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July 23, 2007


Isn't this the same method as is used in duplicate bridge tournaments? It still doesn't eliminate all chance elements.

Exactly, Mr Guest.

In a bridge tournament, all the players play the same hands once each. It also means the hands can be 'designed' to make sure that everyone plays in a variety of circumstances.

This is basically equivalent to team of four duplicate bridge.

There's still some luck though, and not just luck of performance.

The problem in imperfect information games is that part of the game is trying to get information that you "shhouldn't" have and the correct strategies are very different depending on how much information you have. On some hands, it is very difficult to distinguish between finding a "tell" and just getting lucky with a bad play.

For instance, in No-limit Hold 'Em with small stacks relative to the blinds/antes, the game becomes very simplified and it's common to bet all-in with certain hands and fold most others. Your preflop strategy is basically the range of hands that you push with, and the range of hands with which you would call a push. Generally, the lattter is a stronger set, because the caller needs a hand in the middle of the range that the initial bettor bets with in order to make calling correct *if* he only knows the range, and not the specific hand within that range. But sometimes, there might be a tell, particular against a weaker player. Perhaps the player takes longer to bet when his hand is at the weak end of the range, while betting immediately with a strong hand, and the difference is consistent and noticeable. Now, the observant opponent will call with weaker than normal hands when the bet is not immediate, and will fold stronger than normal hands when the bet is immediate.

In the absence of this "tell", either decision would be a poor play, but given the tell, as long as they are correcting the optimal amount given the actual informatin received, it is correct.

So suppose you have this very situation in the duplicate game. computer 1 bets all-in and Laak using a game theoretic equilibrium calling strategy given a correct understand of which hands the computer will bet all-in with. In the other room, Eslami is betting allin with the *exact same strategy as computer 1* and bets all-in with what turns out to be one of the weakest hands in that range. Computer 2 calls and is ahead, ultimately winning the hand. Did computer 2 spot a tell? or did it just make a bad calling decision and get lucky that Eslami had a very weak hand for his action?

It's very hard to know.

This is, however, a good strategy for minimizing the luck.


I wonder if there are games in which this Doubles approach would cause a player to have a different optimal strategy.

Doubles tournaments based on this method could be made for lots of games with chance elements.

Very good idea. This could also finally sort out the respective importance of luck and skill in some games. Could work for games like monopoly and backgammon as well (whith identical sequences of dice rolls).

Duplicate poker is already available on the net. The "come-on" is that it is clearly a game of skill and therefore not subject to laws that purport to limit games of chance on the internet. It also seems drier and less interesting than real poker to me.

Of course it does not eliminate luck in games where the optimal strategy is mixed, ie involves randomness. I would agree that in practice it probably reduces the influence of luck though.

All, "avoid" is not "eliminate."

James, I don't think the doubles approach changes your strategy for no limit hold'em. You know what the computer in the other room has - so you know if you're holding a pair of aces, your human colleague will likely lose that hand. And you know you're likely to win. But that isn't any more knowledge than you'd have if you didn't have a double. The only communication between the games happens at the end, when the chip totals are combined.

Speaking of "tells" and bias - are there any studies showing that poker players really can perceive and act on tells? I mean physical tells like how soon the bet is placed, how forcefully the chips are set down, etc. Or, do strong players beat weak players by pure strategy but chalk up some of their success to finding the tells? It seems to me that it would be easy to fall victim to confirmation bias here - when you won the hand you think you zeroed in on the guy's tell, but when you guessed the tell wrong it was because you had a weak hand, etc.

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