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Know the Price!

Learn the odds of the game, and how to compute hand combinations

by Roy Cooke |  Published: Aug 15, 2007

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All great poker players have "feel," an intuitive sense derived from associating past experiences with the current one and logically associating the reasoning between the two events. Feel is a function of experience; the more you've played, the better your feel should be.

That said, many poker players think they are better at things than they really are, and possess less feel than they think they do! Using your analytical skills between hands to review the previous hand goes a long way in helping you devolop an accurate feel. And the better your grasp of the facts affecting your current situation, the better your results from feel-based decisions will be.

A friend and local pro who beats the game sometimes wonders why he is not performing at the level he sees other pros perform. He brought up a poker situation to me, and it demonstrated why his game is not at a higher level.

Playing $30-$60 limit hold'em, my friend had previously put a couple of beats on a player who was now on "full tilt" (the emotion, not the website). Mr. Tilt limped in, and the pro, looking to stomp on the guy while he was weak, raised from the button with A-10 offsuit. Ms. Predictable - a woman who never made deceptive plays and was an incredibly easy read - three-bet the pro out of the big blind. They took the flop off threehanded for three bets.

The flop came down 10 5 3, giving the pro top pair, nut kicker. Ms. Predictable led into the pot, folding Mr. Tilt; the pro raised and Ms. Predictable three-bet. The pro called, knowing he was beat, but at the $30 price in a $440 pot, Mr. Pro peeled, looking to catch an ace or a 10.

The turn was the 8, Ms. Predictable bet, and the pro called. On the river, the K came. Ms. Predictable checked and Mr. Pro checked behind her. She showed down Q-Q and Mr. Pro mucked his hand. Afterward, discussing the call on the turn, he stated, "I knew she held an overpair, but I thought I was getting the right price to outdraw her."

"What was the price?" I asked, assuming I would get an exact response.

"I dunno," he responded. "It seemed like there was enough money in the pot to draw." He was making decisions based on feel. Now, feel can be fine, but you shouldn't rely on feel alone when there is additional information readily available if you just take the time to access it! Not only didn't he know the price, as he hadn't even bothered trying to figure it out, he didn't even know his chances of improving.

I know lots of winning players who don't do math in their heads at the table. I myself don't bother to figure it out to the decimal point, but instead use rough approximations for quick calculations. I know some math whizzes who always know the price to the penny.

Let's assume that Mr. Pro is right and he indubitably knew that Ms. Predictable had an overpair - jacks, queens, kings, or aces. Mr. Pro had five unseen cards to make aces up or trip tens, and 46 total unseen cards (52 minus the flop, the turn card, and Mr. Pro's two holecards). Mr. Pro was 41-5 to make aces up or trips, just over 8-1 against. So, if Mr. Pro averaged winning $500 every time he improved, he would be correct in calling a $60 bet on the turn, assuming there was no possibility of a raise.

But would Mr. Pro win every time he made aces up or better? What if Ms. Predictable had A-A? Then, Mr. Pro would have only a 10 to win, reducing his outs from five to two. Assuming that Predictable had an overpair, she would be a 6-1 dog to have aces - enough of a chance to affect the equation. And there is one combination of 10-10 out there that she may have, in which case Mr. Pro is getting his money in when close to dead.

How do we know that she is a 6-1 dog to hold aces? We mathematically define the combinations of holdings and compare them to each other. There are six combinations each of pairs of jacks, queens, and kings, and only three combinations of pairs of aces, because Mr. Pro held one. Compare the total and there were 18 combinations in which Mr. Pro was drawing to five outs and three combinations in which he had two outs. Note that we are excluding combinations in which Ms. Predictable might have two overcards and Mr. Pro is leading, because when she three-bets the flop, he believes with a high degree of certainty that he is beat and must improve to win.

I'm not fast enough to do the exact math in my head at the table as far as defining the precise odds, but conceptually I do understand that I need to extend my odds to allow for the fact that I may improve my hand and still lose. In my mind, I approximate the extension of odds required, which is not perfect, by any means, but it's close enough to never put me in real bad shape. In this case, I'd require closer to 10-1 from the pot to make the call.

Mr. Pro made a slightly bad call, but nothing that is going to destroy his bankroll. But the fact that he doesn't understand the equation or, for that matter, how to compute it will affect his bankroll over time.

Keep these numbers in mind for hand-reading, and use them when defining your opponents' hands and reckoning your price. There are six possible combinations of any pair; for example: J J, J J, J J, J J, J J, J J♣. If any one of them is accounted for in your hand or on the board, the number of possible combinations drops to three; for example, if you hold the J: J J, J J, J J. If two are accounted for, there is one possible combination. There are 16 possible combinations of two unpaired cards, including the suited ones; for example, A-K or J-10. If one is accounted for - for example, you hold a king and are analyzing the possibility of your opponent holding A-K - the number of possible combinations drops to 12.

Learn the odds of the game, and learn how to compute hand combinations so that you can roughly figure out your opponents' chances of holding given hands. Your feel will greatly improve, as will your bankroll.

Roy Cooke has played more than 60,000 hours of pro poker and has been part of the I-poker industry since its beginnings. His longtime collaborator, John Bond, is a freelance writer in South Florida. Their latest book is The Home Poker Handbook. Please visit his website at www.roycooke.com.