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How you do that without the flop?
Convergence must be bilateral, on each iteration, the preflop & the flop converge to a nash because both are inseparable (preflop you need the postflop utility, and the postflop utility depend to the preflop range)
I am using a rule based system and not trying to nash solve anything. If you can accurately determine what his hand range is based on his preflop stats then postflop becomes much easier imo. I am thinking that it is only possible to get something in the 65-70% area tops even with quite a bit of historical data on the villain.
Lets assume your facing a new villain and he is raising 80% of buttons HU. So you call the raise and the flop comes Qh8d4s. He c bets and you call and the turn comes a Kh and he leads again.
At this point he is still betting with 100% of his range but he can only be value betting AA, sets, two pair and Kx. Everything else is thin value or a bluff (which is a huge part of his range at this point). Any thin value hand you could potentially get him off of so they are not too much to worry about. So now you can remove all the under pairs including Qx from his range and keep in any gutters and open draws.
The river comes 2s and he leads again. So now you rerun equity leaving in all the busted draws and removing any other non value bettable hands in his range. At this point you have narrowed his range to a very small number of hands.
Sounds easy right? not so much. The key is preflop and getting his range correct. For a player who has polarized his range figuring this out is extremely difficult. Without seeing a bunch of showdowns you will never really know what hands he may be 3 or 4 betting with. Every player is different.
The only solution I have found is to 3 and 4 bet quite often to narrow his range down preflop as much as possible. Many players will not 4 bet or shove with garbage. Maybe somebody like isildur would however...Statistics: Posted by shalako — Wed Jul 10, 2013 6:22 pm
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