Game theory, according to experts is ‘the study of mathematical models of conflict and cooperation between intelligent and rational decision-makers.’ In normal-speak, it’s the mathematical study of games between two or more competing people, where there’s a defined set of rules and an absolute winner at the end.
Lucky Nugget Casino takes a simple approach to the absolute minefield that is Game Theory.’
Don’t mix-up ‘Game Theory’ with ‘Gambling Theory’
The two do overlap, that’s true — but gambling theory applies to games with unknown, or uncertain outcomes. Game theory is concerned with games of skill, as opposed to games or luck, or chance. Video poker, for example, would not be subject to game theory as although there’s an element of skill, it’s a single player game. On the same vein, blackjack doesn’t apply to game theory — regardless of the edge a player might have over the house.
Live poker on the other hand is an ideal arena for game theorists. Simplified versions of poker have been used as a way to mirror game theory, ever since John von Neumann founded modern game theory in the 1920s.
Games are split into two types along several criteria
Prepare yourself for an information overload. The main areas of study in game theory are: cooperative vs. non-cooperative games, games of perfect information vs. games of imperfect information, simultaneous vs. sequential games, zero-sum vs. non-zero sum and games of two player vs. games of multiple player.
The list goes on: symmetric and asymmetric games, discrete or continuous games, population games, stochastic games, meta-games etc.
Those are the terms, but there’s little chance of going through them all. Just a good to know, really.
Game theory was initially invented to predict economic behavior
The economy is something that has baffled even experts for centuries. One minute we’re up, the next we’re down. Fuel prices rise, and then they plummet. Stocks rise and crash. If one could predict the outcome of the economy, they could potentially profit.
It soon became apparent that the wide variety of topics game theory encompassed made it a very powerful tool in a grand variety of fields: evolutionary biology, political science, warfare, philosophy and multiplayer gambling games such as poker. If you’re looking for a great film that directly takes from game theory, then check out hit(ish) 1983 thriller WarGames.
A zero-sum game is pretty simple
Zero sum games must come to a total score of zero. In other words, however much is lost by a/the player(s), must be won by the other player. Poker, for example, is usually a zero-sum game — of course, not including the house rake nor the entertainment value, which is the drive to play in the first place. There are a number of games where players can still lose, but do slightly better or worse than each other. These are used to demonstrate co-operation between competing players.
Perfect information is not just about the future!
When you hold ‘perfect information’, you don’t just know what’s going to happen, but what has happened and is happening. There’s literally nothing hidden that one person knows and the other does not. There’s no moves (like in Battleships) or hidden cards, like in poker.
Here’s a few examples of games with perfect information available:
Since you view every move in clarity and have the potential to analyse all further moves, nothing is hidden from the player.
Game theory has little interest in these games and instead focuses on games with imperfect — or incomplete — information. Monopoly, for example, is a great game for game theorist to study, as is backgammon.
It’s all about being rational
Game theory focuses on the rational and intelligent aspects of human co-operative gaming.
Ultimately, the main aim is to answer the question, ‘what’s the best way to play against opponents that think like me?’ It’s not a one strategy fits all system; it’s about dynamic thinking, knowing your player and playing exactly the way they do. Imagine two mind-reading geniuses each playing poker — that’s what game theory wants to explore.
Pure strategy vs Mixed Strategy
Some strategies cannot be beaten — essentially, they’re perfect.
If you adopt perfect strategy when playing heads-up poker, you can’t lose — these are called optimal strategies. Even if you were to tell your opponent how to play against you, they’d never win. Optimal strategies often involve picking randomly, but with precise preempted probabilities.
Rock-Papers-Scissors is a game where optimal strategy can be played. To stop your opponent gaining any form of advantage, you must play each potentially selection exactly a third of the time. When you start opting for scissors more than rock or paper your opponent can counteract by playing rock.
Of course, adopting the above strategy doesn’t give you advantage over your opponent, it just quashes all possible leverage. The same cannot be said for poker, though.
Last year a bunch of mathematicians managed to ‘solve’ (not solve in the regular sense, but they got close enough with the power of a thousand computers) a game of Texas Hold’em. The sad thing is you could play almost perfectly against their supercomputer for the rest of your life and still stand to lose — doesn’t that sound depressing!
Balancing out equilibrium strategies
Chuck another player into the mix and unfortunately there isn’t an ‘optimal’ or ‘best’ way to play. There is a way to adopt best strategy though — in the form of the Nash equilibrium.
Named after John Nash, Nobel Prize winner in Economics, he found a way of creating the optimal strategy when three competitors go head to head.
There’s also a brilliant movie out there called The Beautiful Mind, starring Russell Crowe. Sadly, both he and his wife were tragically taken from us in a car accident in 2015.
Now you know, go out and play!
There’s not much one player can do against more than one opponent, but you can try to collude with another player to see if that mixes things up.
In poker, when there’s more than two people, you simply cannot guarantee a win. You’ll have to learn how to read your opponents and change your game based on that.
Unfortunately, they’re trying to do the same. If anything, we advise playing heads-up where you can guarantee a win. That’s the best strategy.
So, there you have it. Your next task is to head out there and play — it’s the only way you’re going to learn!!