[grizy]

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I'm pretty sure I have a proof that no mixed strategy is better than a pure strategy of betting when you have the straight and checking when you have no pair. However this is based on certain "standard" game theory assumptions: that he calls you a predetermined amount of the time, that he is rational and that he assumes you are rational.

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The assumption that's broken in Pete's case and my simple game is that your opponent does not have a predetermined mixed strategy; his strategy (his probabilities) are some function of yours (aka he is observant and will adjust). Once your opponent's actions are some function of yours (aka you're the superior player that dictatesthe flow of the game) it becomes possible for you to play a "maximally" exploitative game as long as you know how your opponent will change his strategy. Pete's example is especially poignant because your opponent is giving up a major main pot so if he believes there is any chance at all you're betting without the goods, he would call. However, if you never bet without the straight, after some time, he will never call you, despite overwhelming pot odds. (this is actually a very very relevant concept in limit omaha I imagine)