Monday, September 19, 2011

Math + Psychology = Poker

A couple of posts back I talked about playing medium and small pocket pairs. I said that if you missed the flop with these hands you should not continue on: "no set, not bet." I am now going to contradict myself and say that sometimes you can profitably continue playing such a hand, but your success will depend largely on the read of your opponent.

Once, playing $1-$2 NLHE, I was dealt pocket fours in early position. I believe I had established a tight table image, so I put in a raise that I thought might win the pot right there $15. I got called by the one player I feared the most, Mr. Cool (that's what I called him in my head anyway) a fellow who always seemed to win every pot he played. Everyone else folded. The pot was $33 and the flop was something like Kc 7h 5h. I checked and he fired out $30 and I quickly re-raised to $100. He thought long and hard before folding. "Nice bet," he said as the dealer push the pot towards me. I hope I didn't look too relieved.

So, on the face of it this look like a pretty dumb bluff on my part, but I had a good reasons for playing the hand the way I did. Some reasons were psychological, some math based. Whenever you are heads up to see the flop, chances are that the flop will not improve your hand. The good news is that the flop probably won't help your opponent either. I wasn't just hoping Mr. Cool didn't have a king, I knew it was mathematically unlikely.

When he called my pre-flop raise, I put him on a pretty narrow range AA, KK, QQ, JJ, 10 10, 99, AK, AQ, AJ. Had the flop contained an ace instead of the king, I would have not put another penny into the pot. I figured it was a 50-50 chance he had an ace-something. Actually, if my read on his range was correct, then there was a greater than 50% chance he had the ace. Remember my last post? There are 6 different combinations that make each pocket pair - so there are 6 combinations that make AA. There are 16 combinations that make AK, so 48 different combinations that make AK, AQ or AJ. In total that is 54 possible combinations for the range I put him on that give him an ace and only 30 that don't (6 each for KK, QQ, JJ, 10 10 and 99) so if an ace hits the flop I have to think it's likely I'm behind AND there is little chance I can push him off the pot. Of course at the time I couldn't do these calculations in my head, but the point of my writing this now (and you reading this now) is to give us a feel for the math so we can make better guesses when the time comes.

So I feel better about continuing with a king-high flop. If I could have done the math at the table, I would have found there were only 22 combinations on his range that included a king (16 for AK and 6 for KK) plus 6 for AA (which, obviously, he would not fold) out of a total 84 combinations. So if I strongly represent a king, it is likely I'll take down the pot. Even if I'm not ahead, I can still push him off hands like QQ, JJ and 10 10 if he is convinced I have a king.

I thought a check-raise would be more effective than a straight continuation bet for purely psychological reasons. A continuation bet might be seen as an attempt to buy the pot, whereas a check raise is much less expected. It has the big benefit of rewarding me with a $63 pot instead of a $33 pot, and should win against everything but AA, AK, KK or one of those "invisible" sets.

It worked for me that time, partially because my tight image had Mr.Cool convinced I had lucked out on the flop and hit the king. But try it too often and sooner or later your opponent will come back at you. So be careful

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