Haskell for all: Probability for Slay the Spire fanatics

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2021-06-06 01:00:04

I’m a huge fan of Slay the Spire and I wanted to share a small probability trick I’ve learned that has helped me improve my game by calculating the odds of “greedy” plays succeeding. This trick will likely also benefit other games based on cards or probability, too, but the examples from this post will be specific to Slay the Spire.

I have a deck containing N desirable cards out of D total cards. If I draw H cards from that deck, what is the chance that I draw (exactly / at least / at most) M desirable cards?

This sort of question comes up often in card games, including complex ones (like Slay the Spire) or simpler ones (like poker). Here are some concrete examples of how this relates to Slay the Spire:

“Next turn I draw 5 cards. What is the likelihood that I draw at least 3 Strikes if there are 7 cards left in the deck, 4 of which are Strikes”.

“One Neow bonus lets me lose 7 max HP to select from 1 of 3 random rare cards. Right now I’m only interested in 6 of the 17 possible rare cards, so what is the chance that I random at least 1 of those 6?”