03-12-06 [poker] - 1

03-12-06 [poker]

(see 03-09-06). On trying to reduce the draws :

The board is B, you have a hand H1, your opponent has H2. You're trying to simulate all the draws from the deck {D} which has excluded the cards already on the board or in your hands. You can generate a hand rank which is R(B,H1). A draw card may or may not affect your hand ranks. The hand rank is a list of numbers, the first is the type of hand (no pair, one pair, etc.). The second is the rank of the card of the most important part of the hand (eg. the rank of the highest card in your flush, the rank of the paired card in your one pair, etc.), the next value is the second most important card.

For example, a house 88844 would have a rank {House,8,4}. Two pair JJ44A would have a rank {TwoPair,J,4,A}. One pair 44AQ2 has a rand {OnePair,4,A,Q,2}. Note that only "No Pair" actually has 5 significant ranks.

In some cases a draw card doesn't affect your ranks at all. If you draw card C, and R(B,H1) == R(B+C,H1) and R(B,H2) == R(B+C,H2) , then C was a total blank in terms of affecting your hands. However, you may still need to consider C because it may have been a scare card. We can approximate and ignore any changes to the hand rank beyond the first two. That is, for one pairs we consider cards that change the kicker, but not cards that change the second kicker.

We can define a "scare card" as a card which changes the hand rank of a likely holding, even though neither one of you may actually have that holding.

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