Calculating this chance uses a branch of mathematics called combinatorics. The number of different ways to choose H elements from a set of D elements is called the binomial coefficient is calculated using factorials (!).

The number of different hands of size H drawn from a deck of D cards is "D choose H". A similar formula is used to calculate the number of ways to satisfy each part of your combination. If your deck has D

_{X}cards of type X and you need H

_{X}for your combination, then there are "D

_{X}choose H

_{X}" different ways to choose the type X cards you need. The number of hands with the cards you need is the product of all the different ways to choose each card. This is called a multivariate hypergeometric distribution (without replacement).

The Mathematics of Magic The Gathering: Probability, Statistics, Game Theory, and Strategy by Jon Prywes has an excellent discussion of mathematics for games if you are looking for even more information.

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