12-30-05 [poker]Last night at the live game it was the battle for "Roadhouse player of the year". I was slightly ahead of Dustin going in, so he had to get more points than me by placing better. About half way through the game, I had the big stack and Dustin was on a desperately short stack, and it looked like I was a lock to win. Well, it didn't happen. I made one mistake pushing the A5 late. I (correctly, I think) thought that A5 was well ahead of Dustin's range there, but that still doesn't make it right to push since his calling range has me beat and I have no need to risk my stack like that late in the tournament. I went out in 3rd place and Dustin got 2nd, just enough to edge me by 1 point, 56 to 55. Congrats Dustin, you lucky bastard!
Let's check it out. Blinds were 1000/2000. Dustin raised to 6000. Jim folded the SB. I was in the BB with A5. We all had nearly identical stacks, about 24k. The payout was $40 for second and $100 for first. Before the hand started each of our EV was about $46, but I'd lost a lot from being in the BB already. If I just folded my EV would be $43. If I push, I'll guess he folds about 50% of the time (worse aces, king-highs). In that case my EV goes to almost $57. If he calls I'm probably dominated either by a pair or higher ace. In that case I'm about 30% to win. If I win my EV goes to almost $81. So, what's the EV of a push?
0.5 * 57 + 0.5 * ( 0.3 * 81 ) = $40.6
Compare to $43 for just folding, clearly folding is correct, though pushing isn't horrible.