July 21, 2005

The First Hand of a $10+1 SNG

Last night I was discussing a hand with Alex that he played in a $10 one table sit and go. He got dealt pocket QQ on the first deal and opened for $75 (blinds 10/15). One of the blinds re-raised the minimum, making it $135 to go. Alex decided to raise again, making the call and pushing $200 chips more. Each player in the SNG started with $800 in chips, so after the re-re-raise he had $465 left. The player apparently contemplated for a few moments before raising all-in. So with around $750 in the pot, Alex had to decide whether or not to call off his remaining $465.

Now, it is my understanding that while pot odds are certainly important in tournaments, when the decision is an all-in one they become less important. Other factors which become more significant are how much stack you have left if you fold, what you figure your chances are to recover post folding compared to what you figure your chances are of winning the pot and how winning that pot will affect your chances of winning the tournament. In this case it was the very first hand, so you want to make the correct decision (because you can't win it if you ain't in it). Nonetheless, I believe a little mathematical analysis can help a lot for understanding why calling was the right move.

In this case Alex had to assess his opponent's probable set of hands with which he would make this play. Because it was a low-limit SNG a percentage of this set included any two random cards (they're out there, just visit the GRAMPA site for proof). Provided Alex gives his opponent a modicum of credit for playing good poker we'll say that there are 4 possible hands that his opponent might have: AA, KK, AK, or JJ. Of course there's a small chance that the other player also has QQ, but it's a very small chance and doesn't significantly affect the math. So what are the chances his foe has AA or KK? Well, there's 220:1 against getting dealt any particular pocket pair, so we'll say that the odds are about 110:1 against his opponent having been dealt AA or KK. ***Note - this is not to say that the odds against his opponent having AA or KK on this particular hand are 110:1 against, just the pure odds of him being dealt them on this particular hand.*** The odds of his opponent being dealt AK are only 82:1, so there is a better chance that the opponent has AK than either AA or KK. Now, when you include the hands that you have dominated (JJ, smaller pocket pairs and random hands) then the math seems to indicate that you simply must call with the QQ in that spot. The pot is laying 1.6:1 in this spot whereas if the wager were even-money you should probably still call.

Incidentally, his opponent had KK and Alex busted out on the first hand. Just because the other player happened to have one of the two hands that dominated QQ doesn't mean the the call was "wrong" in that spot. In a large way, if you get dealt QQ and your opponent has KK, you're going broke and that's all there is to it, especially in a small buy-in SNG.

Another Note

We also discussed alternatives for how the hand could have been played pre-flop. Had Alex just called the minimum re-raise he could have at least gotten a look at the flop and had some extra info before making a decision (however, there is no way of knowing that the opponent would shove pre-flop following Alex's re-re-raise, and you don't want to let 'em in cheap!). Often just calling pre-flop with pocket pairs that race against AK and then making a big bet on the flop is a good way of playing the hand. In fact, pretty much any time you get all in with QQ against AK and the other guy hits the A on the turn you recognize that you may have been able to win the pot by closing the action pre-flop and pushing hard at a safe looking flop. Alex said that the flop on this hand came down rags anyway, so I believe that no matter how he played the hand he would have gone broke - except for by folding pre-flop, but we've been over that!