Food for Thought: Is 60 Cards Always Optimal?

Some people claim that if you are playing over 60 cards in your constructed deck you are playing wrong, or at least to your own disadvantage. Why is this? Because you have a lower chance of drawing your best cards. If you run, say, 4 force of will in your deck, you have 56 other cards in your deck that aren't FoWs. If you run 61 cards, then you instead have 57 cards that are not FoWs. Now if you consider FoW one of the best or most powerful spells in your deck, and you want it as often as possible, then of course you should generally chose a 60 card deck over one with 61 and up, as it increases your chances of drawing one.

But is this always correct? Is there a way to beat the odds so that 61 is better than 60? Or, at least, a good reason to run over 60 (excluding battle of wits or EDH as a reason) cards?

I think there might be. One thing extremely important to almost every deck is it's mana base, or land count. The number one reason someone mulligans their hand is because they have too much land or too little (generally over 5 lands or under 2 lands in their opening hand).
Mulliganing is a harsh thing to do yourself. Of course sometimes it is necessary, but all in all you really hurt your chances of performing well when you start with the disadvantage of one less (or even less than that) cards in your hand.

What am I getting at? This: is it possible to run an extra card or two to decrease your chances of getting an "unkeepable" hand?

Well, 60 card decks only have so many possible percentages of land that can be played. For example, when taking the most common land counts of decks (looking at legacy and standard), these are the percentage of lands in each version:
21 - 35.00%
22 - 36.67%
23 - 38.33%
24 - 40.00%
25 - 41.67%
26 - 43.33%
27 - 45.00%

Now, if we played 61 cards, a new range of percentages could be attained. These are the same land counts (plus 28) with 61:
21 - 34.42%
22 - 36.06%
23 - 37.70%
24 - 39.34%
25 - 40.98%
26 - 42.62%
27 - 44.26%
28 - 45.90%

These percentages are not available to a 60 card deck, only to 61. But concerning mulligans, are these percentages any better than that of a 60 card deck? This is where math class comes in. The math is really quite complicated actually, so I'm not going to show how I got the answers. But here are the percentages that you'd get a bad opening hand for each land count and 60 or 61 total cards in the deck (for this chart I have to assume that 5 lands is a bad hand or results will not be realistic):
21/61 - 26.91%
21/60 - 26.21%
22/61 - 25.15%
22/60 - 24.57%
23/61 - 23.80%
23/60 - 23.34%
24/61 - 22.85%
24/60 - 22.54%
25/61 - 22.31%
25/60 - 22.16%
26/61 - 22.18%
26/60 - 22.20%
27/61 - 22.45%
27/60 - 22.64%
28/61 - 23.10%

So, no, while 61 cards adds a lot of more options percentage-wise, 25/60 is still technically the amount that will give you the highest chances of getting a good opening hand. Does this mean it's the best? No. If your deck has nothing with a converted mana cost over 3, there is probably no reason why you need a land count that high. If you run some sort of mana-ramp in standard with explore-type cards, you might want even more than 25.

But, while not giving the best percentages, 61 cards is not completely pointless. Just look at the percentages for 22/61. It offers a percentage that fills the large gap between 21/60 and 22/60. Some deck out there might want that percentage, as it feels 21 is too low and 22 is too high. Am I saying that that deck would necessarily want to decrease the chances of drawing one of it's 4-ofs (would only decrease by 0.1% by the way) to make it's mana-base slightly better? No.

It's just food for thought.

I hope this mini-article blog thing helped you think outside the box a little. People take 60 card decks for granted, when there are many percentage factors (not just land counts) that might work in your favor if you run more than 60 cards in your deck.

Also, just a side-note: the percentage of getting a good hand doesn't increase from 25/60 until after you get past 70 cards in your deck, which is an outrageously high amount of cards just to get a slightly better mana-base. So I wouldn't try it.
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Tom

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