[MarkGritter]

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With 75432, this particular solution is betting about 1/3 of the time but check-raising the other 2/3 of time.

Now, you might argue that you exploit your opponents' tendencies better by betting always, but I think you will actually get paid off a lot by check-raising.

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Aren't you missing the times that the villain checks behind, which sadly is quite often?

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I dunno, are you counting all the times it goes bet/fold on the end and you don't get paid off anyway? [img]/images/graemlins/smile.gif[/img]

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I think those times are rare if the villain is pat (its hard to understand the OP, but I think thats what he was saying), he is usually checking behind with with more weak hands which he would not call a c/r for, yet call on the river with some of the hands which he would check behind with.
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OP says that his opponent drew one. I agree that 1:0 is a completely different situation than 1:1 and should be mostly bet.



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Can you explain your solver equation, perhaps that would help us find the middle ground.

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I don't have a simple explanation, I just have an (unpublished) result. When you put the best 26 1-card draws (7432-8763 plus 2345-2456) up against each other, a game-theoretic optimal strategy for the first player is results in the mix summarized above.

Let's see if we can come up with a silly simple example. Suppose there are 5 bets in the pot. Your opponent has 7432 and:

jams his 5's and 6's
bet-call or calls a bet with his 8's and 9's
bet-fold or calls a bet with his T
checks behind or calls a single bet with JQKA
checks behind or folds 2's and 3's
bluff-fold or folds 4's and 7's

How does check-raising 75432 compare with betting it?
Opponent card, Net value of KR (approx)
5, 0
6, 0
8, +1
9, +1
T, 0
J, -1
Q, -1
K, -1
A, -1
2, 0
3, 0
4, +1
7, +1

That would make it a dead heat between check-raising and betting out. If he calls more (say with deuces) then you are better off betting. If he bets more (any pair, or jacks) or bet/calls more (with a T) then you are better off check-raising.