Cheating in Poker, Based on GTO
Recently, I came across an article on Wired Magazine, titled “The Cheating Scandal That Ripped the Poker World Apart”. As someone who often plays poker with my friends for fun and never with monetary stakes involved, the cheating in professional poker, the scandal surrounding this particular instance, and most importantly the way in which people suspected the cheating, was very interesting to me.
This article details the scandal of Mike Postle’s poker-playing strategies, and how many people in the poker world believed his success came from cheating in high-stakes poker games. Most interesting to me, though, was the idea that people, namely Veronica Brill, came to suspect the cheating: his lack of following Game Theory Optimal strategies.
Game Theory Optimal (GTO) is a strategy in Texas Hold’em poker that involves many concepts that we have discussed in class. I researched the basics of this concept, but I quickly learned that it is a concept that most professional poker players still don’t fully grasp. For the purpose of discussing the case of the Mike Postle scandal, I will broadly describe some of the concepts present in GTO that most relate to this class, summarized from this article. In essence, GTO is a strategy in which you play the game apprehensively against opponents, in order to protect your own money. In this way, you are essentially protecting yourself against other players exploiting you (such as by bluffing). Basically, for every combination of cards in a game, including the first two cards drawn to you (your hand/the “hole” cards), the first three cards played for the whole table (the “flop), the next card played (the “turn”), and the last card played (the “river”), there is a best response for you as the player, in terms of whether you should call/raise the bet or fold. This best response does not ensure that you will win, or even necessarily have a higher likelihood of winning, the round, but it is simply the best decision for you to make in that isolated moment. Additionally, this best response at any given point is impossible to know in real time during every game – you can never know what your opponent has in their own hand, and there are too many possible combinations of cards in a game of poker (2,598,960 to be exact) to know the best response to every scenario in real time. The strategies of GTO involve concepts such as pre-flop hand ranges, bet sizing estimates, and push/fold Nash Equilibrium charts, all of which (and more) combine to form the holistic strategy. One of the many GTO pre-flop charts is shown below, and details whether a player should call/raise (denoted by color) or fold (blank), based on their card combinations (the values and whether or not they are the same suit – o/s) and the position they currently hold at the table. A lot of the fundamental concepts of GTO are based on Nash Equilibrium and the best response of each player at a given time. The game of poker is much more complicated than a one-round, two-player game (like the Prisoner’s Dilemma), which makes it much more difficult to determine the best response and Nash Equilibrium at any given time in a game of poker, but these concepts still lie at the core of GTO. One of the many different Push/Fold Nash Equilibrium charts is also shown below.
Source: https://www.top10pokersites.net/blog/the-beginners-guide-to-gto-poker
Source: https://www.mypokercoaching.com/push-fold-chart/
Along with these concepts of best response and basic Nash Equilibrium, there’s also a decent amount of the mixed strategies concept involved in the game of poker. If one player were to play GTO all of the time, and somehow perfected the theory (even though this seems to be currently impossible in real time), their moves would be entirely predictable. For this reason, most, if not all, poker players play with a mix of GTO and Exploitative Strategy, the strategy where you do whatever will raise your expected value at any point in the game, regardless of whether you will actually win or not. This is where bluffing and deception of poker comes into play, since this game (like many others) is not simply a game of statistical strategy, but also a game dealing with social psychology.
Considering all of these concepts mentioned about poker GTO, it is interesting to come back to the article regarding Mike Postle’s alleged cheating. Veronica Brill, the poker commentator who first announced suspicions of Postle’s cheating, thought that cheating was occurring, based on the fact that Postle was disobeying the strategies of GTO and winning at such a high rate, that it did not make mathematical sense. In the particular game which the article centers around, Postle started with a hand of a queen of diamonds and a jack of hearts, which is a statistically good hand. The flop produced an 8 of spades, a 9 of diamonds, and a jack of diamonds. Again, this flop was statistically very good for Postle’s hand, as he was only one card away from the hand known as a straight. The turn produced a 4 of spades, which did not help him, and he subsequently folded. Brill stated that this move did not follow GTO; however, in retrospect, Postle was correct to do so, because his opponent had a straight before turn had even occurred. Based on his correct choice to fold, and considering that this choice did not follow GTO, she was suspicious of this decision making tactics, and thought that he might not be playing entirely fairly. I find it most interesting that, despite the most skilled poker player still not being able to grasp every concept of GTO in real time, this lack of adherence to the current best poker strategy raised plenty of red flags for Brill.
Sources:
https://www.wired.com/story/stones-poker-cheating-scandal/
https://www.top10pokersites.net/blog/the-beginners-guide-to-gto-poker
https://www.mypokercoaching.com/push-fold-chart/