As I was reading Jonah Swersey's article on mana fixing for the "budgetally" challenged, one particular statement stood out to me:
"A typical 60-card deck runs on 24 lands."
While this is true, it seems that few Magic players actually put a lot of thought into why a 60-card deck typically runs on 24 lands. Was this number discovered through trial and error, as countless players tried to straddle the thin line between mana screw and mana flood? Or was there deeper analysis involved, projecting countless possible hands and methods of minimizing the impact of too many or too few lands? While playtesting was the most probable origin of the 24 land rule, I'd like to think that it can be supported by some statistical analysis, as well.
How I Learned to Avoid Mana Screw
When I first started playing Magic, I didn't know the first thing about building a successful deck. I read in a magazine article that most decks should consist of 2 to 3 colors and should be about one-third lands. So every deck I built was two colors, sixty cards, and twenty lands. Playing against only one person with a similar knowledge and card pool led me to moderately successful results. I think it was important for me, as a beginning player, to have those strict guidelines in place to limit the stupidity of possible decisions. But those guidelines didn't necessarily ensure that my deck had maximized its potential.
Anyone who's ever played Magic understands what it means to get mana screwed. You build a deck, take some test draws, everything seems to work fine, so you go to play it and then... BAM! You get stuck with one land in your hand and not a lot of choices. When I started playing Magic almost ten years ago, there was no such thing as a "Paris Mulligan," so if I drew a hand with one land and nothing to cast, the game was usually over. And I absolutely hated that.
So I did the only logical thing and built myself a one-color deck featuring only cards that cost one mana each. It was a green weenie deck, featuring four each of Llanowar Elves, Fyndhorn Elves, Elvish Scout, Ghazban Ogre, Giant Growth, and every other one-mana green card I could find. The deck featured only twelve lands – all Forests.
Anyone who has ever built a Magic deck and tried to win with it has a basic understanding of the mana curve. Mana curves tell a player where the resources in their decks are committed. A mana curve might be translated into a table as follows:
The top number represents the casting cost of spells in a deck and the bottom number identifies how many spells have that casting cost. Typically, you'll hear that the mana curve should be smooth, peaking around the 3-mana slot. The following graph represents the mana curve for the hypothetical deck above:
This mana curve favors the low (1-3) casting cost cards, so despite having 36 spells, it could probably lower its land count and raise the number of spells. But why is this possible? To answer that question, we turn to some statistics. In a deck with 24 lands, there is an 84.4% chance of having between two and five lands, which I define as a "good draw" for most decks. (Obviously, this largely depends on what cards you have.) Decks with low mana curves (having more 0-2 casting cost cards) only need to ensure that they have one land by the first turn and one land by the second turn. Using the traditional 24 land approach, that equates to a 98% chance of getting that first land and 91% chance of getting the second land. Sounds pretty good, right? Actually, the key to maximizing deck efficiency is to balance the early plays with the late plays. Having a 91% chance at that second land is useless if you keep drawing more lands when all you need is two. I personally try to shoot for an 80-85% chance of having the land I need when I need it. In the case of a deck that has most of its important cards in the 2-mana slot, this happens at the 21 land mark.
Passing the Mana Curve
Going back to my green weenie deck, there was an 81% chance of having more than one land in my opening hand. Ideally, I wanted a hand of one or two lands, which happened 67% of the time, or about two out of every three games. Although that number sounds terrible (I'd basically lose one-third of the games I played) it wasn't quite the case. Remember the mulligan rule at the time. No lands meant a brand new 7-card hand, so my good hands actually contained 0 – 2 lands, which happened about 86% of the time.
So how does understanding the mana curve and land count help make a better deck? First, you want to decide where the essential cards are showing up. If a deck can run on all zero and one casting cost cards, you only need 13-16 lands. The rest of the deck should be filled with spells to prevent loss of momentum early in the game. If the key cards show up at the 2-mana slot, 20-22 lands are probably enough and if the 3-mana slot is essential, you'll need to go to 24. Any deck that has its most important cards at more than three mana will require some mana acceleration at those 1-3 slots in order to survive. Decks with 24 lands can only reliably drop a fourth land by the sixth or seventh turn. Going beyond 24 won't buy much in the way of reliability, but it will significantly hamper subsequent turns.
Ugh... More Math
So now we've used statistics to build a more reliable, more efficient deck. Congratulations. Now let's figure out the logic behind another piece of common Magic knowledge: Always mulligan a one-land hand with no castable spells. As I stated earlier, a deck with 24 lands has an 84.4% chance of getting a good draw. So 15.6% of the time, you're stuck with a bad hand. What are the odds you'll actually get the hand you want by taking a mulligan down to six cards? Pretty good, actually. A six card hand still gives you 74.7% odds of drawing a good hand, much better than the 43.4% chance you have of drawing the second land that you need. Even going down to five cards will still yield a 59.4% chance of drawing something you can work with versus the 42.6% chance of getting the land you need. But be advised never to mulligan to four cards. At this point, you have a 35.6% chance of getting a playable hand and a 41.8% chance of drawing that needed land. Of course, if you have no lands by this point, you might want to reconsider. You'll have beaten the odds three times in a row, so maybe you can do it again.