probability question in multiway pot
One of the few interesting hands I played at in Vegas was a 2-5 NL hand at Caesar's Palace. I only bought in for $500 because I was cash busto at the time, pretty sure everyone else had me covered or close to it.
Reads: Most of the people at the table are realllly bad calling stations, HJ and BB are the two worst. CO is a young kid, obvious online player. He said today is his 21st birthday and he plays 1-2 NL online. He's nothing special, but he doesn't do anything stupid. He knows that these guys can't play and that he should raise big preflop with his strong hands and try to see flops with some marginal suited hands that aren't good enough to raise.
UTG limps, HJ limps, CO limps, I raise to $40 on the button with A:heart: K:heart: (should have raised to $50 but whatever) blinds call, all three limpers call. Flop is 9:spade: Q:spade: A:club: and it's checked to the CO who donks $100 into me. I thought about folding because his range is monsters and big draws but I realized that based on preflop he never has AQ, AA, QQ, or 99, so the only hand I'm losing to is A9s. Furthermore there's only one suit left for him to have (diamonds) so he almost always has KJ, KT, JT, T8, or Ax of spades. With so much money in the pot already, I obviously have to gamble against that range, so I did.
The interesting part is that this gamble can be -EV if one of the clueless guys is waiting to snap me off with a monster. Is there a quick way to look at a flop and figure out what percentage of the time a random limp-caller nailed that flop? Obviously it depends on the flop; a board like 678 monotone it'd be higher than a board like K72 rainbow. I'm sure it won't happen often enough for me to want to fold the AK in this particular hand but it would be a useful thing to know.
