Gamblers often turn to a lucky charm or a superstition to try and coerce Lady Luck into their favour. This is, of course, not something that’s going to work, because many forms of gambling involve significant elements of random chance.
But as visiting casino sites to play online slots and table games has become commonplace in the expanding iGaming industry, players naturally seek ways to gain an edge. Players try to come up with strategies to apply to their gaming, in the hope of gaining an advantage against the house. But can the world of mathematics lend a helping hand?
Game theory is the mathematical study of strategic decision-making. Classic casino games like poker and blackjack require such decision-making, but when making them, players often get wrapped up in emotions and gut feelings and make errors of judgment.
Game theory is an analytical look at strategic interactions between decision-makers with the goal of figuring out the optimal strategy for yielding the best results. Here, we look at it in more detail and how it could be applied to gambling.
Decades of Learning
Game theory first came about in 1944 when a book called Theory of Games and Economic Behaviour by John von Neumann and Oskar Morgenstern was published. It has evolved into game theory concepts like the Prisoner’s Dilemma and the Nash Equilibrium, which states that a player can’t improve their outcome by only changing their strategy, assuming that all other players keep theirs the same.
As an example, Shop A and Shop B are both selling doughnuts for $3 each. Now Shop A wants to raise the price to $5, but that would likely mean customers would go to Shop B. So if Shop A instead sold their doughnuts at $1 each, they’d sell more, but would lose money on each doughnut. In both instances, the outcome for Shop A gets worse. As long as Shop B doesn’t change its pricing, then there’s no need for Shop A to alter its strategy, creating an equilibrium.
What This Means for Gambling
Game theory is logical, and while the above equilibrium example may not be the best outcome for either shop, it’s a stable one. For gambling, if you can predict how other rational players will behave, and assume they will not waver from their typical strategy, it means neither should you. This is great for a game like poker, which has imperfect information, due to hidden variables (cards and bluffs).
Casino games involve risk and uncertainty, and often present imperfect information. A game like blackjack, for example, has fixed rules, payouts and known probabilities, making it excellent for mathematical analysis. The basics of game theory for casino games, therefore, mostly focus on finding the optimal play against any standardised rules and by studying Expected Value (EV), which is the “long-run average” of how much you’d expect to win or lose from playing the same game many times over. Game theory attempts to dig into whether an instance (game) has a positive or a negative EV.
Poker
Highly relevant, most players use Game Theory Optimal (see below) in an attempt to become unexploitable.
Blackjack
Blackjack doesn’t have a strategic opponent and is largely ‘solved’ through probabilities. But there is an element of hidden information (dealer’s hole card), so game theory can help find the optimal move for basic strategy. Largely, however, it’s just a mathematically solved grid (Blackjack Probability Chart) that players use to potentially get the house edge down to around 0.5%
Roulette
Game theory becomes less relevant for a roulette application. That’s because there are no player decisions that can be accounted for that will affect the outcome.
Slots
Not applicable as there is no user influence or decision-making happening on any slot machine.
Sports Betting
Game theory can be applied in sports betting to find value bets, where a bookie’s odds underestimate the actual probability of an outcome.
Game Theory Optimal (GTO)
Game Theory Optimal (GTO) is a defensive style based on rational mathematics, which means that even if other players at the poker table are aware of your strategy, beating you in the long run will still be tough. It’s defensive because GTO attempts to break even against an opponent who plays perfectly, so any mistake from them then benefits you.
GTO balances human behaviour with actions, like bluffing precisely enough times so that an opponent can’t profitably fold or call every time. What’s important about Game Theory Optimal is that it takes into account a larger sample size of instances, and by no means guarantees every hand will be won.
Complexities
Game Theory is very complex, and using it on the fly in a gaming session is a little impractical because it takes into account other players’ actions. You won’t know the other player’s actions until you are in the thick of things, and because it’s based on logic, it can strip away the fun and emotions that go hand in hand with gambling.
