Mulligan Math
Deck Help forum
Posted on June 1, 2022, 4:36 p.m. by zeonrain2
I am playing a game of Commander and I have a deck of 99 cards. In this deck are 37 lands. Using a hypergeometric calculator it returned a 29.12% chance of drawing exactly 3 Lands on a 7 card draw using the probability density function. My question is how do I calculate the probability for drawing 3 lands with one or more mulligans?
Not sure if this is the right place to post this, any help would be greatly appreciated. Also I've been googling a lot so I don't understand half of what I'm doing lol
@wallisface in the future, please use a #2 pencil and remember to fill in the circle completely.
June 1, 2022 6:24 p.m.
wallisface says... #4
Note also that your math odds for drawing 3 lands is only kindof accurate. Yes, you have 29.116% of drawing exactly 3 lands from a hand, but you actually have much better odds of drawing at least 3 lands from a hand (52.468%), which might be more relevant to you. This tool here is of great use for getting those stats instantly
June 1, 2022 7:09 p.m.
TypicalTimmy says... #5
If you draw seven cards, decide you do not like it and shuffle the seven cards back into the deck, then draw six cards... Why does your percentages go up?
Even if you draw 7 cards ten times in a row and never go down in hand size, why are the percentages going up? You're not changing the number of cards or lands. It's all the same data. Shouldn't the percentages be the exact same?
June 2, 2022 1:02 a.m.
wallisface says... #6
TypicalTimmy The percentages do stay the same for each particular draw - i feel like you misread my initial post. To give you context, I’m saying that if you’re willing to mull once, you have 49.6% of getting exactly 3 lands in your opening hand OR your first mulligan. You effectively have two chances of succeeding, instead of one if not mulliganing at all.
The percentages are increasing not because the hands themselves have any kind of differing odds, but because you’re seeing more hands, and you only need any one of them to succeed.
June 2, 2022 1:13 a.m.
TypicalTimmy says... #7
Well there's a reason math was my weakest subject in school :3
wallisface says... #2
Your odds of getting 3 lands in any hand will be the same regardless of whether its your first deal, or a mulligan. So, i think you need to reword your question to be “if i’m willing to mulligan X times trying to find a 3-land hand, what are my odds of success”.
If your odds of succeeding in any given hand is 29%, then your odds of succeeding given 2 hands is 29%, plus 29% of the remainder (i.e 29% of 71, i.e 20.6). You can keep this process going to give you the following stats (rounding to 1dp):
June 1, 2022 5:54 p.m.