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Head Games: What’s Math Got To Do With It?

by Craig Tapscott |  Published: Apr 20, 2022


The Pros: James ‘SplitSuit’ Sweeney and Reid Young

Craig Tapscott: Why is there such a big aversion for some players to go deeper and really utilize the mathematics of the game?

James Sweeney: In the first chapter of my book, I wrote the following: “Here is the truth. Most players suck at poker math.” Math is rarely a person’s favorite subject in school and most people identify as being below-average in mathematical ability. Couple all of that with the fact that most poker players have been out of formal education for years, if not decades, and the idea of studying math seems awful.

The truth, though, is that poker is a math game disguised as anything but. Which all leaves an opportunity for you to develop a sizable edge. And the good news is that poker math is fairly simple. Once you know how to do the basic calculations and memorize a few shortcuts, being able to make better estimations at the table gets much easier. 

One of my favorite students over the last few years was ‘Joe,’ a winning $2-$5 live player who was struggling to move up to $5-$10. Every time Joe took a shot, he would instantly lose a few thousand bucks, move back down to $2-$5, rebuild, and then take another failed shot at $5-$10.

It was obvious he had a great feel on his normal stake. He’d been playing $2-$5 for years, knew his player pool well, had extensive notes on the regs in his game, and most of his reasoning during hand history reviews was based upon his reads and feel. There was almost zero discussion of math when Joe reviewed hands. Just a bunch of reads, thoughts about Joe’s specific hand strength, and a vague mention of villain’s range.

So, what Joe and I did was focus a lot of attention on poker math. We focused on the technical considerations in a hand, used a few tools like Flopzilla Pro to take a deeper look at ranges, and ran drills during coaching sessions.

“Your actual goal is to tie together the math and your reading ability,” I told him. “Use your reads to inform the range assumptions you’re making, and then run that through your math brain to output a +EV play.”

That little tidbit right there, the idea that you aren’t just a math player or just a feel player, is crucial. And players who are naturally gifted with the ability to read people have a real advantage. It’s much easier to teach someone math than it is to teach someone how to read people. 

After another couple of months, Joe had fully moved up to $5-$10 and was finding both playing and studying time more lucrative. Plus, given the smaller player field at his $5-$10 game, his reads were even more valuable since he could put them to use more often. 

Reid Young: People love to believe in shortcuts to the high levels. Truly understanding what game you’re playing requires work and facing adversity, plain and simple. Adversity and work aren’t shortcuts and they’re uncomfortable ideas for a lot of people, especially people who feel entitled to a goal.

Truly successful people are happy to fail and understand that failure as part of a process of becoming great. Any hesitation to embrace the inner workings of what you want to do well is counterproductive hubris.

Emerson said that you can’t teach a man what he believes he already knows.

Craig Tapscott: What are some of the biggest mistakes players make when it comes to calculating the mathematics behind any poker decision?

James Sweeney: Most players don’t think in ranges, and the ones that do, tend to not think about them correctly. For instance, I recently reviewed a hand where I opened UTG with A-Q, faced a squeeze from the player on the button, and I ended up four-bet shoving. A few comments I received about that video looked something like, “I would never get A-Q all-in preflop for 100 big blinds. That’s terrible.” 

Players typically land on this sort of decision because they look at A-Q and know it’s a huge dog against a normal stack-off range, and they conclude that four-betting with A-Q would be utter suicide. However, if you think more deeply about villain’s range, what becomes apparent is the importance of the gap between villain’s squeezing range and the range villain would call the shove.

That gap is part of the EV equation that represents how often you will pick up the preflop pot uncontested. As that gap gets larger and larger, the EV of a shove can get quite high, even when villain’s calling range absolutely dominates our A-Q.

The same sorts of range mistakes happen post-flop, too. I also reviewed a hand where I bet and called an all-in with J-9 on K-Q-10-Q-3. In smaller stakes, it’s rare that players are bluff raising rivers often enough, and debatable if they would even shove with Q-X hands given the action.

I ran the math in the video with villain only shoving a strong range and J-9 was (obviously) a clear fold. However, I went a step further and looked at the EV of calling the all-in if villain had a bluff combo, then a few bluff combos, and then many bluff combos. It didn’t take very many bluff combos for J-9’s equity to rise enough to make calling profitable given the pot odds.

If you only play poker using rote qualifying statements like “never stack off with A-Q preflop” and “never call a river raise without the nuts,” your strategy will 100% stagnate. And besides, a little exploration and math practice can disprove those rote strategic ideas quickly.

Reid Young: Garbage in. Garbage out. That’s the saying used in any data-backed exercises.

Faulty assumptions create miscalculated results. Acting with an understanding that your assumptions are based on small sample sizes should create a confidence interval within which you can make a more accurate decision.

If you assume your opponent is going to fold to your bluff 50 percent of the time, then you can solve for a bluffing frequency. In a real game, guessing that frequency with insufficient information and relying on weak assumptions rather than mathematics might result in your bluffing too frequently or not frequently enough and cost you portions of the pot that you would have kept with a better understanding of the game and situation at hand.

Craig Tapscott: What are a few tips toward a consistent and diligent approach to the study of the math of the game? It can get overwhelming for some people with ranges, equity, pot odds, implied odds, etc.

James Sweeney: Prioritize learning about the concepts you are weakest in. Poker books are great for this, as are YouTube videos and strategy guides online. Spend one week on each concept, and whenever you review a hand that week, give some extra time to see if the math concept applies to that hand.

Most concepts in poker are interrelated with other key concepts, so you will end up finding new areas to focus on in future weeks. For instance, say you are working on pot odds one week and studying a hand where you faced an all-in on the river to work out if you should hero call with second pair. While knowing the pot odds you are getting is great, you can only know if the call would be profitable with knowledge of equity, and equity relies on range assumptions, and all of that informs the EV of your call.

Try not to get frustrated. Remember that 85 percent of players will never bother doing this sort of work, and that by doing this work you are developing a natural edge. You will be able to look at spots, deduce the important math concepts at play, assign ranges better, and as a result, make better decisions.

Reid Young: All those math terms fit together to describe the game. It’s the language of mathematics.

Players aren’t combining a set of named ideas to arrive at a full arsenal of solved problems so much as you want to describe how equity changes from player to player and why. You can create toy games, simply solved example hands, and then gradually expand the combinations of hands involved in the scenario, for example.

You can also change other factors in isolation, like bet sizes, betting frequencies, hand strength, etc. Keep your exercises solvable so that you can act upon them. ♠

James “SplitSuit” Sweeney is a prolific poker coach having trained more than 500 students. Find his content on The Poker Bank’s YouTube channel, The Red Chip Poker podcast and discord server. You can also check out his books and Poker Math & Preflop Workbook at Find him @SplitSuit.

Reid Young is a software engineer, app developer, and professional poker player with a focus on cash games. He is the author of The Blue Book: An Advanced Strategy Guide for No-Limit Hold’em Cash Games. He can be found on Twitter @Shootaaa.