Most people who play games can intuitively understand how games that only consist of known information, like tic-tac-toe, checkers, and chess, can be solved by computers. But they cannot comprehend how games with unknown information, like poker, can be solved.
The truth is that with enough computing power and time, even the most difficult games can be solved using math and game theory.
A game is considered to be “solved” when the Game Theory Optimal strategy has been determined. The GTO strategy is quite powerful because it either breaks even (when the opponent plays the same strategy) or wins (when the opponent plays any other strategy).
Games that have fewer options than no-limit hold’em, like limit hold’em, were solved a few years ago, and even no-limit hold’em is close to being solved. In 2017, Libratus, a poker bot developed at Carnegie Mellon University, beat four of the best heads-up no-limit hold’em players for more than 14 big blinds per 100 hands. With $1-$2 blinds, that would be $28 per 100 hands, which is an incredibly high win rate.
Some players may not understand how a bot could possibly know how and when to bluff intelligently, but it turns out bluffing is a common tactic discussed in game theory classes. For example, you will regularly find yourself on the river with a polarized range, which consists of premium hands and junky hands, while your opponent will have a condensed range, consisting of mostly marginal made hands that lose to your premium hands and beat your junk. In this situation, the polarized player can win the pot on average simply by betting an amount that will result in their opponent winning an amount of the time equal to their pot odds.
If you know your range consists of 67% premium hands and 33% bluffs (which is possible using in-depth range analysis, which I teach at PokerCoaching.com), bet an amount that requires your opponent to win 33% of the time.
In this case, a pot-sized bet will give your opponent 2:1 pot odds, meaning he needs to win 33% of the time to break even. So, with a polarized range, a pot-sized bet will win you the pot on average, no matter what your opponent does!
If your range was instead 83% premium hands and 17% bluffs, betting one-fourth of the size of the pot, giving your opponent 5:1 pot odds, will win the pot on average. One interesting concept that comes from this is that as you have more bluffs in your range, you can use a larger bet size. If your range is perfectly polarized with 51% premium made hands and 49% bluffs, you could actually bet 24.5 times the size of the pot, which almost no one does.
If you study using the two main GTO solvers available today (PioSolver and MonkerSolver) you will find patterns that repeat over and over. For example, when determining which hands to continuation bet on the flop against one opponent, your main concern is how your range fares against your opponent’s range. If you have the equity advantage (meaning your equity with your entire range on the flop is a decent amount higher than your opponent’s equity with his entire range), you should often bet with a large portion of your range using a small bet size.
If you do not have the equity advantage, you should bet infrequently using a larger size with a polarized range consisting of your premium made hands and some draws, while checking your marginal made hands and junk, plus a few traps. Using this knowledge, you can develop an implementable system to determine roughly the ideal betting and checking strategy in any situation.
While the GTO strategy is quite powerful, it is usually the ideal strategy against only the best players in the world. As your opponents play worse, you should adjust to take advantage of whatever they do incorrectly. If you play strictly the GTO strategy, you will leave a ton of money on the table.
Passive exploitation is when you play GTO and whatever your opponent does wrong wins you money, while active exploitation is when you deviate from the GTO strategy to further take advantage of your opponent’s mistake. The maximally exploitative strategy is when you deviate from the GTO strategy in a way that maximizes your profit from your opponent.
While it is sometimes difficult to know what your specific opponent does incorrectly, many times it is obvious. For example, many small-stakes players almost never bluff on the river. So, if you get to the river and your opponent with this tendency check-raises, you should fold all but your best made hands. Other players bluff way too often, allowing you to easily call down with all sorts of marginal made hands. These are both examples of actively exploiting your opponent.
The major problem with using the maximally exploitative strategy is that your assessment of your opponent’s strategy could be incorrect. If you think your opponent never bluffs yet he actually bluffs a lot, if you fold to most of his bets, you will get demolished. If you think your opponent bluffs a lot, so you call down with lots of marginal made hands, but it turns out your opponent essentially never bluffs, you will also get demolished. If your opponent quickly and correctly counter-adjusts to combat your maximally exploitative strategy, you will lose way more than you could have potentially won by making your initial adjustment.
Playing the GTO strategy sidesteps this dilemma, but will also result in you winning less money in the long run from your non-world-class opponents, assuming your assessments are generally correct. So, until you are fairly certain about what your specific opponent does incorrectly against you, it is wise to play a fundamentally sound strategy that is adjusted slightly to take into account what you know the average player in your game does incorrectly. ♠
Jonathan Little is a two-time WPT champion with more than $7 million in live tournament earnings, best-selling author of 15 educational poker books, and 2019 GPI Poker Personality of the Year. If you want to increase your poker skills and learn to crush the games, check out his training site at PokerCoaching.com/cardplayer.