Poker, a non-zero sum game played like a zero sum one

[laja]

I know that poker is a non-zero sum game because of the rake that is payed. Not everyone's losses is another's gain, (I don't consider the house a player) But my question is:

Is poker a non-zero sum game that is played exactly like a zero some one?

There are no instances in which players, who aren't colluding, to work together. The only situation in which players can work together and all gain is when the nuts is flopped and they don't bet/cap trying to get idiots out, but also increasing the rake.

What do you guys think?

[Kaz The Original]

You can play slightly looser in a zero sum game, if your asking how it changes. Just like you can play slightly looser in a Time Charge game than a raked one.

[Al Mirpuri]

Could you define "zero sum game" and "non zero sum game" for me?

I hear these terms bandied about but have yet to discover their exact meaning. Are they part of game theory?

[axioma]

a zero sum game is one in which one players loss directly translates into another players gain.

[jtr]

[ QUOTE ]
I know that poker is a non-zero sum game because of the rake that is payed. Not everyone's losses is another's gain, (I don't consider the house a player)

[/ QUOTE ]

Not trying to be difficult, but I think you should consider the house to be a special kind of rather boring player. Then the game really is zero-sum and can be analyzed accordingly. (The house strategy is obviously just to take a fixed level of rake and doesn't need to be optimized unless you're looking at the meta-level and comparing the success of two casinos with different levels of rake.)

The reason I suggest this is that all of the theorems / approaches in game theory that are limited to zero-sum games are then available to you in your analysis.

Non-zero-sum games are often games where cooperation is possible, and tend to be harder to analyze or reason about.

Clearly poker without a rake is zero-sum, so I don't see why a simple tax on each pot should bump our analysis from the easy and productive ZS category to the trickier NZS category.

And nothing I've said rules out the possibility that if the rake is big enough, the optimal strategy for a particular player may be not to participate in the game.

[Rasputin]

[ QUOTE ]
a zero sum game is one in which one players loss directly translates into another players gain.


[/ QUOTE ]


More specifically, a zero sum game is where all the gains by the winning players are exactly equal to all the losses by the losing players.

If there is one winner who has won $100 then all the losses by all the other players must equal $100.

[tek]

[ QUOTE ]
Non-zero-sum games are often games where cooperation is possible, and tend to be harder to analyze or reason about.

[/ QUOTE ]

I would agree with the zero-sum label. However, I would also suggest a degree of cooperation is sometimes evident. If you notice, the good players will not play against each other, but will instead take turns playing against the fish.

I'm not talking at all about collusion. Just that the good players will not risk their chips against each other when they have better EV against the bad players.

(Note: I just play NL cash games.)

[Ryno]

There are some instances where the rake makes a huge difference in how to play the game. Many $100NL tables in Southern California (2/3 blinds) have a $4 rake + $1 jackpot drop regardless of pot size. So, if there is one limper and you are on the button, in most spots you'd raise enough so that there is a good chance no one calls and there is no flop.

[bobbyi]

[ QUOTE ]
The reason I suggest this is that all of the theorems / approaches in game theory that are limited to zero-sum games are then available to you in your analysis.

[/ QUOTE ]
Eh? Most of game theory is going to work the same for any constant sum game. Note that you can make a constant sum game into a zero sum (or positive sum or negative sum) game merely by changing the baseline of your utility function, so it doesn't really matter whether a constant sum game is zero sum or not. Raked poker technically isn't a constant sum game because how we play affects the total amount of rake collected, but it's close enough that I think we can safely pretend it is constant sum. So, in response to the original question, yes poker is a negative sum game, but i pretty much plays like a zero sum game (which is just a long way of saying that it is a constant sum game).

[jtr]

[ QUOTE ]
Eh? Most of game theory is going to work the same for any constant sum game.

[/ QUOTE ]

Agreed. I'm trying to contrast zero-sum games with games in which the total payoff is variable, such as the ultimatum game in which the refusal of an offer can lead to zero payoff for both players, or an investment game in which players can choose how much to put into a common pool for mutual profits. Note that in neither of these examples would the net payoff be constant.

I completely agree that constant sum games and zero sum games are only trivially different.