The Statistics of Magic the Gathering, part 1

There are lots of cool things about playing Magic the Gathering: putting together a board state where you deliver six points of unblockable damage every turn; pulling off a nifty inversion of control that forces an opponent’s most valuable creature to block your tiny little death touch attacker; or fighting your way back from a huge deficit to claim victory over a formerly smug foe.

Oh, it can be an awfully satisfying game.

But that is playing the game with the cards you find in your hand. Designing decks is where you try to make sure that the right cards end up in your hand when you need them, and a great deal of the basic techniques of deck design are based on statistical principles.

These notes are aimed at relatively inexperienced deck builders with questions about why some of the guidelines for deck construction exist. I would be lying if I did not say that I am also writing these down here for my own reference.

Having Mana

Casting spells costs mana, and to get mana you have to have land on the table. Ideally, you want to be playing down one land card every turn for the first few turns at least.

Standard deck-building guidelines are that you should have 16-17 land cards in a 40 card deck, and 22-24 land in a 60 card deck. In each case this proportion is about 40%.

The reasoning for this is simple: on your first draw you will take seven cards to make your opening hand. This hand wants to have 3-4 spells and the rest land, just so you can have things to do early in the game. Three out of seven cards being land is a little more than 40%, so to have a fair chance of drawing the desirable amount of land you need that proportion of land in your deck.

The Bend of the Mana Curve

Above I mentioned “having things to do”. This is what the mana curve is about.

Having land is great, but not very useful if you have no spells to cast. On average, with 40% land in the deck providing the mana, the other 60% should be spell cards which use that mana. So, you would expect to draw a spell every other turn or so*.

The trick is to make it so that you stand a fair chance of having spells to cast when you have the mana to cast them. Since you can put down one land card per turn you would expect to have one mana on the first turn, two on the second, and so on. Hence, you would hope to have a one mana cost card to play on the first, a two mana cost card to play on the second, etc (“mana cost” here is the total amount of mana to cast a spell, regardless of colour – this is often termed Converted Mana Cost or CMC).

This is where the mana curve comes. The mana curve for your deck is the number of cards playable at each mana cost. In particular, you want to have cards in your deck which will allow you to play early spells if they come up, but to raise your chances of having a strong card you can actually cast on the third or fourth turn**.

Let’s take a 40 card deck, the standard size for a draft deck, and consider a reasonable distribution of card casting costs. For this deck size the total spell card count of is likely to be around 23 while the number of creatures is going to be about 18, distributed thus:

  • 1 mana – 1-2 cards
  • 2 mana – 2-3 cards
  • 3 mana – 3-4 cards
  • 4 mana – 4-5 cards
  • 5 mana – 2-3 cards
  • 6+ mana – 1-2 cards

So if 40% of your cards are creatures, and more than half of those are going to be castable on turn 4 (assuming your land draws behave themselves), then the chances are very strong that that you’ll have things to do in the first few turns. Similarly, there are only a handful of cards that are very expensive because otherwise you run the risk of getting stuck with too much uncastable stuff in your hand.

When to Break The Mana Curve

The most common build for a deck has this kind of skewed bell curve distribution where there are a lot of medium weight spells and not much on the high or low end, but some build strategies will lead you to make different choices:

  • aggro – this is a fast deck where the goal is throw out lots of little guys fast that can attack your opponent early before any of his creatures are even our to defend. In that case, you’d end up with a lot of low end cards that can be cast in the early turns, but you never ramp up to larger stuff.
  • tribal – in these strategies, there are lots of creatures of a similar type. Elves, for example, or goblins – perhaps even squirrels. In this case the goal is to have creatures and other spells which have synergies, such as effects like “all warriors gain first strike” or “all slivers have flying”.
  • control – the goal with these kinds of decks is to delay the game until you can play a big creature which stomps your opponent. Here the creature base is going to skew big, but there would be a lot of smaller spells for removal and countering.

These strategies are all valid, but usually in a constructed deck rather than a draft simply because of the limited pool of cards available to you.

That’s the first part of this series on the statistics of Magic the Gathering. The second part will be along next week.

[*] the law of averages doesn’t exist, but regression to the mean does.

[**] third or fourth turn is important because many decks don’t really start being aggressive until this point.

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