[Jerrod Ankenman]

[ QUOTE ]
If you are playing an optimal game without taking into account how your opponent is playing then you are playing an equilibrium stategy and breaking even before the rake. Playing at equilibrium means you force your opponents to break even no matter what action they take (unless they make mistakes by making dominated decisions -- like calling a bet on the river with the nut low). Playing optimally does not offer your opponents the opportunity to make mistakes (except for dominated decisions which are always availble no matter how you play). In order to offer your opponents the opportunity to make mistakes, you must deviate from the balancing point of optimal equilibrium -- you must tilt. To do so profitable requires that you tilt in a direction that exploits the direction in which your opponent is tilting, but in doing so you open yourself up for exploitation by another player.


[/ QUOTE ]

Someone else responded pointing out that this isn't true, but I wanted to comment specifically on the idea that your opponents have to employ dominated strategies in order for you to profit when you are playing equilibrium/optimally. It's true that you will sometimes benefit when they do this, but it's definitely not true that this is the only way.

Suppose we define "X makes a mistake" to mean "X takes an action x1 such that X has lower expectation against Y's equilibrium strategy than X would if X played the action from X's equilibrium strategy."

According to your statement above, against an opponent playing optimally, X can only make mistakes if he takes actions which have lower or equal equity against all possible Y strategies than his equilibrium action.

Hopefully it's clear that this isn't the case (simply imagine a guy who bluffs a little too much - bluffing with a hand close to the bluffing threshold clearly isn't dominated, as some Ys will play too tight).

Jerrod