sexta-feira, 20 de julho de 2012

Two to one in the big blind - easy decision with PPP

You hold T2o in the big blind with 3.2 BB left after posting. Antes are already in play, so the starting pot for this 8-man table is 2.3 BB. You came to the table ten hands ago, right after being crippled on your last table when a pair of Eights became a set against your Jacks.

You were kind of dizzy from that, but even so managed to observe your new opponents, and one of them, in first position for the current hand, counts his chips to play for the first time since you arrived. He happens to have only 15 BB and be the second shortest stack. He cuts 3 BB, hesitates, and finally shoves all-in. The other six players fold, and it´s your turn to decide what to do with your T2o. Call or fold?

"Guys, you don't mind if I check my phone mid-hand, right? Mom's in the hospital."

You may have already heard that generally 2-to-1 pot odds is hard to turn down preflop. I consider this to be good advice, but there are exceptions where you need greater pot odds to call correctly, and in these cases if you call getting only 2 to 1, then there´s no other way to put it - you´ve made a mistake.

No, you didn´t play like an idiot, you´re not the worst player ever, and your mistake is not obvious to everyone else. But still, technically, using Sklansky´s definition, you´ve made a mistake. That is, you´ve made a play you wouldn´t have made if you could see the hole cards and had time to do all the math. You have basically reduced your expectation relative to your other choice of play. You know that thing you're always trying to get your opponents to do?Yeah, that's the one.

All right. So first, we see that the starting pot was 2.3 BB and the villain shoved for 15 BB but, since you´re shorter, his effective push from your point of view is just 4.2 BB (exactly enough to put you all-in). Out of those, 1 BB is already paid in the form of posting the big blind, and you need to call an extra 3.2 BB in order to have a chance to win the current effective pot of 6.5 BB. Those are pot odds of 2.03 to 1. The 2-to-1 rule is generally useful because, getting 2 to 1, you only need to win 33% of the time, and most hands will beat most ranges more frequently than that. So it´s a good rule to remember, but it doesn´t give you mathematical certainty for all situations.

By typing T2o in PPP (available here)  and looking at the "with antes" screen, we must select one of 6 ranges to describe our opponent´s hand. If he were on the button, or very active, or shorter, then we could estimate his range to be "aggressive" or "psycho," but with the information we have, my guess is his range is either precisely our "ultratight" option, or pretty close. So curb your anger at having lost almost all your chips and the urge to just double up or go home early to watch the game, because you have a chance to win money right now. It may seem like your tournament is already over and that the critical hand happened a half-hour ago, but the truth is, right now, you have two options with very different expectations. This, right here, is the decisive moment of your tournament - not that the previous one wasn´t too, but you can only make decisions from the present forward, so stay focused.

As we´ve seen, the best guess of the villain´s range is ultratight, and looking at the PPP results screen we see that, against that range, your T2o needs at least 4.08 to 1 pot odds!! That´s because you will only beat this range once in 5.08 times, or about 19.7% of the time (hence much worse than those 33%). Out of the resulting 9.7 BB pot after you call, you will walk out with only 1.91 BB on average, whereas you retain 3.2 BB by folding. In fact, with PPP in hand, folding is so obviously superior that calling only becomes profitable if your opponent is playing more than half of all hold´em hands (against the psycho range you can pay as much as 3.7 BB), which is completely absurd here.

Note that, in this kind of example played during a tournament, a mistake made even with only 3.2 BB can be very costly. If you were playing a cash game with a big blind of one dollar, then you would really only lose $1.29 by calling. It´s not wise to throw money away, but the truth is that money would probably not be missed. In a tournament, however, everything depends on structure. Even in a typical 22-dollar buy-in tournament on PokerStars with thousands of players, if you´re already in the money with your lowly 3.2 BB, your stack represents an average expected payout in cash - which, depending on the stage and size of the tourney, may be 30, 50, 100, 500, a thousand dollars. In the extreme case of being at a final table, your little 1.29 BB mistake may cost you a very relevant chunk of your cash expectation. In a WSOP event, that could easily cost you thousands of dollars. So yeah, improving your supershort stack play is a legitimate goal, and I have yet to find a better tool for that than Perfect Preflop Play.


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