Sure. But you do it for a river-subgame with ranges calculated from the tabled preflop-to-turn strategy.
You are doing it for the whole tree obviously. From leaves to root.
So basically you are pitting a GTO-strategy against its nemesis and this - by definition - should give an exploitability of zero.
No. You can calculate it for the whole tree going to one river at a time (depth first). The imperfections would come from not perfect preflop/flop/turn strategies and from not getting the rivers exactly (just replicate the way the bot is playing). It's easy to get rivers almost perfectly although I guess they are not doing it because it's hard to imagine some of the plays would occur no matter what the ranges were.
I mean, it really is simple I am amazed you can do a poker AI project and not measure this.
Tbh the conversation should go like that:
-"I have this Nash equilibrium estimation algorithm"
-"great, how good is it?". "I think it's pretty good! I am convinced it's great!"
-"What's the number though?"
-"Well we didn't measure but we are doing it for 4 years now!"
-F-, come back next year
Again, it makes 0 sense to optimize for something you can't measure. It's like trying to play high stakes poker not knowing if straight beats 3 of a kind.
This is bad but claiming anything about "pretty good estimation" while not measuring it is well... not really something you should say.
Last edited by punter11235; 05-07-2015 at 06:36 AM.