quinta-feira, 19 de julho de 2012

How to recover the cost of PPP in one hand

Perfect Preflop Play is going to be used more frequently by MTT and SNG players, who are faced all the time with situations where they must decide whether they call, say, an 8 BB all-in bet with K2o in the big blind. In this type of situation the app is incredibly useful, as it immediately tells you the number of big blinds you can call against each type of opponent. Effectively, in these cases PPP counts the pot for you, sparing you the work.

But the column showing the minimum pot odds necessary can be used to show you the correct decisions in raising war situations, even though in these cases it is you who must count the pot. The clearest way to show you how PPP may earn you more than 8 dollars in a single hand is through such a war during a cash game hand.

You hold a pair of Deuces in a game played with no antes, and you have $300 on the button. Both you and the big blind are pretty aggressive players. You´ve had a good session so far, and you feel confident to run another big play, thinking your opponents may expect you to play cautiously to conserve your $200 profit in this $0.50-$1 game. You bet $3, the small blind folds, but the big blind decides he won´t let you bully him and re-raises to a total 9 BB. He started the hand with 72 BB after posting, so the effective stacks for this hand are 73 BB. The re-raise doesn´t necessarily mean much, because you have seen him do it several times, and you even recall him having 76s once. You believe you have fold equity if you raise again, and that´s what you do, bringing the total bet to 23 BB. The pot is now 32.5 BB, and the villain escalates the war by moving all-in. What to do?

First of all, let´s see what we´re playing for. To call your 4-bet, the villain would have had to call 14 BB, which would bring the pot to 46.5 BB. What he did was, beyond calling, to raise his last 50 BB on top of your bet. 50 BB is what you must call if you want to have a chance to win the pot that is currently 96.5 BB. That spells pot odds of 1.93 to 1.

Second, let´s note that this is the first time you see your oponente 5-bet preflop, so he does not seem to be a complete maniac, the kind that would do this with 73o only because he believes he may catch you on a bluff, with complete disregard for the mathematical factors that would make that play horrible. The “all hands” range is definitely out and, frankly, so is the “psycho” one (64% of hands, including crap like T2s). It seems very safe to say our opponent is playing less than 50% of all poker hands – agreed?

Your intuition tells you his range is probably around the “semiloose” – in fact, the very character of this range seems to describe your foe: definitely active for the situation, challenging what he perceives as an active player, but not completely inconsequent. However, you think it´s possible this may be just an impression. Maybe, despite being capable of 3-betting light, he is much more cautious facing a 4-bet. You are in doubt, thinking maybe you´re overestimating the villain´s aggressiveness. What now?

My advice for this type of case is: if you think you have a reasonable idea what your adversary´s range is, but you´re also afraid you may be wrong because you haven´t seen them in many similar spots, then work with the range that´s immediately more narrow. If calling is profitable even against the more narrow range, then chances are you should call.

And that is exactly the case here. Getting 1.93 to 1, the call against the “semiloose” range is obviously very good, because you need no more than 1.31 to 1. But even versus the “tight” range you need no more than 1.5 to 1. Everything points to the call being correct. You call, bringing the pot to $146.50, and he shows you KQo.
Turns out you were necessarily right, for it´s impossible for the villain to have been playing the “ultratight” range (which does not contain the class-B hand that is KQo) or tighter. The most narrow range he could have been playing is the “tight” range or similar, and it´s even possible your guess of “semiloose” was spot on – although PPP gave you the confidence of knowing that your hand was enough even against the “tight” range.

So let´s do some conservative math to find out how much you gained by calling the last bet instead of folding your lowly pair:
Deuces have 40.1% equity against the “tight” range. This means that, out of the final pot of $146.50, you will walk away with an average $58.75, which, added to the $227 you had behind after calling the last bet, result in an expectation of ending the hand with a $285.75 stack. On the other hand, we already know that your expectation (or rather, your certainty) as you fold your hand after the 5-bet is to remain with $277. The call that PPP convinced you to make with 22 versus the “tight” range is worth $8.75 more than folding.
And there it is – PPP is paid for.


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