Re: Update #1
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Then player B constructs a strategy, B1, that tries to beat A1. B doesn't know which cards A has in any given confrontation, but he knows how A1 will set the possible opposing hands.
How does this work? Does player B oterate all the possible settings for Player A's hands, and then index an arbitrary "ballance" for the setting?
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B examines each of his hands one by one. He looks at all possible arrangements of his hand, and how they do against the fixed layouts described in A1. He chooses the arrangement which has the highest expected value against that hand distribution. (For example, if A1 has very strong middles, B might choose to abandon the middle entirely.)
Here's an example from the current run: B's hand is 2s3c3d5h6h6s7c7s8d9cJcJhAs. The hands and arrangements in A's latest strategy that don't contain one of these cards are:
9h9sKcKhKs 2d3h4h6d7h ThQdAh
9d9hAcAdAh 2d4s5d6c9s TsJsKh
5c5dTcThTs 2h3s4c6c8h KdKsAc
8h9dTdJsQd 2d4d5d8sTs 4hAdAh
TdThQcQhQs 2h3h4c5c9d 3sKhKs
4d6dQdKdAd 2c4h5s6c7h 9sTsJs
5c5d5s9d9s 2c3h4c6d8h ThKhAc
QcQdKcKdKs 2d4d5dJsAc 9d9h9s
2c4c6cTcKc 2d3h4s5d8c 3sThKd
6cJdJsKcKh 2h4d5d6d9s QdAcAh
TcThQdQhQs 2c3s5d6c9d 6d9hKd
TcJdQcKhAc 2d3h4d7h8h 9dThTs
4d6dJdQdAd 2h5c6c8s9h 4h4sTh
TcThTsKcKd 3s5d8hJdQh 4d4h4s
4dTcTdThTs 2c2d4h8h9s QdQhAc
4c4d4sTdTh 2d3s8c9dQh 9sAcAh
4dJdQhQsKh 2d3s4s5c9h 2h8c8s
8hTsJdKcKd 2c3h5c6d7d QcQhAc
7dJdQdKdAd 3h5c8h9hTs 5sKcKh
etc. (113 possible hands out of 10000) All are treated as equally likely.
Here are some of B's possibilities, with their EV (in points) against these 113 hands listed.
-1.51327 3c3d6s7c7s 2s5h6h8d9c JcJhAs
-1.48673 3c7c9cJcJh 2s3d5h7s8d 6h6sAs
-1.38053 6h6s7c7sAs 2s3c5h8d9c 3dJcJh
-1.35398 3c6h6s7c7s 2s3d5h8d9c JcJhAs
-1.32743 3c6h9cJcJh 2s3d5h6s8d 7c7sAs
So, B picks 367JJ 24568 77A as his arrangement. (However, in the previous iteration he picked 36677 23489 JJA.)
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(Because A and B are dealt from the same deck, not all the settings are revelant to a particular hand--- in fact, given a specific A hand, only 1% of the B hands are possible, which gives us about 10 possible opponents hands on average.)
By the "same" deck, do you mean that both hands are coming from a 52-card deck, or is A's from a 52-card deck and B's from a 39-card deck?
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The sets A and B are coming from a 52-card deck. I generated them separately. So, when A is considering his options, only a fraction of B's hands are immediately relevant, and similarly for B. The rest of the hands have at least one card in common and so could not occur.
It would be possible to generate them at the same time to ensure that every A hand had at least one relevant B hand, but this is not necessary in practice.
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