“If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties.” - Francis Bacon, The Advancement of Learning

When your daily working life begins and ends at a computer screen it’s all to easy to be sucked into the maelstrom of clickbait, trends, and sensationalist Youtube videos. In the poker world the emphasis on solvers as some kind of Oracle is great for quickly generating content and has led to many poker players submitting to the idea that the best investment of their time is to become amateur data scientists.

And the solvers certainly are seductive! The rows of cards, numbers and percentages offer an apparent certainty that is comforting in the otherwise rocky, shifting game that is PLO. Yet the results that solvers give are very specific, and highly contingent, and meanwhile every day players commit errors at the PLO tables that would be easily avoided with a broader understanding of the structure of the game.

In the passages that follow, I present an analysis of straight draws in multi-way pots, which provides the justification for a number of action-generation heuristics that you can use to immediately improve your play at the tables. I am confident that many of you will learn more of practical use from this article than you would from several hours of self-study with a solver. The acute reader will understand that my choice to discuss a multi-way pot is no accident, but elaboration on that topic will have to wait for another article.

[Disclaimer: Not only have I worked extensively with solvers myself but I have, with my team, developed my own in-house solver. They are certainly wonderful tools and I applaud those developers of commercial solvers for their work. The purpose of this introduction is to draw attention to the reader’s investment of his time as he works to improve his PLO game.]

What is my Straight Draw Worth?

A regular opponent opens from the CO, and the BT and SB call. We elect to overcall with most of our continuing range here, rather than squeeze, and the flop comes down as:

The CO bets into the flop, the BT calls, and the SB folds. The questions that we are exploring in this article are,

How valuable are hands with straight draw components here?
What effect does the bet size have on our decision to continue in the hand?

First, some statistics detailing range interaction frequencies on this board. If we consider a range of {JJ,TT,66,JT,J6,T6,hh,KQ,Q9,98} a ‘hit’, then at least one of the four players in the pot will hit this board 97% of the time and at least two 77% of the time. (For the Hold’em players here only one player would hit the board with this range 53% of the time and two players 14% of the time in that game. This should give a player new to PLO some idea of quite how poor his intuition will be in this multiway situation.)

If we instead consider a tighter range of {JJ,TT,66,JT,J6,Ahh,Khh,(KQ,Q9,98):hh,KQ9,Q98,987,KQJ,KQT,AKQ} as a ‘hit’, then at least one of the four players in the pot will hit this board 86% of the time and at least two 46% of the time. If your instinct is making you feel queasy about the prospect of straight draws on this board given these numbers then your instinct is serving you well. For those of you who are thinking, “Three players to the turn is standard here,” the next part of my analysis will serve as a revelation.

Let’s start with the generous assumption that the CO initiates with this entire subset of his range and the BT continues with that same subset of hands in his range. The table below shows the 3-way equity of a selection of hands to illustrate the relative value of straight components.

Hand3h Equity facing a bet and a call

They do not fare well.

In fact, a similar analysis of the relative value of hands which already have two pair or a set will demonstrate that we should really consider even tighter ranges for our two opponents:

Hand3h Equity facing a bet and a call