Chances of Winning Versus Improving

"You sure did that ass-backwards," I said to myself.

I was in the small blind with the 6 5, two players limped in, and a local doctor raised from late position. Playing $30-$60 limit hold'em, it was an easy call, as I was one-third in already and had three opponents, four if the big blind came. The big blind folded, and the early-position limper, a young player, reraised. I had seen him make this same play from early position previously in the session. The way that hand had played, I read him for having a big pair, even though it hadn't been shown down. The middle-position limper called, and the doc made it four bets. I called the additional two bets, and it was capped by Mr. Young Player. We all called, ready to take the flop off four-handed for $150 each.

I grimaced inside; this was not the situation I'd envisioned getting myself into when I made the first call - putting in five bets four-handed with low suited connectors. I had a volume hand, and volume hands inherently tend to do better with cheap entry prices, and the more opponents there are, the better. I didn't think I made a mistake by calling preflop; I just encountered an unlikely bad scenario. That said, in poker, as in life, you have to accept the current situation and play on.

The flop came down J 6 4, giving me second pair, a three-straight, and a backdoor-flush draw. I was virtually certain that it wasn't the best hand. But, it did have potential. I checked, Mr. Young Player fired, the middle-position limper folded, and Mr. Doctor raised! What should I do? I didn't like my position, being first to act and in between two players who were looking to gamble and likely had big mitts. I analyzed my situation.

I thought I was between two overpairs, likely A-A and K-K; Q-Q equated to the same. There was some chance that one of them had J-J, but I felt it very unlikely that Mr. Doctor would four-bet or that Mr. Young Player would cap it with only J-J. That being the case, I very possibly might get trapped between two raisers, making the current price [pot odds] of 720-60 inaccurate. This could get capped on the flop. In order to accurately assess my price, I needed to include the likelihood that I would get raised in the equation.

Did my hand merit a call? I was about a 3-1 dog to beat an overpair. Would the pot lay me more than three times the amount I would call if I won? Even if it was capped on the flop and bet on the turn, it would cost me only $210 to draw. Would I win more than $630 if I hit? There currently was $720 in the pot. It was an easy, though potentially quite expensive, call. I tossed $60 forward, hoping it didn't get raised, thereby giving me a better price. But my hopes were soon shattered. It came back to me double-raised. I tossed another $60 in, then another $30 when it was capped - my worst-case scenario on the flop.

What made this call easy was that my opponents' hands were precisely defined, enabling me to exactly measure my chances of winning. Many players define their odds by their chances of improving versus the size of the pot. That's right as far as it goes, but it's only part of the equation. The accurate equation to compute your equity is your chances of winning versus the size of the pot. Since both are indubitably not quantifiable with cards to come, you must make your best estimate. Estimating your chances of winning involves accurately assessing the range of hands that your opponent(s) may hold. Once you put together a range, you need to determine the likelihood of each of those holdings and how your hand does against each of them, and blend the equation.

Accurately estimating the pot size is a function of reading hands and accurately assessing how your opponents will play their holdings. Once again, determine their range, the likelihood of each holding, and how they will play each holding, and blend the elements to obtain a result. Being accurate with any consistency involves great "feel" for both your opponents and the game. At best, it is an inexact science, but putting forth the effort to make these judgments will improve your reading ability and, as you improve, your heat-of-the-battle decisions.

The J hit on the turn, crushing my hand, since I now needed a 6 and only a 6 to beat an overpair. My wins [outs] were down to two! I checked, Mr. Young Player bet, and the doc called. There was $1,200 in the pot and it was $60 to call, 20-1 pot odds. I was 44-2, or 22-1, to catch a 6. If I could get two more bets in after I caught, the bet would be exactly neutral, assuming that I would win. In terms of edge, it almost didn't matter what I did. Thinking I was taking slightly the worst of the bet if there was a chance, albeit very small, that I could make my hand and still not win, I tossed my hand into the muck!

Bang! The 6 rolled off. I would have made a full house! Mr. Young Player bet with K-K. The doc called, and won the pot with A-A.

This hand speaks to adjusting to your opponents' holdings when analyzing your price. If my opponents' holdings weren't so well-defined and included sets, I would have had to extend my odds dramatically for the times that I was practically drawing dead, and the flop call wouldn't have been correct. Yeah, I wish I had called the turn bet, as the chips would have been in front of me instead of Mr. Doctor stacking them. But I didn't beat myself up over not calling. I judge myself by the accuracy of my decisions, not by where the chips landed, knowing that over time, that is what matters.


Longtime poker pro and author Roy Cooke's Card Player column has appeared since 1992. A successful Las Vegas real estate broker since 1990, his website is www.roycooke.com. Should you wish to inquire regarding real-estate matters - including purchase, sale, or mortgage - his phone number is (702) 396-6575. Roy's longtime collaborator John Bond's website is www.johnbondwriting.com. Find John and Roy on Facebook.