Hey guys, I am keeping myself busy evaluating Power of Creation and hit a math problem that I don't know how to solve.
Assume we want to find odds to hit X number of outs out of Y cards in discover pool. If all options are neutral cards, formula for that is quite simple 1-((Y-X)/Y*(Y-X-1)/(Y-1)*(Y-X-2)/(Y-2). For example if we need two outs from a 10-card pool, it is is 1-(8/10*7/9*6/8)=0.5333
But there are a problem when we add class cards. One can say that they have x4 higher chance to appear, so you can simply count them for 4 card. But this is incorrect. If we'll do that, we'll assume that it is possible to hit the same class card twice, which is not true. For example: in the most basic case of 3 cards(1 of them is a class card) and 1 neutral out, we'd get a formula like 1-(4/5*3/4*2/3) giving us 0.6 instead of the correct result of 1.
Are there any elegant mathematical way to solve this problem? Or is the brute force simulation is the only practical way to do it?
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Hey guys, I am keeping myself busy evaluating Power of Creation and hit a math problem that I don't know how to solve.
Assume we want to find odds to hit X number of outs out of Y cards in discover pool. If all options are neutral cards, formula for that is quite simple 1-((Y-X)/Y*(Y-X-1)/(Y-1)*(Y-X-2)/(Y-2). For example if we need two outs from a 10-card pool, it is is 1-(8/10*7/9*6/8)=0.5333
But there are a problem when we add class cards. One can say that they have x4 higher chance to appear, so you can simply count them for 4 card. But this is incorrect. If we'll do that, we'll assume that it is possible to hit the same class card twice, which is not true. For example: in the most basic case of 3 cards(1 of them is a class card) and 1 neutral out, we'd get a formula like 1-(4/5*3/4*2/3) giving us 0.6 instead of the correct result of 1.
Are there any elegant mathematical way to solve this problem? Or is the brute force simulation is the only practical way to do it?