61 Cards – Magic Russian Roulette

What to cut? The eternal question. While sixty cards is the benchmark, many mages refuse to acknowledge the detrimental effect suffered when forcing those extra power-cards maindeck. Pat breaks down the logistics of such a ploy, and argues that while it may seem innocuous on the surface, the damage it can do can be telling….

Playing 61 cards is a sin. One may not see why it is so bad without careful examination, but it is. Bad, that is. Don’t get me wrong… at this point, most competitive spellcasters run 60 most of the time. However, be honest, you have to admit it: you’ve run 61 or more, and more than once.

Even if you play 60 cards religiously, you may not realize why it is so important to do so. In addition, a look at the probabilities behind adding or removing a card from your deck will reveal other interesting and useful information.

To start with, some of your cards are better than others. No matter how good your deck, some of the cards have to contribute to your winning more than others. The most inherently powerful cards in your deck may not be the best in conjunction with the rest of your deck or in the metagame. For instance, you may have a Sensei’s Divining Top in your deck to “smooth out your draws,” but if you don’t play many shufflers, it will probably not be one of the stronger cards. Likewise, Cranial Extraction is an exceptionally strong card, though in many metagames it usually won’t make the maindeck.

So we know some of your cards are better than others, taking into consideration your deck and the metagame. You even have a “best” card. Only one card can be the best card. If you have multiple copies of it, typically the first copy is the best (the first Meloku is better than the fourth). Occasionally, the fourth copy is the best, as is the case with Accumulated Knowledge.

Now if you have a best card, in general, it is obvious you have a “worst” card. Again, only one card is your worst card. Typically, it is the fourth or last copy of something, though it could be the first copy. This means if you cut one, you aren’t cutting the worst card at all, though it may still be right (ffeJ and his two Aether Burst).

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.

How can we measure how much this 61st card really hurts us? Well, it would be extraordinarily time consuming to try to figure out how often a particular deck wins when it draws every conceivable mix of cards. You could try playing, recording every card you drew, and cross referencing them to your wins, but this might take weeks or months just to get started.

Let’s use a highly simplified example instead. Let’s say you are playing some particular control deck versus some particular aggro deck. Let’s also say that if you draw at least one Wrath of God by the fourth turn, you have a 75% chance of winning. If you don’t have a Wrath, your chances are only 20%. Obviously Wrath won’t win the game immediately, but eventually you will win 3/4 of the games you have it and only one in five that you don’t. If you play a 60 card deck with four copies of a given card, discounting library manipulation, your chances of drawing at least one coy of the card by the fourth turn are 52.8% if you play first, and 56.6% if you draw first.

If the situation was the same, but you played a 61-card deck, your chances would be 52.2% on the play, 55.8% on the draw. That is a drop of 0.7% in your odds of drawing a given four-of, on average.

While this does decrease your chances of drawing your weaker cards, it decreases your chances of drawing better cards more so. In an oversimplified linear example, let’s assume your best card is as good as your “worst” card is bad, and so on. So that the 31st card in your 61 card deck is the average.

First of all, your average has already gone down, as the average would have been 30.5 if your deck were 60 cards. Also you now have a 1.6% chance every turn of drawing a card that is weaker than any of the other 60 cards. This will hurt your win percentage in the long run.

The decrease in probability of drawing your 30th best card is negated by the same change in probability of drawing your 31st card. This is true all the way up to your second card and the 60th. This leaves us with the first and the 61st cards.

The effective cost of that 61st card is that 1.7% chance every turn of drawing something even worse than your 60th card, as well as a drop in your chance of drawing your best card. All of the other probabilities cancel out, though you have lowered your mean average.

In the example given, your loss is a 0.7% drop in your chances of drawing that Wrath you need (i.e. best card from this perspective). We assumed you won 75% of the time you have the turn 4 Wrath (for simplicity, I am not considering mana; it is assumed that is factored in the 75%). You only win 20% of the time you don’t have one. You should win this matchup 50.1% of the time.

However, if your deck is 61 cards, you expected win percentage drops to 49.7! With a 0.4% drop, this matchup actually goes from being slightly favorable to slightly unfavorable! This is solely due to the addition of a 61st card. It doesn’t even take into consideration how your win percentage will be harmed by drawing the 61st card (which will be more than zero in all matches combined).

To put things in perspective regarding just how big 0.4 percentage points are, that is one extra loss every 250 games. The average match is 2.5 games. That means that by playing 61 cards one would take an extra loss roughly every 600 matches.

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.

Of course, this assumes the best card in your deck is going to lead to your winning 55% more than when you don’t draw it. This isn’t unthinkable. It doesn’t just apply to specific cards in specific matchups. For instance, we could have been talking about Necropotence in all matches combined.

The point is, your best card increases your chances of winning at all. Even if your best card only increased your win percentage by ten percent – or even one percent – it would be more than zero. Also, your 61st card will decrease your win percentage by more than zero.

By adding a 61st card, you are decreasing your chances of drawing a four of by the fourth turn by 0.7%. Your chances of drawing a one-of drop by 0.2%. The examples given have been greatly simplified; however, remember that in all cases the odds go down more than zero. This hurts you. It is a way to affect your win percentage that no opponent can take away from you. Only you can lose that one in one hundred. It’s up to you.

As with many sins, people will claim there are exceptions, special circumstances that justify the atrocity. Let’s look at the so-called “exceptions” to the 60-card rule.

1) I’m (possibly) going to deck my opponent.

No you’re not. No one ever really decks anyone the hard way. In order to deck someone the hard way, you have to play no card drawing and hope they have nothing like Compulsive Research to aim at you. If you are thinking about decking someone, you will surely have library manipulation, ensuring 61 will almost surely not be enough. This doesn’t even consider how much time it takes to play 53 turns.

If you honestly want to deck someone or have it as a backup plan, run Compulsive Research; Cranial Extraction; Gaea’s Blessing; or Duskmantle, House of Shadow. These cards are all fine on their own, and can actually realistically deck someone.

Note: In Limited, it is not unforgivable to run 41, or even 42 with a few decks (though this is rare), as the hard way is actually an option (ask Sean “Hammer” Regnier, who won the second Pro Tour this way). Still, be honest with yourself. Is it realistic? Necessary? You are actually decreasing your chances of drawing your best card (which is presumably a bomb) even more than you do in Constructed. In Limited, your best card is often far better than the mean.

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. First, you have so many ways to add the equivalent of fractional amounts of mana to your deck. Ending up with a fractional amount (if it’s even really what you need / want) should not be a problem.

For instance, add a Karoo and count it as 1.5, or add a Signet and count it as 0.75, or whatever. Cantrips that cost one can usually be counted for slightly less than your mana ration worth of mana. If you have four one-mana cantrips in your deck with 23 lands, count the four cantrips as approximately 1.5 land. Four two-mana cantrips might count as 1-1.25, and four three-mana cantrips might count as 0.75-1. Obviously, cheap cards that let you look at multiple cards like Brainstorm or Sensei’s Divining Top can add to your manabase, too.

You can also use lands with spell-like abilities or ways to convert them to action – like Vitu-Ghazi, the City-Tree or Tranquil Thicket – and count them as 0.75 mana or so. If you honestly can’t find any cantrips, alternative mana cards, or library manipulation, the truth is you should probably round off. Err on the high side (most people play too little mana when they build a manabase from scratch).

3) I have a lot of “must have” cards that I don’t want to draw.

Yeah, but you have cards you do want to draw more than others. It would be a rare deck indeed that would actually have so many “must have” cards that you never want to draw, and no cards you particularly do want to draw.

Remember, your Enduring Ideal deck may have Form of the Dragon and Zur’s Weirding, but you still want to draw Enduring Ideal itself. Do you really need all those Faith’s Fetters and Confiscates?

I don’t think there has ever been a deck that fit this criterion.

4) None of my cards are better or worse than the others.

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.

Go ahead and play 61 Mishra’s Factories, if that’s your thing.

5) I’m playing Battle of Wits

Oh, I’m with you on this one. Battle of Wits is insanely powerful, though it does have the drawback of only being playable in mediocre decks.

Why do you suppose Battle of Wits has never been Tier 1, despite “3UU, win the game”…? We’ve already seen how much adding a 61st card hurts. Imagine adding 180 more!

If Battle of Wits didn’t have the 200-card clause, it would be at least restricted in Vintage. As it is, it is not really good in any regular format. This is all because of how much you must lower your mean average to play it. It is the embodiment of why you want 60 cards.

That said, Battle itself is so powerful that it can be played in Standard as rogue Tier 2, or more likely Tier 3 strategy. However, all too often people choose to run 250+ cards in their Battle deck.

While there can be little doubt Prismatic-style formats have suggested the number 250, this is surely terrible. Realistically, how many cars will you have taken out of your deck by the end of the game? Even if the game goes 12 or 13 turns and you draw or filter through another ten cards, you won’t have ever taken out 30 cards and that is a long game. Does your deck really need more than 235? Fifteen cards would offer a significant advantage over 250, when it comes to drawing Battles.

Besides, if you are still alive after looking at 35 cards, just Brainspoil to one of those Melokus you are playing. He’s probably better than a Battle at that point.

6) I don’t know what to cut and the tournament starts in two minutes.

Fine, I guess. It’s better to make a small mistake (playing 61 cards) than it is to make a big one (cutting a random, or worse, a key card from your deck). Just be aware that you are definitely worse off than if you cut the worst card (or any card below the mean average).

It is usually worth making an educated guess, unless it is a particularly intricate deck. Look to cut something that doesn’t do something unique or vital. For instance, cutting your 12th Counterspell is relatively safe, whereas cutting one of your two Simic Sky Swallowers would be suspect. Ten minutes is enough time to cut that 61st card!

Some final statistics on deck thinning and such:

  • If you activate Sakura-Tribe Elder on turn 2, it increases your chances of drawing a given four-of by 0.2% every turn.
  • If you are playing Heartbeat and activate a turn 2 Elder, you increase your chances of drawing a spell by 1.3% every turn.
  • If you cut five land from your deck (with 24 land) and add four Karoos and a spell, aside from the raw power of the Karoos, you will also have 1.7% better chance of drawing a spell every turn. You also see a 2.8% increase in spells in your opening hand.
  • If you Gifts Ungiven for four land in a deck with 40% land when you already have seen 15 cards (turn 8-9, with no library manipulation), your chances of drawing a spell increase 5.9% every turn.
  • If you Cranial Extract someone for four on the fourth turn, and they play 60% spells, you decrease their chances of drawing a spell by 3.5% every turn.
  • If your Battle of Wits deck is 250 cards and has 20 Battles and Demonic Tutors, if you’ve seen 15 cards by the fifth turn, your chances of having a Battle of Wits or the means to get it are 71%. If you play 235, your chances are 74%.

Every percentage point counts. It is edges like this that can tip the scales in your favor. Remember, all these points add up and give you chances to “get lucky.”

In closing, it is a sin to play 61 cards. Just don’t do it. Have discipline. If you are ever contemplating the 61st card, just picture Russian Roulette. Remember, Russian Roulette is not nearly as much fun as Magic: The Gathering.

Patrick Chapin
“The Innovator”

P.S: Flores… repent your sins!