Two Concepts from Game Theory that Every Poker Player Should Know

Before my title topic I can’t help mentioning this strange coincidence. My last two columns were a 2018 version of how and what every poker player should do to get ready for the World Series of Poker. I had previously written a similar column in 2015 that made the following recommendation: “Amazon lists a huge number of books with puzzles and exercises for improving cognition and memory. My current favorite is Mastermind: How to Think like Sherlock Holmes by Maria Konnikova. I combined reading chapters of the book with reading various Sherlock Holmes stories. This book makes reference to a number of modern psychological studies…” Strangely enough, Maria has taken a break from writing about psychology to play and write about poker, and has been fortunate to acquire poker genius, Erik Seidel as a mentor.

Concept 1: Balancing

Back in my earliest days playing poker (over 50 years ago) I was taught that one crucial element of winning play was to play the same hand differently and different hands the same. Playing high draw poker, it was right to draw one card not only with two pair, a four-card straight, and a four-card flush, but also with trips. Thus, you played different hands the same way and confused your opponents. If you had K Q as the button in no-limit hold’em, saw a flop of J 10 9 and were lucky enough to have the original raiser bet, then you sometimes called, sometimes raised small, and sometimes raised big. You played the same hand different ways. Back then, no one called this game theory optimal (GTO), just being tricky or hard to read.

Now game theory has provided the mathematical underpinning for this strategy. Without getting technical, just try to play the same hands differently and different hands the same. Someone raises, and you decide to three-Bet. Your re-raise should contain some very good hands and some draws or bluffs. Different hands played the same way! Theory suggests that you should have more draw/bluffs than value bets preflop and on the flop. If the hand continues the frequency of value bets increases until the river. If you bet the size of the pot on the river, the GTO play is to be evenly divided between value bets and bluffs. This brings us to the second crucial GTO concept.

Concept 2: Bluffing and Defending Frequencies

These are really mirror images of each other. Game Theory allows us to calculate the optimal bluffing and defending frequencies for any bet size. Here is a chart that presents GTO bluffing and defending frequencies:

General Rule: As bet sizes get bigger the bettor should have a higher percent of bluffs in his range, but caller doesn’t need to defend as often. When bet size is small, caller is getting a good price and must defend more, but bettor should bluff less.

Bet % Pot Min Defense % By Caller Bluff % By Bettor Value % By Bettor
25 80% 17% 83%
33% 75% 20% 80%
50% 67% 25% 75%
75% 57% 30% 70%
100%
(pot size) 50% 33% 67%
125% 44% 36% 64%
150% 40% 38% 62%
200% 33% 40% 60%

Also note that it is never theoretically correct to bluff more than 50 percent of the time, no matter how large your bet is. Your opponent could always call and show an immediate profit. Bet size was expressed as a percentage of the pot. The general rule is that larger bet sizes should contain more frequent bluffs but should be called less often. Smaller bet sizes, should contain fewer bluffs, but be called more often.

I know this sounds counterintuitive. If he’s bluffing more, shouldn’t I be defending more? Not when the bet size is increasing. If there is 100 in the pot, and he bets 25. You can lose four out of five calls, and break even (you lose 25 times four, but get back 100 once.) If he bets 200, now you lose 200 when you’re wrong, but only gain 300 when you’re right. You shouldn’t call as often.

If your opponent varies too much from these optimal frequencies, you can exploit them. If your opponent bluffs more than is optimal, the more you must defend. But, of course, trying to exploit him leaves you open to exploitation. You think he bluffs too much, so you call a lot to try to take advantage of his over aggression. Unfortunately, he notices and seldom bluffs. You are now mistakenly calling too many bets. By following GTO calling percentages, you could have avoided this headache. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years. With two WSOP bracelets and few million in tournament cashes, he is easing into retirement. He currently devotes most of his time to poker. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City -The Library near Houston and Doc Holliday’s on 9th St. are his favorites.