Creating the Best Expectation

Most players evaluate a bet as equaling the bet’s face value. If they pay off a $60 bet, they believe that they lost $60. Of course, they really did, but great poker players quantify their bets in terms of their expectation. If you lost $60 when calling a player, you didn’t lose $60 in expectation unless your hand could beat only a bluff, and your opponent never bluffs! The call had equity in the scenarios in which your opponent could have been bluffing, assuming that he was capable of bluffing. Thinking in terms of expectation is important in analyzing the play of hands.

I was on the button in a $30-$60 limit hold’em game. A couple of players had limped in, and the player in the cutoff had raised. I looked down at the 9 8. I had commanding position, and there was high potential for a volume pot, since both blinds were the type of players who would see the flop loosely, so I tossed in $60.

The small blind called, and the big blind, a player who called loose but raised tight, three-bet to $90. Everyone called, so we saw the flop six-handed for $90 each.

The flop came K 7 6, bestowing upon me an open-end straight draw with a backdoor-flush draw on a rainbow board. Mr. Three-Bet led into the field, and was immediately raised by the upfront limper. The players between Mr. Upfront Limper and me folded.

I considered my options. I thought Mr. Upfront Limper held a legitimate hand, and that I had little chance of moving him off it. Also, Mr. Three-Bet was likely to have a quality holding, further reducing my chances of successfully bluffing. I could three-bet in an effort to take a free card on the turn, but that might cause the small blind and Mr. Three-Bet to fold hands with which they might otherwise call, thereby reducing the implied price on my draw. I thought flat-calling was my best play. I tossed in $60, the small blind folded, Mr. Three-Bet three-bet the pot once again, and Mr. Upfront Limper called. Now, inasmuch as circumstances had changed and I no longer had the negative situation of folding other players, I chose to attempt a free-card play, and I four-bet. They both called.

My dream card came on the turn, the 10, giving me the nut straight with a flush draw on top of it. To my surprise and delight, Mr. Three-Bet led out once again, and Mr. Upfront Limper raised him. I went into my “thinking huddle” and thought about what play would obtain the highest expectation.

What were my opponents’ hand ranges? Mr. Three-Bet had represented a strong starting hand, plus a king had come on the flop and he had continued to play his hand very strongly. I put his range on A-A, K-K, or A-K, although I felt that K-K was less likely, as he didn’t five-bet the flop. Mr. Upfront Limper was a good enough player to know all of this, so while I was unsure of his holding, I felt that by raising the turn, he presumably could beat A-K. That put Mr. Upfront Limper’s range on two pair or better. I felt that Mr. Three-Bet would fold one pair if I three-bet, and would reraise a double bet if he held K-K. Since he was drawing dead if he held one pair, I wanted him to call with one pair, and the bet(s) from him held more value than if I obtained a bet from a player who was drawing live.

Here’s the way that I felt the scenario could play out: If Mr. Three-Bet held one pair, I could get in four bets by getting three from Mr. Upfront Limper and one from Mr. Three-Bet, or I could get two from each of them by flat-calling. The added value from flat-calling was that I did not give away my hand and could play the river without my opponents suspecting the strength of my holding. I flat-called, enticing Mr. Three-Bet to overcall, also.

The river was the 7, pairing the board. Mr. Three-Bet checked and Mr. Upfront Limper fired a wager. I wasn’t too keen about my hand. The only plausible hand that I felt Mr. Upfront Limper could hold that I could beat was K-10. I tossed in $60, knowing my chances of winning were limited, but feeling I had the right price to call if he had K-10. Mr. Three-Bet overcalled behind me. Assuming that Mr. Three-Bet wouldn’t call two bets cold on the river, his overcall obtained the same value as if I had raised Mr. Upfront Limper with the best hand. But by not raising, I had not assumed any risk of being reraised by a superior holding, or risked any extra bets.

Mr. Upfront Limper showed 6-6, having flopped a set and rivered the full house. I slid my hand into the muck, and Mr. Three-Bet tossed in A-A faceup.

While I wasn’t happy about losing the pot, I knew that I had played my hand to its optimal potential. And I have enough experience to know that if I play each hand to create its best expectation, over time the chips will get pushed my way.

Roy Cooke played poker professionally for 16 years prior to becoming a successful Las Vegas real-estate broker/salesman in 1989. Should you wish to get any information about real-estate matters — including purchase, sale, or mortgage — his office number is (702) 396-6575, and his e-mail address is [email protected]. His website is www.roycooke.com. You also may find him on Facebook.