## 3-card Hand Rankings

For the record, I’ve done the math (correctly–I think) for the various kinds of three card hands, and have come up with the result that a straight flush definitely beats three of a kind in three card poker.

As with any kind of poker, the harder it is to make a hand, the more the hand is worth. It turns out there are 48 ways to make a straight flush (12 possible straights, from {A,2,3} through {K,Q,A} in each of 4 suits equals 48 possible ways) and 52 possible ways to make three of a kind (for any given rank, there are 4 ways to make three of a kind–“without spades”, “without hearts”, “without diamonds”, and “without clubs”– and there are 13 ranks, so 52 possible ways).

Since it’s harder to make a straight flush, the straight flush wins.

For completeness sake, here’s what I worked out for the number of ways to make each kind of hand in 3-card:

 # Hand 48 Straight flush 52 Three of a kind 720 Straight 1096 Flush 3744 Pair 16440 Ace High or Less

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