Playing more than 60 cards

[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" article, plays 61 cards decks once in a while), 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" plays 61 cards decks once in a while), 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//deck...p?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).