an objective look at the hand
First of all, I did not fold, though I thought about it.
Let's say that the only hands he could have are AA, A2, and 22. He would only play AA this way 10% of the time preflop, but A2 and 22 he would always call with a 3rd person in.
By the river there are 6 ways he could have A2, 3 ways he could have AA, and 1 way he could have 22.
I think this guy would 3bet my river raise with A2 50% of the time, and every time with AA and 22.
{Note I didn't really error check this but I think it's right}
AA: 10% * 3 * 100% = 0.3
A2: 100% * 6 * 50% = 3.0
22: 100% * 1 * 100% = 1.0
I have the best hand 3/4.3 = 70% of the time so I should 4-bet.
Now he 5-bets. How often does he need to do this with A2 for me to call? It turns out the answer is 1.1% of the time:
AA: 10% * 3 * 100% = 0.3
A2: 100% * 6 * 1.1% = 0.066
22: 100% * 1 * 100% = 1.0
0.066/1.366 = 4.8% chance of winning.
So a fold would have been pretty terrible.
He had 22.
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