Here's the information on how the expected value was computed for the How would you play this hand? posting. It's a lot less complicated talking about keeping both the 7's and the 3's, so let's start there. If you keep those 4 cards, then there are only 47 possible outcomes. You start out with a deck of 52 cards, but the 5 you see - two 7's, two 3's, and the king - are already used. That leaves 47 cards to fill in that spot of the card you didn't hold. Out of those 47 cards, there are two 7's remaining, two 3's remaining, and four 2's remaining. That's 8 cards that would give you a full house. The expected value is the odds of getting that full house (which is 8 divided by 47) times the payout (which is a variable in our case). If the payout is 3, then the expected value is 8*3/47 = 0.5106 and for a payout of 4 it is 8*4/47 = 0.6809 Keeping just the 7's is a lot more complicated. There are now 3 cards that will be filled in by using ...
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