Nearly Useless Numbers I Worked Hard to Find
When I first started playing Magic, I thought I could use my knowledge of probability to get an advantage over other players, which didn't work as well as I hoped. But probability can be helpful for some players, or interesting for knowledge's sake, so I'll share my mathematical findings here.
Land Curves
(Forty card decks. The red is less than 50% chance of drawing that many lands or more, green is better than 90% chance.)
Here's a nifty picture with many bright colors! But what in the heck do all those numbers mean?
Here we see the first problem with using calculation: The numbers are very difficult to translate into real strategic decisions. I know I can have a 79.5% chance of drawing between two and four lands in my opening hand, but without something to compare it to, that number is meaningless. How important is drawing the right number of lands anyway? What will other decks be doing?
Underneath the main graph I put some numbers that might help with mulliganning decisions, and that brings up the second problem with calculations: any decision the player can make during the game will throw off the numbers wildly if we can't predict the player's choice. The choice to mulligan is extremely difficult to make optimally in some cases, and if we can't predict whether the player will mulligan, how can we predict what cards will be in his or her hand later?
Magic is designed to be extremely resistant to number-crunching.
I think calculations like this might be useful for pro players trying to precisely tune their decks, or mid level players trying to learn new archetypes, but playtesting several actual games will almost always help you understand more. And for very new players, using general rules of thumb like "Use 17 lands, 2 colors" is much better.
Calculations for drawing a certain kind of land or combination of lands might be more helpful but are much more difficult. I might post some other graphs later. I can help you find numbers for your deck if you are curious enough to ask.
Here are some graphs for other numbers of lands,
More than 17 lands
Less Than 17 lands














