In cash game poker, some of the biggest decisions actually don’t matter very much. Let me explain.
We try to make the decision on each betting round that results in the highest expected value, or EV. There is guesswork, since we are working with incomplete information. We estimate the long-term result if the same situation were to be repeated millions of times, apportioned across the full range of possibilities for each bit of incomplete information. On average, we will win money or lose money; making the action +EV or -EV.
Of course, we don’t play out each scenario millions of times. We play one hand at a time, occasionally splitting the pot but usually winning all or none.
Consider this example from the turn round of betting in a $2/5 game at Harrah’s Cherokee casino last night. It was the wee hours of the morning and the table is short-handed. There was a pre-flop raise, call and re-raise to $50. The original raiser and caller both called the 3-bet, putting a total of $150 in the pot.
I have J♦8♦, a hand that I could have easily folded pre-flop. We’ll save that analysis (or self-flagellation) for another post. The flop is Q♦9♦2♥, smashingly good for me. There is a C-bet, I raise to $155 and both villains call, increasing the pot to $615 and setting up the turn for a big decision.
The turn card is the 6♠, basically changing nothing. Both of the villains look eager to get all their chips in. One of them – the guy on my left – tried to ship it on the flop, shouting “I call all-in!” before sliding out his chips. The dealer ruled that his first word, “call,” precluded his option to raise. Knowing that he wanted to go all-in, the other villain – the guy on my right, also called my raise.
First, let’s look at the chip stacks. The guy on my left has about $430 remaining. I have $510 and the guy on my right has us both covered. If all three of us go all-in, the final pot will be $2,065. I’d really like to win that!
Now some math. My remaining stack is 24.7% of the final pot (including my bet), which means shoving is a +EV decision if my equity is greater than 24.7% and -EV if my equity is less than 24.7%. The closer my equity is to 24.7%, the closer my decisions is to break-even EV… in a theoretical sense. In the moment, I’ll either bust or drag home $2,065. Or I could just check/fold and still have over 100 big blinds to continue playing. This is a big decision.
On to the villains’ hands, which was part of the incomplete information in the moment but I now know. The guy on my left has AQo. He’s madly in love with his top pair, top kicker hand. The guy on my right, who was the 3-bettor pre-flop, has A♥A♦. The A♦ takes away one of my flush outs.
And finally, an equity calculation. After eliminating the A♦, I have 11 clean outs – eight remaining diamonds will make a flush, plus three additional T‘s that make a straight. While it would be extra special to see the T♦ for a straight flush, that doesn’t change the outcome and there are no bonuses or jackpots to be won. With 42 cards remaining unknown, we don’t need to run millions of simulations. On average, I’ll win 11 times out of 42, or 26.2%. A 3-way all-in is slightly +EV.
If I folded here, my ending stack would be $510. If all three of us go all-in (which is what actually happened) and we kept reshuffling the remaining cards to play out the river a million times, on average my ending stack would be $541. This is $31 more than the result of folding, so a 3-way all-in has an EV of +$31.
At $2/5 no limit Texas Hold’em, decisions with an EV of +/- $31 simply don’t matter that much to your long-term win rate. Sure, it’s better to be right than wrong (which I was, according to the math), but even being wrong sometimes for $31 isn’t the kind of play that destroys any chance of being a winning player.
Just a few orbits earlier, I got another player to call my all-in bet on the turn for a $500+ pot in a spot where he had 10 outs. He hit one of them, took the pot, then immediately cashed out from the table.
This time, I have 11 outs. Surely karma will be on my side, amiright? Nope… the river is another 9, and the guy on my right with AA scoops this large pot.
As I made the long walk just after 4:00 a.m. from the poker room to the parking deck, that sure didn’t feel like a $31 profitable decision, the kind that doesn’t matter in the long run.
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The problem in this hand is the raise, not the equity/EV parlay. While SFDs do perform well with polarization – the raise of a first price – the 2x on the board drastically reduces the number of strong hands in your range. You are not likely to have top set as the caller or any two pair hands – possibly only 3 to zero q9s. Hence the point of polarization should not be the flop on the whole. When an eight or jack or ten or 8 fill the turn, a raise or price if checked to makes sense, as the board now favors your flatting range and diminishes the value of the PFR’s.