Add up your Equity

Poker calculations generally aren’t simple logical equations. Multiple concepts and alternatives often apply to a given situation. As a player, you need to understand the concepts of equity and accurately blend the equity of all the possible scenarios and quantify a best answer; mostly it’s just an estimated guess. This “best answer” includes your “best guess estimate” of how the hand will play on future streets. Often, the inclusion or exclusion of a given concept or possible scenario can change a play from negative equity to positive or vice versa.

Two off the button in the $20-$40 limit hold’em game at Bellagio I peered down at the A 7 and open-raised, folding the field to Joey in the BB, who called. Joey’s a highly-aggressive Canadian tourist with ample poker experience who had been there all night.

The dealer flopped the 9 6 5 and Joey checked to me. Having an ace, likely the best hand with a gutshot and backdoor flush draw, it was an easy fire, Joey check-raised.

I contemplated Joey’s range. Being highly aggressive along with the board being draw-rich, semi-bluffs and bluffs were a large part of his range. Additionally, he could have hands like a low pair which he deemed best. That said, he could also hold a big mitt. I called, looking to see what the turn brought and formulate a strategy from there.

The turn card came the J, Joey fired again. While my hand wasn’t very strong, it possessed some value. I could beat most of Joey’s bluffs and semi-bluffs, I was 39-to-7 to catch an ace or an eight, maybe even a seven would draw out. That said, an ace wasn’t undoubtedly good, and an eight didn’t have to be a “hogger” either. I estimated bluffs and semi-bluffs to be about a third of Joey’s range. Consequently, I was likely calling the river with ace-high anyway.

I thought about raising, feeling Joey might fold some hands containing outs as well as some superior holdings to mine. There was $210 in the pot, a raise cost me $80, and I was calling one turn-bet anyway. Was raising a viable play?

If I got reraised, I would be getting $370-to-$40 to see the river, a call I’m going to make though I understand it’s very marginal. While 8-7 would be a portion of his three-bet range, there were many other possibilities he would reraise with that a gutshot would be about the right price to draw to. I would not call the river with ace-high after being three-bet, so the cost would be the equity lost on the additional $40.

Additionally, I would lose equity should raising set myself up to be outplayed. For example, if Joey three-bet a draw and fired the river causing me to fold the best hand. And, if he would check a better holding than mine on the river if I flat called the turn, I would save a bet by not raising. What I would gain by raising would be the equity received by the times I prevented him from drawing out, the equity I would gain the times he folded a winner, along with any extra bets won which occurred due to my raise.

The scenarios in which I lost equity were probably fewer than the scenarios in which I gained equity, though that’s irrelevant anyway. What counts is the sum of the blended equity from all possible scenarios, those that gain equity and those that lose. And in the cases which Joey would fold a winner, either by folding a hand that would have drawn out or by mucking the best hand, I would gain considerable upside equity, far overlaying the downside risks. Additionally, raising would make me a tougher read on future hands.
I Hit It a Lick!

Disappointingly, Joey called. The river came the J, pairing the turn card. Joey checked and I knuckled behind him. “Nines,” he announced. “That’s good,” I responded. Joey turned over the Q 9, and I pitched my hand into the muck.

In the current scenario, my raise had made no difference. Had I flatted the turn, Joey would have bet the river, I’d have called, and the nominal cost of the turn and river call would have equaled my raise. But that didn’t have to be the scenario that played out. Since at my decision point I didn’t know Joey’s holding, there were many other possibilities. And with the information available to me at my judgment point, the size of the pot, my opponent’s hand range, and my knowledge of his play made raising the correct play. Had Joey not been so aggressive with bluffs being such a large part of his range, then raising wouldn’t have been the best play.

Conceptually understanding how equity is gained or lost is a key component in evaluating poker situations. By raising, I’d reduced my chances of being bluffed, created a situation in which Joey might fold the best hand, initiated a play that limited my chances of being drawn out on should I hold the best hand and generated a situation in which case I might have made extra bets. The combination of the equity gained from all those plausible scenarios was greater that the equity lost on my assumption of any plausible risks of the raise.

All gambling equations need to be quantified in terms of equity. And the sum of the equity of all possible scenarios, including how the hand will play forward, based on the best information available at the point of decision is what determines a good or bad poker decision.

Make better decisions than your opponents, and over time, cash is coming to your bankroll. ♠

Roy Cooke played poker professionally for 16 years prior to becoming a successful Las Vegas Real Estate Broker/Salesman in 1989. Should you wish any information about Real Estate matters-including purchase, sale or mortgage his office number is 702-376-1515 or Roy’s e-mail is [email protected]. His website is www.roycooke.com. You can also find him on Facebook or Twitter @RealRoyCooke