Friday, April 14, 2006

All-in Math

Let's suppose that you're playing with a whack job who'll make huge pre-flop bets blind, and he's just made one to open the pot. The amount is 60% of your existing stack. You make the call w/KQo, since you've had a cold spell and you don't mind gambling against a random hand. Two other players call behind you, apparently also in the mood to gamble.

The flop comes AT8, so you've got an inside draw to a straight and you check praying for a free miracle. The player to your left, with a bigger stack, pushes his remaining stack in and has you covered, and the other two players fold (including the whack job). Is an inside straight (with a runner-runner flush draw) a clear fold to you?

If there is 240 percent of your stack in the pot, and with this players all-in, you can see the remaining two cards for a pot of 280 with an investment of 40. In other words, you're putting in about 14% of the existing pot to see the next two cards.

We can safely assume your opponent doesn't have trip aces, as he would have pushed. He may reasonably have two pair, trip tens or eights, but probably no worse.

Cardplayer gives odds of 16.57% to win for you against trip eights, and 19% to win against top two pair. Even though your odds are slim, if you've come this far, it is not a statistical mistake to throw your last chips into the pot.

Just be sure to leave cab fare off the table.