Playing The Nuts and Ockham's Razor

You know I like to fantasize about poker hands. Actually, it helps me think about various situations that I have not specifically come across yet so when I do encounter them I can think lucidly about the situation when I am actually in it. In the following situation you are playing a $100-$200 NL cash game (I told you it was a fantasy). You can put yourself in the shoes of either player in this scenario and hopefully get something out of it.

You open raise from middle position to $700 after looking down at KK, folds around to bb who calls. $1,500 to the flop. Flop is AKK. Check-check to the turn, which brings a Q. Your opponent bets $1,000, you raise to $3,000, he calls. $7,500 to the river, which brings a blank, say a 5. Your opponent bets $8,000, you raise all-in (you have $16,300 total), your opponent calls. He flips over AA for AAAKK and of course you show the nuts and take the pot of $40,100.

Pre-flop action
Your opponent flat calls your raise with rockets. That works of course. He did this for a few reasons: i) He is disguising his hand, ii) He is already heads-up with you, so a re-raise here is not necessary, iii) A re-raise to say $2,500 and he risks you folding (sure, it's better to win a small pot than lose a big one of course) - he does not want you to fold, he wants to get maximum value out of his rockets, and iv) If he does raise to say $2,500, he "risks" you making a third raise, which at that point essentially commits his stack. Naturally he doesn't mind that at all, but seeing a flop allows him greater room to maneuver and may bring greater rewards than getting you off your hand pre-flop. If the small blind had called then it would make sense for the big blind to re-raise.

On the flop
It's difficult to argue against slow playing the stone cold nuts here. Certainly you're hoping for a juicy turn to stir your opponent to action.

On the turn
On the turn the board is now AKKQ. When your opponent comes out betting $1,000 into the $1,500 pot, he: i) Is trying to buy the pot right there [I would consider someone trying to buy the pot in this situation if they did not have at least an A or Q] since you checked behind him on the flop, ii) Has QQ, and would bet out since he wants to see if you have any of the hands that beat him such as KK, AA, AK or KQ, iii) Has a big ace, and thinks he could either win it there or may be in a chop situation [any two hands like AQ or worse (AJ, A-10, etc.) is a chop since the hand would be AAKKQ], or iv) Has AA. Why the bet then? Well, it's a value bet that may get your attention regardless of what you have. And if you do have a big hand, your opponent figures, like AK or QQ perhaps, then he may be able to induce a raise out of you figuring that he has disguised his hand pretty good up to this point. Also, if you don't at least call a bet on the turn with this board, your opponent thinks, then you may not call another bet on the river anyway.

So when you raise on the turn, your opponent ought to be putting you on AK, QQ or KK at that point. Why raise with the nuts when you know that only one card on the river is truly a scare card (the ace, which of course would be a sick quad over quad situation)? The same reason that your opponent bet out on the turn - you think to yourself if your opponent does have a big ace or AA then they would certainly at least call your raise, and if they didn't have much, they would fold and you wouldn't have got any more value out of them on the river anyway. From your opponent's perspective the chances you hold the following hands on the turn: a) AK -- (1/46 X 2/45) = 0.00097 or 0.097% or about 1 in 1,000; b) QQ -- (3/46 X 2/45) = 0.0029 or 0.29% or about 3 in 1,000; c) KK -- (2/46 X 1/45) = 0.00097 or about 1 in 1,000 [same as AK]. So it is three times more likely you have QQ than you do either AK or KK, and the only hand that your opponent cannot beat is KK.

As an aside, another option on the turn is to smooth call your opponent's bet. That would have made the pot $3,500 to the river. Say your opponent again bets out on the river to the tune of $4,000, you are raising big anyway. If you go all-in, at this point your opponent has some chance to get away from his aces full with $5,700 committed still sitting with $14,300 behind, "your money" left on the table (if your opponent is good enough to get away from aces full here). And if you raise to $12,000 for example, he can call and if he loses does have $6,300 left, which was again "your money" left on the table. Thus I believe the best thing to do on the turn is raise and you force an even bigger bet on the river which would commit your opponent, or you may induce a re-raise on the turn from your opponent right then and there.

On the river
Here is the thing about Ockham's razor, which paraphrased is generally accepted to translate to, "The simplest solution is the best, however implausible it may seem." On the river your opponent makes a slight overbet of the pot, perhaps trying to give the impression that he is buying the pot (assuming you don't have at least an ace), then you go all-in. At this level your opponent knows you don't have QQ (which would be afraid of KK, AA, AK or KQ), and thus you have either AK or KK. He is committed to calling another $8,300 (remember he has $12,000 in already) since he now is a 50% chance to win and as I demonstrated with the math, either hand is equally likely. Is that true? From the action and the math, either AK or KK are equally likely indeed. However, can the 14th century theorist help us out here? If you're your opponent, can you get away from AAAKK, knowing that the only hand that beats you is KKKK? It sure is possible if you think about it in this way: i) "The simplest solution is the best..." Would AK go all-in on the river knowing that AA beats them? (KK is not possible for your opponent to have if you do in fact have AK) Probably not in this spot. Would they (you) go all-in with AK for just a chop, if the opponent also has AK? Probably not. Thus they (you) must have KK. ii) "...however implausible it may seem." From a deduced math perspective (don't know the exact term, if there is one) the odds that you have either AK or KK are 1 in 1,000, your opponent thinks to himself, but the fact that you went over the top all-in on the river now makes that chance 100% (that you have either) and 0.5 not 0.001 for each hand - an increase of 500 times! It is 500 times more likely you do have KK now, consistent with point (i).

If you were your opponent, would you be able to fold AA in this spot?

This hand is an example of the nuts versus the second nuts. If you held KK would you play it this way for maximum value? If you held AA would you be able to get away from the hand on the river? If you were the player who held AA and you thought they were the nuts the whole time, should you have also checked on the turn? I hope this entry helps the reader to think about similar situations they may have been in and invite additional comments for this post.