Calculating The Risk

Good players understand the importance of obtaining value from their hands. But few have enough conceptual proficiency to understand how assumption of risk affects the value equation. Any risks you assume need to be calculated into the expected value (EV) equation. Fail to do that, and you’ll repeatedly miscalculate.

I was up early on a Saturday morning and meandered down to the Bellagio for a little $40-$80 limit hold’em. The game was ablaze, with many players lingering from the night before. Vahe, a local high quality pro, raised under-the-gun (UTG) plus one and was called by three tourists behind him. In the small blind (SB), I glanced down to the 7 7 and flipped in the extra $60. The big blind (BB) called, and we took the flop six-handed for $80 each, $480 in the pot.

I flopped bottom set, A J 7, and contemplated my best play with my main focus on Vahe, the preflop raiser. While this flop hit much of his range, I believed Vahe wouldn’t bet any hand that wasn’t solid into this large and call-prone field. And while I was ecstatic that the board was rainbow, it also held many gutshot draws, and I didn’t want to risk giving a free card. Additionally, anyone turning a flush draw would generate a big overlay that would reduce my equity. I fired, and the BB folded.

I was delighted when Vahe raised. It furnished the prospect of thinning the field or at least costing my opponents more to draw. Since the pot was big, increasing my probability of winning added significant value and devalued winning additional bets. One tourist called, and the rest folded back to me. I three-bet, understanding that Vahe might have A-A or J-J. He flatted, and Mr. Tourist called. The turn came the 10, completing the rainbow board.

I bet, Vahe called, and while the tourist was deliberating I thought through how the hand had developed so far. I read a huge portion of Vahe’s hand range to be A-K or A-Q, feeling that he wouldn’t flat the turn with two pair or a set on a board possessing a large three-straight. His upfront preflop and flop raise signified a strong preflop holding that hit the flop. I contemplated how to play the river should a king or a queen come, while taking Vahe’s tendencies into account.

Vahe’s great at getting value out of his hands; he just doesn’t ever seem to miss value. If he has any weakness there, it’s betting too light. Knowing that, I discerned he would bet the river if either a king or a queen hit, giving him top two pair or a straight. He’d bet the two pair because he’s the sort that couldn’t live with himself if he missed a bet should I hold two pair. In the midst of my contemplations, Mr. Tourist called and the dealer turned the Q. I detested that card.

Now, I couldn’t beat A-K, but knew that Vahe would wager whether he held A-K or A-Q. I knuckled, knowing that, if I bet and he held A-K, I would get raised, but if he held A-Q he would still bet.

Let’s evaluate the plausible scenarios: If he had A-K and bet, Mr. Tourist might raise and I could get away from my hand with no river cost. If Mr. Tourist folded, I would call and lose one bet, one less bet than if I bet, got raised and paid off. If I folded to a river raise, I would assume the negative EV of being played off the winning hand.

If Vahe had A-Q and bet, once again I would get away from my hand if Mr. Tourist raised, but would call and win the pot if Mr. Tourist folded. If Mr. Tourist flatted, I’d overcall and should my hand be good, possibly pick up an extra bet in that scenario. But if Mr. Tourist held a superior holding, then I’d lose the same amount as if I bet and folded without assuming the risk of being outplayed.

If I led, I’d be subject to potential raises, some of which might be bluffs. Vahe, being a good reader, would know that a king is a small portion of my range. So betting would risk being raise-bluffed or losing two bets with my set, should I pay off. Additionally, while I would think river raise-bluffs would be a small portion of his river-raising range, Mr. Tourist might also take a shot.

I knuckled, and Vahe fired. Mr. Tourist mucked, and I called, knowing I was an underdog. I instantly felt better when Vahe announced “I can’t beat a set.” Then I knew he held A-Q and my set was good. I flipped my three sevens over, and he showed me A-Q. I cheerfully stacked the chips!

The hand speaks to analyzing how a hand plays and strategizing how to obtain the best equity. You do this not just by quantifying how to get the most bets into the pot, but by analyzing what play generates the highest level of EV by calculating the EV of all scenarios, including all assumption of risk.

I often see players, even some very good ones, make plays that have little or no upside, but have a meaningful downside. In most situations their play made no difference, but when it does matter, they have needlessly cost themselves equity.

So think about how your hand plays against the ranges of your opponent(s). Weigh any risks you’re assuming and make your best educated guess about how it affects the situation.

Poker is a risk versus reward analytical game; quantify it as such! And let the chips come your 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 any information about Real Estate matters-including purchase, sale or mortgage his office number is 702-396-6575 or Roy’s e-mail is [email protected]. His website is www.roycooke.com. You can also find him on Facebook or Twitter @RealRoyCooke