Heriot-Watt Poker :: Game Theory

Guest

From reading an Interview with Chris Ferguson he has qualifixation or degree or something in "game theory" can someone please in layman's terms explain to me the basics of what game theory is and how it is useful?

Stephen · Royal Flush

I believe (although I may be mistaken) its an economic theory which can be applied to a decision in any 'game' type situation which, when properly applied, leads to a strategum which is unexploitable i.e. whatever your opponent does you can't lose in the longrun. However I think for the purposes of lowstakespoker its much better to come up with exploitative strategies than unexploitable ones.

Alex · Five of a Kind

Agreed. Vanessa Rousso wrote a couple of articles in recent InsidePoker issues about Game Theory. I'll try to find one of the little tests she set as they're quite interesting.

There's also a good albeit brief section on Game Theory in David Sklansky's 'Theory of Poker'.

Stephen · Royal Flush

Game Theory in action.

Link

You still would tho, but I hope someone ghostwrote those articles Alex.

Stuart · Royal Flush

Haha you beat me to it Stephen. Love that hand.

Card Rack · Royal Flush

Agree with basically what Stephen said apart from when asking for 'laymans terms' you used the word strategum!!!!!

I did an 'interesting' course at Durham on Decision Theory with one of the world's leading Probability/Game Theorists.

The simplest example I can think of is noughts and crosses, basically the simple strategy used to never lose at that game is an example of game theory, no matter how the other person plays you will never lose. £100 a game anyone?

There's a distinction between perfect information games like noughts and crosses and chess where you know exactly how the games is being played, and then imperfect information games like poker where a person's hole cards are unknown.

If the cards were turned over you would know whether based on the odds you'd have to call or not. Game theory in poker, in one instance helps you to work out how often to bluff so that it's unprofitable for your opponent to call you even if you told him you'd bluff once in a certain number of hands.

When you don't know your opponents cards if you can reasonably accurately put a range and probability on his set of hands, game theory will let you know the correct decision based on that range and probabilities, similar to what Harrington goes on about when he talks over hands and ranges.

Game theory has proved that there is even a perfect strategy for chess, which if you played it no matter what your opponent did you would at least not lose. Only problem is it's such a hugely complicated game, it may never be found, and chess would probably die if it was worked out.

Stephen · Royal Flush

Strategum is quite lay its just strategy for when you are trying to sound clever ! Also I wouldn't worry too much about the future of chess, that sounds to me like the kind of thing that goes on abstracts/research proposals to get people interested/money but is actually never going to get done, but then I'm a big cynic !

Manson · Two Pair

Woooo something I know something about!

Game theory is used in economics to analyse the behaviour of two or more 'players', for example two companies operating in a particular market. The players have different strategies to choose from (high prices or low prices) and the payoffs they get from the game depends on the strategies they choose.

Sometimes there is an optimal strategy available to the players - so you get the best outcome regardless of what your opponent does. Otherwise, you can use a randomised strategy so that you maximise your payoff when the game is repeated. For example, the best way to play Rock, Paper, Scissors is to randomly decide every time which one to play, giving each a probablility of 1/3. This way no matter how your opponent plays, you should win about half the time (if you don't count draws).

Applying it to poker is complicated but the principle is the same. Like Marcus was saying, you could try and work out the optimal proportion of hands to bluff in. If you bluffed every time, you'd be beaten by someone who called every time. If you never bluffed you'd only ever win pots where you are dealt the best hand. So depending on your opponent's propensity to call you (which I normally find to be very high - why is this I wonder) you can bluff just the right number of times. Of course every time some information is revealed, which is the case almost every hand that you play, this might change what the optimal proportion would be.

Even if we could find the perfect strategy for chess, this wouldn't destroy the game. The perfect way to play draughts (checkers) was worked out long ago - you can play the perfect sequence of moves and your opponent could never beat you. So nowadays at draughts tournaments games start from a position in the middle of a game - somewhere you wouldn't get to if you played the 'perfect' game - and you have to play it from there. This already happens in chess circles anyway.

Having just said that, those damn Canadians have just worked out the best way to play from any position in draughts, although presumably this takes more computing power than you can practically bring with you to the tournament. http://news.bbc.co.uk/1/hi/sci/tech/6907018.stm