This is the third installment of my weekly poker column in the Economic Times, Range Rover.
If Jimi Hendrix was a poker player, he might well have come up with an album called ‘Are You Balanced?’ The higher you rise up the stakes, the more you hear about balance from people. ‘Are you balanced in this spot?’ ‘I called because I thought, no way you’re balanced here.’ And so on. What does balance in poker really mean?
Balance has all to do with game theory, so let’s first look at it in the context of another game: Rock, Paper, Scissors (RPS). You are asked to design a strategy for an RPS bot, and to reveal it to your opponent before the games begin. What is the best strategy you can design? Game theoretically, it is to randomise completely, so that in the long run you will have an equal number of Rock, Paper and Scissor in your range. This is the only strategy you could have that your opponent simply cannot beat, even when he knows it in advance. It is game-theory optimal (GTO). And it is balanced.
Let’s turn to poker. You raise with AKcc, I call from the big blind. The flop comes KQ3 with two hearts. I check. You bet. I raise. What do you do here?
If you think I would only raise stronger hands such as KQ and 33, you can correctly fold here. If you think I tend to slowplay those hands and would only raise with a draw, you should continue. However, if my range is balanced here, and includes hands that beat you as well as draws and some air, your decision is harder. You could make a mistake by calling; and you could make a mistake by folding. You need to estimate the equity you have against my made hands, the equity you have against my semi-bluffs, the frequency with which I have hands in those two categories and then figure out the best line to take. If I am perfectly balanced, you’re in trouble.
In this example, there are future streets of betting left, so let’s turn to a simpler river spot. You and I are in a hand that reaches the river, where I make a pot-sized bet. You are getting 2-1 on a call, and my game-theoretical aim is to make you indifferent to calling or folding. Therefore, one-third of my hands should be bluffs. (Note that balance does not mean an equal number of bluffs and value hands. It depends on the odds being offered to the opponent.) If this is the case, I can never lose in the long term, but win if you fold too much or call too much.
It’s remarkable that if you can play GTO poker, you don’t have to take into account your opponent’s ranges or tendencies. You simply need to get your own frequencies and bet-sizing right, and design your ranges accordingly. But this is almost impossible to do in practice, and even the best players only try to approximate it. Besides, you’d need to play GTO poker only in high-stakes online cash games. In all the local live games you are likely to encounter, you should aim to be exploitive rather than balanced.
Let’s go back to RPS.If someone tends to go 70% Paper, playing GTO is not the most profitable line to take. You should exploit this player by increasing the Scissor in your range. In the first poker example above, against a guy who never folds top pair, I will only raise there with better made hands; against someone who folds too much, I will raise with a greater proportion of bluffs and semi-bluffs than is GTO.
Note that an exploitive strategy, by not being balanced, is also exploitable. If I adjust to the 70% Paper guy with more Scissor, it becomes easy for either him or another observant player to adjust to my adjustment with more Rock. If two players keep adjusting to each other optimally, they will eventually both be perfectly balanced. But in practice, this rarely happens.
All players make mistakes; all players have leaks. It is usually more profitable for you to be exploitive (and exploitable) than balanced. But knowing what is GTO in many spots will help you avoid mistakes and spot exploitable imbalances in others. In poker, as in life, balance is a good thing.
For more on the use of game theory in poker, here are three recent books I recommend highly:
Applications of No Limit Hold’em by Matthew Janda is a primer for GTO play in six-handed games. It’s an outstanding book, and I also recommend checking out his training videos on Cardrunners.com.
Expert Heads Up No Limit Hold’em by Will Tipton uses game theory to analyze heads-up play.
Poker’s 1%: The One Big Secret That Keeps Elite Players On Top by Ed Miller deals with optimal betting and calling frequencies, and how to construct ranges that can help you conform to those. Here’s Miller’s website; and you’ll find a recent interview of his on Andrew Brokos’s podcast here.
If you want to learn more about game theory in general, outside the context of poker, The Art of Strategy by Avinash Dixit and Barry Nalebuff is a fantastic introduction.
Previously on Range Rover: