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Old 09-09-2007, 01:10 PM
TNixon TNixon is offline
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Join Date: Apr 2007
Posts: 616
Default Re: Game Theory Resolution

In this game, you are going to be raising with a certain percentage of numbers that are lower than what the BB will call with.

You're raising everything higher than .625, and .1875 lower than .625, so 1/3 of your hands are lower than .625.

But it *does not matter* where that 1/3 comes from. It could be 0-.1875, it could be .4375-.625, it could be 0-.09375 and .531-.625. It simply does not matter, because anytime you're raising with a number lower than .625, you only win if your opponent folds. The solutions are all identical in this game.

And since you're still playing the same number of hands, (and since he can safely assumes you're not being stupid, playing 0-.5625 and folding .5625+) if the big blind calls with anything lower than .625, then he is no longer playing optimally.

But as I mentioned originally, at that point, this game becomes more about third-level thinking than it is about the numbers. If you can get the BB to play sub-optimally, then you can exploit his adjustments. But playing 0-.1875 instead of .4375-.625 should not cause him to adjust, unless believes you're playing more than 43% of the time. The problem here is that you have to believe he's capable of adjusting to your play, and willing to, because if he simply calls .625 no matter what you do, he will end up ahead in the long run, since the SB has a very clear disadvantage in this game.

If we equate these numbers to percentage hand ranges, this is all very different from poker, where there are certain "bluffing hands" that are going to be better than others, because they have a better chance to win against the top 62.5%, for example, and do better when you do get called. In poker, 56 suited has a better chance to beat AA than just about every other 2 cards. But in this game, 44 loses to 100 every single time.
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