Let’s face it: Texas Hold ‘Em has changed for good and it’ll never be the same again. But what did we expect? Since the boom of the mid-noughties, not even the American justice system couldn’t kill off a sport that, just a decade before the game’s most important tournament managed just a tenth of the entrants it does today.
With that momentous shift – from seemingly-dark and underhanded card game played by math geniuses and rednecks, to the glitz and glamour enjoyed by other casino games – came, with it, a momentous social shift. More and more of the math genius stereotypes came forward the age of tournament goers plummeted and new, mathematically optimised strategies dominated the field.
Math brings us two basic theories of play that can help us optimise our play. Much of it, like calculating pot odds and outs, is rudimentary poker knowledge and imprinted in the minds of many of us. But not all of it is. The calculation of odds and chance all fall squarely under the category of gambling theory and it’s a solid understanding of this math that almost comes as a prerequisite for sitting down at a cash table these days.
Calculating your outs is easy – if you count the number of cards that could possibly improve your hand – and, if you correlate that information with the remaining number of cards in the pack, and compare the subsequent ratio with the total size of the pot, you have your pot odds.
It is, of course, possible to take that up a step by calculating pushing ranges and bluff frequencies, but the necessity is considerably more in favour of the fundamentals. However, this is another aspect of mathematical eventuality that serves an, albeit minimal, purpose in the game of poker we see today.
Game Theory, or the concept of GTO (game theory optimised) is a commonly banded around phrase by mid-level grinders and naive upstarts alike. The theory itself suggests that, given enough hands and the play-through, and subsequent counter, of enough strategies will end in a strategy that can only be beaten by other GTO fixed strats.
While the concept itself is enough to make the brain ache, it has been tested in one case. The University of Alberta simulated a heads-up game between two AIs with different strategies. They were also both equipped with a piece of coding that allowed them to recognise and counter the strategies. After an infinite number of hands, both AIs settled on a strategy that couldn’t set a 1% advantage between the two.
But, would knowing either strategy really help your play? No, of course not. Not unless you wanted to play against a high-level network of supercomputers for an infinite number of hands. The reality of poker suggests that nothing is perfect and, even if you identify an opponent who plays a fixed strategy, there’s nothing to stop them making a mistake, changing their strat or becoming tilted. There are too many variables with which your opponent can suddenly become derailed from the tracks you identified.
Both theories hold their place in the game, and supposed GTO fixed strats, created by humans exist – but have as much success as any other, as far as any research can do. But, truly optimised game theory applied strategies to play against humans don’t exist and, to find one, you’re going to have to examine a seriously large volume of poker hands.