightened tutor with 2-3 tutor targets + counterbalances and tops which you would run anyway.

In survival I would say its boarderline, if the list contains any 4 ofs other than Survival, goyf or mana dorks than its probably better to find another card to cut.

[grahf]

This is getting a little off topic but...

Is a deck with 20 Swamps and 40 Relentless Rats functionally any different or better than 100 Swamps and 200 Relentless Rats? (besides the shuffling mechanics)

Pat Chapin seemed to think so:

What are you playing? Seriously, 36 Relentless Rats and 24 Swamps? Even in a Relentless Rats deck, you only want to play 60. You aren't decking anyone, and the more cards you play, the more inconsistent your mana.

If the ratios are exactly the same, I don't see how the percentages would be any different. But statistics was never my strong point.

Finally, there is a deck where more than 60 cards is correct, but it's definitely not a toolbox deck: 40 Black Lotuses and 40 Wheel of Fortunes. In that "deck," you need a bigger library than your opponent to outlast them.

[Nihil Credo]

This is getting a little off topic but...

Is a deck with 20 Swamps and 40 Relentless Rats functionally any different or better than 100 Swamps and 200 Relentless Rats? (besides the shuffling mechanics)

If the ratios are exactly the same, I don't see how the percentages would be any different. But statistics was never my strong point.

A bigger library means a bigger variance in your draws, which is something undesirable.

Look at it this way: if your deck is made of 3 lands and 4 spells, you're guaranteed to have a 3 land/4 spell opening hand 100% of the time. If it is made of 30 lands and 40 spells, you won't always get 3/4: a part of that 100% will become 0/7, 1/6, ... , 6/1, 7/0 draws instead. If you have 300 lands and 400 spells, the 'weird' draws will become even more likely, and so on.

[4eak]

Statistics isn't my strong point either (had to graduate early to provide for my family, so I wasn't able to take advanced classes on the topic [I'm a philosopher, not a mathematician], although I've read on the topic). Forgive my concrete approach to the issue. From a million hands per test:

20/40 -- Land/Spell
0 Land, 7 Spells = 4.83%
1 Land, 6 Spells = 19.9%
2 Land, 5 Spells = 32.4%
3 Land, 4 Spells = 26.9%
4 Land, 3 Spells = 12.4%
5 Land, 2 Spells = 3.11%
6 Land, 1 Spells = 0.412%
7 Land, 0 Spells = 0.0189%
Total= 99.9%

40/80 -- Land/Spell
0 Land, 7 Spells = 5.32%
1 Land, 6 Spells = 20.2%
2 Land, 5 Spells = 31.6%
3 Land, 4 Spells = 26.2%
4 Land, 3 Spells = 12.6%
5 Land, 2 Spells = 3.49%
6 Land, 1 Spells = 0.526%
7 Land, 0 Spells = 0.0309%
Total= 99.9%

80/160 -- Land/Spell
0 Land, 7 Spells = 5.59%
1 Land, 6 Spells = 20.3%
2 Land, 5 Spells = 31.0%
3 Land, 4 Spells = 26.0%
4 Land, 3 Spells = 12.8%
5 Land, 2 Spells = 3.71%
6 Land, 1 Spells = 0.570%
7 Land, 0 Spells = 0.0388%
Total= 100%

160/320 -- Land/Spell
0 Land, 7 Spells = 5.76%
1 Land, 6 Spells = 20.4%
2 Land, 5 Spells = 31.0%
3 Land, 4 Spells = 25.8%
4 Land, 3 Spells = 12.7%
5 Land, 2 Spells = 3.77%
6 Land, 1 Spells = 0.601%
7 Land, 0 Spells = 0.0419%
Total= 100%

Because I suck at programming, I'm impatient, and I don't have a supercomputer, I dropped down to 100,000 hands for this:

1600/3200 -- Land/Spell
0 Land, 7 Spells = 5.86%
1 Land, 6 Spells = 20.5%
2 Land, 5 Spells = 30.7%
3 Land, 4 Spells = 25.7%
4 Land, 3 Spells = 12.8%
5 Land, 2 Spells = 3.81%
6 Land, 1 Spells = 0.619%
7 Land, 0 Spells = 0.0450%
Total= 100%

More educated folk may need to correct me. Perhaps I am missing something vital.

The argument is that by increasing the quantity of cards in the deck, but not changing the ratio of functions in the deck, there will be a higher chance to draw hands which are different from the average hand.

If these numbers are correct (I'm only showing the results of the program), and I'm interpreting them correctly, then it doesn't seem that the quantity of the deck has a very significant impact on the chance to draw our "golden hand" in the context of the difference between 60 to 70 card decks. Ratio seems to do the majority of the work.

From my perspective, even including the odds of seeing your 'MVP' cards, it is certainly possible to build 61 card decks (and even higher) which are actually the best way to build the deck according given the proportion of the functions.






peace,
4eak