Why 60 cards is NOT always optimal

[MadRhetoric]

I know, before you even read anything, you're thinking, "Not 60 cards? BLASPHEMY!” I’m not advocating 100 card decks or anything, I just wanted to share my thoughts on how 60 cards is not always optimal for a deck.


To get right into it, I think that seeing 60 cards as always optimal has been set to the default and not explored as much as we should. I think the reason is because for a very long time now we’ve used the logic “in a 60 card deck, we are most likely to draw the most important cards.” I don’t think this is the right mindset. Instead of thinking there is an optimal decklist that confines to 60 cards, I believe instead there is an optimal “ratio” for a deck. To explain this, I first must explain what I think every deck is composed of. I think we can all agree every card in a deck can be put into 3 categories: Mana, Utility, or Threat. And different decks have different logics behind them. A very low threat and high utility (Tog) or maybe a very low utility and high threat (FCG). What I’m suggesting is that in building towards the optimal decklist, there exists a perfect ratio of these three card types to fit the decks basic gameplan. By doing this, we find the chances of getting better hands and seeing better cards down the road.

Now, I’m not suggesting going up a huge amount in cards, but most importantly in decks with a low amount of one of the three card types, going up one or two cards over 60 may be the best option. Adding another land to combo or adding a triskelion in addition to your other threat creature base in Slaver may see better results. This may not be profound, but I just hate seeing that people feel the need to cut cards in order to get to 60, when having 61 may be better. Even when it’s one more card in a deck, with all the draw and search in the format, having it in the deck may make a difference.

I hope that this spurs some discussion and is a little food for thought for those looking for that last card to cut.

[Malhavoc]

I understand your discussion, but keep in mind that in Vintage there is a huge amount of cards which can really turn the tide, take for example Yawgmoth Will during midgame. It is a card you want to draw as soon as possible during midgame (or at least when your graveyard is full enough). Let's say that for some reason card limit is lowered to 30 cards. Would you still play 60? 40? 31? No, because having 1 yawgmoth (or lotus, or ancestral, or anything else) every 30 cards is better than having one every 60. It would almost be like having 2 of them in a 60 cards deck. Would you play 1 ancestrall when you are allowed to play 2? Would you then, in a 60 cards deck, play 1 ancestral or play 1-1/60 ancestral (because you are using a 61 cards deck)?. I prefer the first. Your discussion would be right if cards were divided ONLY in mana, utility, threat, with these groups of cards being almost equal inside them. That' not true. Ancestrall is better than Opt, no way. You were simply forgetting about a fourth set of cards: Broken cards.

However, your ideas *could* make sense in a cheap unpowered deck, were most of the cards are about the same: having 25 mana 20 threats and 16 utilities could be better than having 25,20,15, but that's just because you don't play broken cards, due to money limits. But when we talk about good decks, there is no reason to play more than 60 cards.

[dandan]

The only reason I could imagine for going over 60 cards (Battle of Wits aside) is in a combo deck that uses decking or if a new card used the library as a resource Arc-Slogger. Such decks does not exist at present but I am sure we would all agree that in a world with no B&R list a Wheel/Lotus deck would use more than 60 cards.

Having said that I agree that it is right to question the automatic use of 60 cards even though I find it hard to imagine the 61st card ever giving a large enough advantage to counteract the downsides of larger decks that Malhavoc ponts out.

Can a 61 card deck ever be optimal? Possibly.
Can a 61 card deck be optimal given the current rules and cardpool? I strongly doubt it.

[Malhavoc]

As Dandan said, there are in fact decks that coul benefit from having more than 60 cards. I have played Stasis deck counting 61-62 cards for decking reason. However, since Stasis runs better with a couple of cards more than 60, Stasis is not really a tier 1 deck    In the end, with the current card pool (as dandan suggested) there are no competitive decks that benefit from having more than 60 cards. Those decks like Stasis or budget decks that could/do benefit from that are anyway a lot inferior those in the current metagame, and then not worth considering.

[TheWellknownBrownie]

I'm going to say that Malhavoc makes more sense. Maybe in formats where every card you can play you can run 4x, the argument makes sense. I've run 61 card decks in Type 2 and 1.5. But in Vintage, the ability to draw ridiculous cards seems to valuable.

[Bulls on Parade]

I think you guys looked right past the point MadRhetoric made. His example really got it across clearly I thought. The way I interpreted it was this:

You have a 60 card deck before a tournament begins (let's say Control Slaver, for example). You've done a little looking around and seen tons of Welders, so you want to fit in that Trisk pretty badly. Rather than cut something good from an already tight deck, is it truly suboptimal in this case to run the Trisk as the 61st card?

I'm not saying I agree with this, just saying this argument makes more sense than whatever you're talking about Malhavoc with Stasis being a bad deck because it runs better with 61 cards. That's not why Stasis is shit.

[MadRhetoric]

I agree with both of you. However, I don't think that considering broken cards as a fourth category would change anything. I think of it this way.

Let's say in traditional Control Slaver, you have these threats:
2x Mindslaver
1x Pentavus
1x Platinum Angel
(I'm including Mindslaver because against many decks it's crippling and because of its likelyhood to recur.)

Also, I'm assuming we won't change anything else, as the maindeck has proven to be incredibly tight. Adding a Triskelion to your deck, putting it at 61 cards, may seem small, but it's actually increasing your threats by 25%.

Now when we look at what Malhavoc said, you would be decreasing your chances of drawing a "broken card", but I believe increasing your threats by a relative large amount by adding one card, is completely worth dropping the likelyhood of drawing a "broken card" from 1/60 to 1/61. Again, this is especially true in Slaver where you have a ton of draw and search.


I must also admit, that I had Slaver in mind when I first began thinking about this, so most likely this will only apply to a very small number of decks.

[Malhavoc]

I'm not saying I agree with this, just saying this argument makes more sense than whatever you're talking about Malhavoc with Stasis being a bad deck because it runs better with 61 cards. That's not why Stasis is shit.

Maybe I've been misenderstood, but I've never said that! I've said that Stasis runs better with 61 than 60 cards. Despite that, Stasis is not a good deck. But just because of many other reasons, not because he is better with 61 cards.  

[MadRhetoric]

I'll elaborate on what I said above. Like in the situation above, the relative increase in threats greatly outweighs the apparent decrease in drawing specific cards.

An increase from 4-5 is MUCH more significant than an increase from 60-61, even though it is just one card in both situations.

It's kind of like the Magic theory of relativity. Relative to the size of the deck, it may seem insignificant, but relative to cards with similar purposes, it may make a big impact.

[Gabethebabe]

Your statement is not true. 60 cards is optimal and anything else is suboptimal.

If you play more than 60 cards you dilute your deck.

I don´t care if your deck is tight. Cut something.

The statement that there is very little difference in 1/60 and 1/61 is true, and these are exactly the little differences that make you win or lose.

[Toad]

You have a 60 card deck before a tournament begins (let's say Control Slaver, for example). You've done a little looking around and seen tons of Welders, so you want to fit in that Trisk pretty badly. Rather than cut something good from an already tight deck, is it truly suboptimal in this case to run the Trisk as the 61st card?

Yes, It is suboptimal in this case to run the Triskelion as the 61st card.

If you are expecting tons of Welders, just cut the Platinum Angel, for example.

Drain Slaver is designed around Goblin Welder. You'll draw more Goblin Welders if you run 4 in a 60 cards deck than in a 61 cards deck. The one card difference will cost you games.

[MadRhetoric]

Your statement is not true. 60 cards is optimal and anything else is suboptimal.

If you play more than 60 cards you dilute your deck.

I don´t care if your deck is tight. Cut something.

The statement that there is very little difference in 1/60 and 1/61 is true, and these are exactly the little differences that make you win or lose.

Did you even read the above posts? You didn't give any explanations and it didn't add to the discussion at all.

[MadRhetoric]

You have a 60 card deck before a tournament begins (let's say Control Slaver, for example). You've done a little looking around and seen tons of Welders, so you want to fit in that Trisk pretty badly. Rather than cut something good from an already tight deck, is it truly suboptimal in this case to run the Trisk as the 61st card?

Yes, It is suboptimal in this case to run the Triskelion as the 61st card.

If you are expecting tons of Welders, just cut the Platinum Angel, for example.

Drain Slaver is designed around Goblin Welder. You'll draw more Goblin Welders if you run 4 in a 60 cards deck than in a 61 cards deck. The one card difference will cost you games.

I never specified welders. What if you had a meta full of FCG, where both Trisk and PA were useful. The benefit of having both in your deck will most likely win more games then the VERY rare situation where having a 61st card in your deck somehow cost you a game.


Also, take into account this was more of a theory then an application. It may not apply to decks now, but somewhere down the line it might. Most people are very caught up in convention, and thinking outside convention is what has developed T1.

[Ephraim]

I tend to side with MadRhetoric on this matter. I've done some very simplistic number crunching concerning this matter and I'd like to discuss the ramifcations of some of those numbers. Obviously, this analysis is very elementary and doesn't take into account a lot of factors. It only analyzes opening hands, which both fails to recognize the importance of a strong draw-engine and the relative value of some cards during different periods of the game. (If these remarks look familiar, I'm cutting and pasting them wholesale from remarks I made in a similar topic at The Source.)

Suppose you have a deck that contains 60 cards, exactly one of which is a singleton. That card is not restricted and you could add a second copy if you wanted to, except you're afraid to increase your deck size above 60 cards.

Probability of having one copy of a card in your opening hand if:

You have 1 copy in the deck: 11.67%
You have 2 copies in the deck: 22.15%
You have 3 copies in the deck: 31.54%
You have 4 copies in the deck: 39.95%

Now, suppose you add one more copy of that singleton, so you have 61 cards in the deck and no singletons.

Probability of having one copy of a card in your opening hand if:

You have 1 copy in the deck: 11.48%
You have 2 copies in the deck: 21.80%
You have 3 copies in the deck: 31.08%
You have 4 copies in the deck: 39.40%

The card that was previously a singleton will appear in your opening hand (21.80/11.67) = 1.87 times as often as it did previously. A card that remains a singleton (something restricted, for example), will appear (11.48/11.67) = 0.98 times as often as it did previously. To compare the impact of this change, take the ratio of the frequency changes of the various cards. One copy becoming two results in a frequency change of +0.87. A card that remains a singleton has a frequency change of -0.02. The relative frequency change between the two cards is (0.87/0.02) = 43.5. That is to say, if a singleton is 43.5 times more useful  than the card one is proposing to add, then the addition is a bad decision. Of course, it's difficult to quantify the relative value of cards in numeric terms, except for the simplest examples (ie: Lightning Bolt is 1.5 times better than Shock.)

Obviously, anytime one would add a 61'st card, it is also important to consider removing a different card. Using a similar analysis based on ratios, as illustrated above, one can determine the requisite relative value of any pair of cards. I hold that it is hardly inconceivable that a deck be constructed such that a particular 61'st card has sufficient relative value that it merits inclusion without the removal of another card. As previously noted, I can definitely see this being the case for a toolbox variety deck and others have acknowledged that it is possible that the addition of a single land could also be a significiant contribution. Furthermore, if one classifies the cards as MadRhetoric has suggested, the analysis becomes somewhat easier. Suppose a deck has three threats and it is desireable to add a fourth threat. (39.40/31.54) = 1.25, for a frequency change of 0.25. Even in this example, the broken card would have to be 12.5 times more useful to the deck than the additional threat to make this addition a poor choice.

[Bram]

Some more highschool math.

Adding a Triskelion to your deck, putting it at 61 cards, may seem small, but it's actually increasing your threats by 25%.

While it may in your example increase your number of threats by a quarter, this is sort of misleading. The odds of getting one of your defined threats in your opening hand (for example) only increase by 7,5%.

The drawback of all this is that you reduce the chances of drawing ANY of your four-ofs on opeing hand (which is of vital importance for the deck) by 0,55%. This means:
0,55% less chance of getting a Welder on opening hand.
0,55% less chance of getting a FoW on opening hand.
And so forth.

This may seem a small percentage, but the benefit of having a 'bomb' in my opinion really doesn't outweigh the detrimental effect it has on a deck's performance.

If the card is really such a bomb, you should be able to find room for it. If you can't find room for it, it's apparently not strictly better than anything you're already running. And in that case I ask: why would you reduce your decks consitency by adding a card that's strictly worse than all the other cards in your deck?

Also, the big-ass artifacts are really not the threats of the deck the way I see it. The real threat is the consistency with which it builds up and eventually finds one of the finishers. You reduce that consistency by adding a 61st card.

I can see your point, but I must side with Toad here.

[Mike Panas]

First off, Lightning bolt cannot be exactly 1.5 times as useful as shock, because either card can be used to kill a welder, but only lightning bolt can be used to kill a 3/3 creature, which confuses the issue of whether its 1.5 times more powerful.  
Ok, so yes, i would agree with your argument that if you want to see one of these non restricted cards more often, increasing the count is the way to do it.  However, you have to want to see it more than you would want to see a restricted card if you are going to 61 cards.  If that is indeed the case, then it must be a pretty darn powerful card in your deck (perhaps your win condition).  So why not cut something else out and return the deck to 60 cards by removing something else? not every non-restricted card you have in your deck can be as powerful as restricted cards or this one particular "win condition" card.   Now you've increased your chances of drawing brokenness by 2% and this other powerful card by some percentage as opposed to a 61 card deck.

[MadRhetoric]

Some more highschool math.

Adding a Triskelion to your deck, putting it at 61 cards, may seem small, but it's actually increasing your threats by 25%.

While it may in your example increase your number of threats by a quarter, this is sort of misleading. The odds of getting one of your defined threats in your opening hand (for example) only increase by 7,5%.

But in most decks, especially Control Slaver, you don't want the card in your opening hand.

I think some of you are looking at my arguement wrong. It's not the power of one card vs. the power of another, it is how often a card would be more useful than another. Look at it this way, even though you want to see lots of FoW or Goblin Welder, they are not always what you want.

This goes back to how I broke down cards into three categories. How good are the most broken cards in a deck without the mana to cast them? How good are FoWs when they already got their threat into play?

What I'm saying is that theoretically, there exists a certain ratio of Utility to Threat to Mana that would give a deck the most likely probability of having the optimal hands. This is especially true in decks with a small number of a certain type of card, because even though you may only need one threat to win, you want that threat at the right time. Going from 4-5 may improve the chances. The power level of other cards in the deck shouldn't even be taken into account.

[Bram]

But in most decks, especially Control Slaver, you don't want the card in your opening hand.

If that's the case (and I definitely agree with you) then you obviously want to either draw it in late game or tutor for it somehow. Hence, f you can find a threat later on in the game anyway, your argument of 'increasing threat density by 25%' becomes useless.

The question should be: do I need to run ~cardname~? If the answer is yes, one should build the most consistent deck around it, which ALWAYS consists of 60 cards (note how I'm not saying 'optimal' here). If the answer is no, then you should just not run it, and don't make your deck less consistent by adding it.

Consistency is key here. As a sidenote, let me indulge in an example.

If you have a Relentless Rats / Land deck with a ratio of exactly 1/3 (meaning 20 rats in a 60 card deck for example), the odds of drawing AT LEAST one Rat on opening hand reduce when you increase the deck size (remember, we're keeping the ratio constant). It drops from close to 100% (for a 9 card deck...the lowest number you cn fit a 1/3 ratio in and not deck yourself when drawing your opneing hand) to 94.16% for, say, a 6000 card deck and doesn't noticably drop when the deck size becomes arbitrarily large (there's a nice limit there). The number for a 20 rat, 40 land deck (60 cards!) is 95.17% whereas the number for a 2000 rat, 4000 land deck (6000 cards) is 94.16%. Here's the graph:



Adding cards to your deck, even while keeping the ratio constant, reduces the odds of drawing into a four-of you need. The fewer cards are in a deck, the more consistent it will be.

If you need Trike for a certain matchup (meaning it is better than all other cards in your deck) then run it and cut something else. Your argument would likely be something along the lines of 'but I can make one specific matchup better'. Yes, but that's what sideboards are for. Because you'll be making every other mathcup worse by adding it as #61.

[MadRhetoric]

Bram, while I agree with what you say, I don't think it applies to what I originally had in mind.

While that applies for decks of such high consistency, I was thinking of decks with many 1-of's or with a small amount of one type of card.

Also, even though Trike might not be optimal, cards like Sundering Titan might be useful in the majority of matches in your metagame. In situations like this, I think it is better to go to 61 cards and have that advantage in those matches and take the small penalty of being 61 cards.

Again, this will only apply in very specific situations. I think most of you are blowing out of proportion the "inconsistency" caused by adding 1 card. Especially in decks like Control Slaver, where having that one additional bomb artifact can make a difference, the "inconsistency" is negligable.

[virtual]

I think the one can play 61 cards when the additional card is a mana source.  By adding to 61 cards, you can obtain mana percentages that are different.  

The tradeoff here is that you decrease your likelihood of drawing broken openings for the positve of gaining consistency.  

This goes against people's blood in Type 1.  Type 1 players optimize down to the fewest # of lands, Type 1 players play Meandeck Tendrils because even though maybe it isn't as consistent as other decks, it is uber-broken and it is so fast.  

In certain decks, if the idea behind the deck is that you want a force of will in your opening hand, or you want a trinisphere on the first turn.  In decks like these, the 61st card goes against your game plan, so it isn't worth it.  

However, assume we have a computer that spits out the optimal % of cards that we need to play in a deck to make it perfect.  Now lets assume that the computer says these are the optimal cards, each with a probability of 1/61.  Each card is unique and required in the deck for some functionality.  

Because we cannot play fractional cards, 61 cards in a deck may in some cases be optimal.  

-Virtual

[strick09]

I think the issue Bram brought up (nice graph btw!) is saying, specifically, that although you may keep the *ratio* the same between your land and non-land-bomb-diggity cards, your opening hand size does not increase, which effectively decreases your odds. (HS Math: Take a given fraction and slowly increase the denominator while keeping the numerator constant...the number gets smaller and smaller as the denominator [decksize] increases).

Traditionally, the only reason a deck played 61 cards was if it had a hard-lock and relied on decking the opponent as a win condition. (Feldon's Canes were nice for that too).

I agree with the other people on here that if something is that good that you want to include it, you should find a card that's worse than it and cut it, or just change your sideboard.

Situation (A): A card should be added in because the environment requires it as an answer (eg. Trikes in a heavy Welder environment, or Plats in a heavy combo environment).

Situation (B): A card should be added in because certain matchups will benefit greatly from its inclusions (eg. Trinispheres to stop Belcher, etc.)

In Situation A, the percentage of times that inclusion will come in useful will heavily outweigh, in theory, the times when it is not useful. Since your deck was not already geared to handle it (if it were, you wouldn't need to change it), then it was geared to handle SOMETHING ELSE, which can be removed in lieu of the added card. Continuing the Trike/Welder example, let's say you were expecting a heavy combo environment, so you maindecked 4 Trinispheres. We all know that Workshop decks (Welder decks) wipe their ass with Trinisphere cards, so removing some of the Trinispheres in lieu of Trikes should be preferable, right? It is better card quality in more matchups in that particular example.

In Situation B, merely sideboarding the card should be sufficient, for obvious reasons.

Getting away from playing decks that were larger than 60 cards was a tough habit to break, but I haven't looked back to my scrub-days since.

[MadRhetoric]

I guess I'm going to have to argue against myself for a moment.

I think the flaw in my logic is that the 4-cards-to-a-deck rule exists. Even though there might exist a perfect ratio, because we cannot include more copies of the cards already seen to be optimal for a deck, we will dilute the deck with inferior cards.

And this is why I don't think this will apply for the vast majority of the decks. Think of it this way. If I'm running some combo deck, and I cut Lotus Petal from the deck as the 61st card because I want to get to 60 cards and everything else is pretty much necessary. I don't think it's right to exclude it without testing as it might prove having that extra mana source does come in handy.

[Ephraim]

The argument I am commonly seeing is this:
Because conventional wisdom dictates that a 60-card deck is best, if a new card is found that is better than a card already present or if a card that is already used is found to be better in higher quantity, remove the lesser card and replace it with the better-suited card.

The case I am trying to make is this:
The 60-card deck containing the better card will be better than the 60-card deck containing the lesser card -- I agree fully with that point. However, be absolutely certain that both decks are not inferiour to the 61-card deck containing both cards. Although I've been challenged to find empyrical evidence of this ever happening (which I am unable to do), I've provided statistical evidence of the possibility.

It is not, by the way, a valid argument to say that 61-card decks are inferiour by definition, QED. I'm not convinced at all that the "years of empyrical evidence" supporting the superiority of 60-card decks is anything more than evidence that nobody wants to look stupid by challenging what everybody else says is true.

[Machinus]

The analysis which puts emphasis on cutting the 61st card is correct, because magic decks have a finite number of cards and you can only draw so many of them during a game. As the game progresses, that extra card can and WILL ruin your game, and it is definitely not a 'very rare' occurence.

Sixty cards is not that many, when you think about all the draw and tutoring that occurs. So even one extra card can basically stall you for a whole turn or even more. Do you want to give your opponent free time walks?

[Thug]

It is very deck dependend. Some decks can't get away running more than 60 card, some can, some even ask for more than 60 cards.

Deck very reliable on a certain card (like clamp deck, belcher, doomsday, etc) will almost always be better as a 60 card deck, since you just want to see the card asap.

Decks that do not rely on a single card to win and with a couple of tutors in it can become better if you add another bomb to tutor for.

Last tournament I played a 62 card Slaver deck (ok, it should have been 61, but there simply is not a single card I would cut to go down to 60 cards). The deck is very very tight, but rarely needs a certain card to win (not even welder, there is a reason why people actually went down to 3). The only thing that might hurt is that you get a very very little decrease in mana artifacts in your openings hand, but having 2 DA etc easily outweigths this.

Koen

[dandan]

I think we need to divide the reasons for going up to 61 (or more cards)

1. More cards because the deck requires more cards. Examples include decks that win by decking, use the number of cards in the library/deck as a resource, need a specific number of cards in the library at a certain time or some other reason due to new cards. I won't go into specific cases like Stasis and argue if it is optimal but so far everyone has agreed that it is at least piossible that more than 60 cards could be optimal for such a deck.

2. Going to 61 cards to add a card that is worse or equal in power/utility/'whatever you want to call it' to cards already in your deck (if you don't like that statement, swap the 61st card for the card in your deck that you consider it is better than)
I think we can agree that if the added card is a singleton or merely an additional copy of a card (cards) already in your deck, it increases the chance of drawing it in your opening hand and indeed of drawing it at any tome drawing the game. We can also agree that it decreases the chance of drawing all of the other cards in your deck, both in your opening hand and in the rest of the game. We also seem to agree that the increase in probability of drawing the added card is far higher than the decrease in probaility of drawing the other cards.

Given this we can say

1. In Vintage you are reducing the chance of drawing 'bombs', specifically restricted cards that everyone agrees are higher in power level other cards (talking about restricted cards in a good deck, not some of the crap still polluting the B&R list :lol: ). This is a bad thing.
2. The increased chance of drawing a card that is worse or equal to the worst card in your previous 60 card deck is not an advantage if we are considering purely probabilities and statistics.

Purely from a mathematical point of view, it is not a good idea.

However the point that has been made about the number of threats is a valid one. I would put it another way:
Increasing the number of options may be worth slightly decreasing the chance of having the chance to make that choice.
IF one of your 5 'threats' would win the game then a slightly lower chance of deploying that threat might be worth it rather than having 4 threats and the chance that none of the threats is optimal. I prefer to call them 'options' rather than threats as then we can include utility cards/mana etc.

The best example I can think of the highlight this point of view is a SotF deck that wants a utility creature to handle every opportunity but needs a set number of mana/utility cards to function. In this case the added card has a chance of being 'chosen' far higher than merely drawn and although a lower 'power' card than cards already in the deck, would be THE optimal card in some circumstances. Such a case leaves a pile of poo on statistical probabilities as the probability of drawing the additional card vs other cards is not that relevant and the idea of rating the 61st card in power relative to the other cards is also rather hard to judge.

I concede that such a possibility exists although I think that in 99% (and probably higher) of cases, the 61st card is not the right choice and is merely an example of failing to optimise your deck.

I'll call this 'handbagging' because I am sure many of you would appreciate that one of the fundamental differences between men and women is the ability to not carry around stuff that, although very useful some of the time, are not useful often enough to be worth carrying around all of the time. I once had a girlfriend that carried an iron (not the golfing type) in her handbag, although she did not carry around an electricity supply nor unironed clothes. Perhaps she really needed that iron, and perhaps you really need that 61st card.
(I am aware that an iron can be a savage weapon if used to beat off a mugger, just be aware that the sort of person who carries around an iron is the sort of person who also carries around enough other junk to make swinging the handbag a feat beyond most people, although I did see her accidently catch a few unfortunate guys in the groin as it swung by her side on the (presumably) titanium-reinforced shoulder strap)

As the man walking in the hills says "I think I am starting to ramble" so I'll shut up.

[Gabethebabe]

Your statement is not true. 60 cards is optimal and anything else is suboptimal.

If you play more than 60 cards you dilute your deck.

I don´t care if your deck is tight. Cut something.

The statement that there is very little difference in 1/60 and 1/61 is true, and these are exactly the little differences that make you win or lose.

Did you even read the above posts? You didn't give any explanations and it didn't add to the discussion at all.

I did read them, but that doesn´t stop 61 cards from being worse than 60 cards. You´re on the wrong side of statistics. More cards doesn´t only mean that you draw less bombs, it also makes your mulligan rate higher because chances increase you will draw lotsa land or no land (see also Bram´s post)

Example: compare a 60 card deck with 20 land to a 63 card deck with 21 land. They both have the same ratio of land. But the 60 card deck is more consistent, look the numbers:

----------60--------63--
0 land 04.83% 04.88%
1 land 19.88% 19.91%
2 land 32.37% 32.29%
3 land 26.98% 26.91%
4 land 12.39% 12.42%
5 land 03.13% 03.17%
6 land 00.40% 0.041%
7 land 00.02% 00.02%

You can talk this thread to death, but you can´t beat math.

[dandan]

Gabethebabe - Nobody disputes the fact that an optimal Lotus/Wheel deck had more than 60 cards. There are circumstances (outlined in my point 1 above) where it is desirable to have more cards. In addition I agree with MadRhetoric and Ephraim that IN THEORY it is possible that the added option of having the 61st card in your deck could outweigh the disadvantage of reducing the probability of your deck functioning in as orderly way as if it had 60 cards (reduced probability of drawing cards plus higher variation plus reduced effectiveness of some search methods).

I do not think that any current strong Vinatge deck could benefit from the addition of a 61st card but I think it is wrong to automatically assume that 60 cards is a must. As a guideline to beginners, it is reasonable but, just as good non-60 card decks have existed in the past, it is possible that we will see such decks in the future. Assuming we are looking that is.

[Bram]

The argument I am commonly seeing is this:
Because conventional wisdom dictates that a 60-card deck is best, if a new card is found that is better than a card already present or if a card that is already used is found to be better in higher quantity, remove the lesser card and replace it with the better-suited card.

That's ALMOST right. Except I'm not saying conventional wisdom dictates that 60 cards are best, but that math dictates that 60 cards are most consistent, which leads to:

Since math dictates that 60 card decks are most consistent, if a new card is found that is better than a card already present or if a card that is already used is found to be better in higher quantity, remove the lesser card and replace it with the better-suited card.

That's more or less exactly what I was saying. My rat example showed clearly that even when keeping the ratios constant, adding cards will decrease consistency. If one, such as is the case here, adds a random Trike to a 60 card deck, you even reduce the ratio of everything but your big-ass critters and hence the consistency of drawing them.

The thing is you're not just helping one specific matchup by adding a certain card, you're also making all your matchups worse by decreasing deck consistency. I just don't see the point in doing that.

Did you even read the above posts?

I did read them, but that doesn´t stop 61 cards from being worse than 60 cards.

Hear hear :-)

[dandan]

Imagine a world where player interaction is kept to a minimum (Vinatge 2004-5?). Wizards have decided to make Green strong by printing the 'Month' set with cards like

Ultimate R&D Spoon-fed Win Condition
3G
Instant
Win the game if it is the 31st day of the month
(obviously 31 such cards)

You have to make a deck for a tournament, and register it before knowing when the tournament is to be held. Note that waiting for several days would be considered stalling.

Clearly you would need a reasonable amount of mana to be able to reliably cast such cards. You would also want a certain number of search cards and quite possibly draw cards. IF you stuck to 60 cards you might struggle to fit in all of these 'Win' cards. You might find that the mana base and search take up 35 cards and have to decide if a slick deck that can cast the above cards should select 25 Win cards or 26 or 27 or 28 or 29 or 30 or 31. Can you see that the optimal deck size MIGHT be more than 60? (I think I'd still back 60 cards)

This is an extreme example but the above deck might sacrifice the smooth running of 60 cards in order to allow a greater number of options but at a lower efficiency. My previous example of a Survival deck fishing for solutions is closer to home. A wider range of silver bullets might be worth the cost of a less accurate gun.

All cards are not equal and if you treat them as such (via probability and statistics) then I have a number of Homeland commons I'd like to trade with you.

Having said that although I believe that such a possibility exists I do not think that any current Vintage deck would be improved by adding a card.