Decisions, Decisions

“Did I make the right decision?”

A friend posed this question after a recent PLO hand. For purposes of this blog, I’ll call him “Mark.”

Facing a big turn bet, he folded in this spot:

Let’s review Mark’s decision.

On the turn, the pot was $112. The J♠ made Mark’s hand super sexy, with an open-ended straight flush draw. Ooh, give me some of that! He may have additional outs if he improves to three Ks or 5s or two pair.

Villain 1 checked, Villain 2 bet $84 (75% of pot) and Mark called. He could have raised right then, but that decision isn’t the focal point of this post.

After Mark’s call, Villain 1 lowered the boom with a pot-sized check-raise to $450. While not shown in the image above, Villain 2 responded with a re-raise all-in. When the action returned to Mark, he should expect Villain 1 to call $200 more.

Mark would have to risk $566 more for a chance to win a total pot of $2066. Dang, that added up quickly, didn’t it? Remember when it was only $112? Alternatively, he could keep his $566.

How much equity did Mark need to justify calling? How many outs is that?

To get there, divide Mark’s final bet by the final pot, including Villain 1’s call. 566 / 2066 = 27.4%. Don’t include the $84 Mark already committed in this betting round… those chips were no longer his.

Unlike NLH, you can’t put PLO players on specific ranges and do combinatorics. However, we can make a few smart guesses about the types of hands that lead to such betting enthusiasm –> already strong and/or draws to the nuts.

This means some of Mark’s apparent outs may not actually be good. This happens often in PLO and is really important. For example, it should be no surprise if one of the villains had A♠ x♠ for a higher flush draw that destroys many of Mark’s outs.

Here are the actual hands and equities:

Villain 1 does have the A-high flush draw, leaving Mark with 27.8% equity. He’s just a very thin slice of bad pizza above the 27.4% equity target.

How do we calculate this? At this point there are 16 known cards and 36 unknown cards. Each out represents equity of 1/36 or 2.78%.

Mark has 10 outs and 10 x 2.78% = 27.8%… A♥, A♣, K♥, Q♥, Q♦, Q♣, 9♠, 9♥, 9♦, 9♣. He’s right on the cusp.

A math purist would tell you Mark should have called. On average, this particular slice of pizza is worth about seven dollars.

A more practical mathematician would tell you it really doesn’t matter. Always calling a hand like this vs. always folding has very little impact on Mark’s long-term win rate. Folding is much more conservative and lowers variance. Calling leads to great joy about two times out of seven, and great pain the rest of the time.

My advice?

If Mark is an action junkie who enjoys the roller coaster AND has a deep bankroll AND never tilts over a tough loss, he should call.

On the other hand, if Mark is prone to tilt when losing a large pot like this one (i.e., he’s human), he should fold. The -EV of tilting surely costs more than the slice of pizza.

There’s a third, much less common, scenario where a player tilts after folding and seeing they would have won, but doesn’t tilt when they lose. That player, who I’ve never met, should call.

When the math makes it a close call, forget about the math and make tiltlessness your main goal for long-term poker survival.