Monday, September 17, 2007

One more time

I was really bored and couldn't sleep on the flight back from Phoenix to Honolulu, so I ended up doing some lengthy poker math.

Here's what I wanted to find out: When you hold QQ in the big blind against a late position raiser and a small blind re-raiser in a 5/10 shorthanded game, is it better to call or push?

I addressed the first part of this question in a few previous posts, where I estimated the EV of calling with QQ and pushing any flop without an Ace or King. The number I came up with was $180.12, which is a high estimate because it doesn't consider the ~7:1 chance of my opponent flopping a set. But I think it's safe to say that making this play is well in positive figures.

So on the plane, I figured the EV of pushing with QQ in that same situation. The results were much worse: -$40.90.

Pushing with QQ preflop against two raisers is a donkey move. Call and push any undercard flop in this specific situation.

---

The Math:

(Chance that both LP and SB will fold * winnings) + (Chance that LP will fold and SB will call with QQ * winnings) + (Chance that LP will fold and SB will call and be ahead * losses) + (Chance of LP or SB calling when ahead but QQ sucking out * winnings) + (Chance of both LP and SB calling when ahead but QQ sucking out * winnings) + (Chance of both LP and SB calling when ahead and QQ losing * losses) + (Chance that SB will fold and LP will call when behind * winnings) + (Chance that SB will fold and LP will call with QQ * equity * winnings) + (Chance that SB will fold and LP will call when ahead * equity * losses) =

(.75 * $145) + (.016 * $17) + (.16175 * -$1,000) + (.03325 * $1,035) + (.0075 * .15 * $2,000) + (.0075 * .85 * -$1,000) + (.0315 * .15 * $1,110) + (.0315 * .04 * $55) + (.0315 * -$1,000 * .81) =

-$40.90

1 comment:

HighOnPoker said...

Next time you are bored on a plane, I suggest a magazine. Jebus! That is some math you got there!