[TTChamp]

Warning:long post that might make your brain hurt.

Let me first say that I have a conceptual error that is leading me to a paradox. Help me find my way out! This post is written form the point of view of limit HE, but applies in NL or other games as well.

The statemet "over the long haul, you make money in poker when your opponents make mistakes" makes perfect sense to me. A mistake in this context is not refering to table selection or BR management (though that is also true), but instead is refering to putting money into the pot when they don't have the right odds to do so. That may be an imprecise definintion, but there can be no arguing with the mathematical basis of this statement.

So say you are in the BB with Q9. The CO raises with AJ and you call. The flop comes 952r. It is fair to say that at this point you are in good shape against your opponets range. In other words, over many hands with this scenario, you will profit from the money going into the pot on the flop. The specific example is not important, if you don't like it just choose some other scenario where we are ahead of the opponets range on the flop.

So we now have 2 choices: we can donk the flop or check. Sometimes he will check the flop and other times he will raise our donk, but lets zero in on two specific (and probably the most likely) lines:we c/r and he calls and we donk and he calls.

Say we donk; he is making a mistake by calling because he has pot odds of 4:1, but is only about 6:1 to hit his pair. Again, the details of the scenario are not important, just the fact that he is not getting the right odds to call. So when he calls our donk, he is making a mistake therefore we profit.

Now when we check and he bets, his bet is +EV against the range of hands that we have when we call a pf raise in the BB. In otherwords, his flop bet in response to our check is profotable over the course of many hands (because we frequently fold). Again, you could argue that this particular board is actually profitable to us if we bluff enough. If you want to make that arguement, just think up a different board where against our range his flop bet is profitable. The point is that given the information that the villian has, his flop bet is not a "mistake".

When he bets we c/r him and he calls. Has he made a mistake when he calls? He is getting 7:1 to call and he is about 6:1 to hit his pair. So he has not made a mistake.

So in conclusion his when we donk and he calls, he made a mistake. But when we c/r him, niether his bet or his call is a mistake.

Now for the paradox: when we c/r him, he has put 2 bets into the pot when he is behind. When we donk him he has but 1 bet into the pot when behind.

So when he plays "mistake free" poker he loses more than when he makes a mistake! This seems to contradict the idea that we make money from our opponents mistakes!

HELP!!!!