search

bupticybee / TexasSolver

🚀 A very efficient Texas Holdem GTO solver :spades::hearts::clubs::diamonds:
https://bupticybee.github.io/texassolver_page
GNU Affero General Public License v3.0
1.65k stars 295 forks source link

What does a negative exploitability mean? #176

Closed aipoker39 closed 10 months ago

aipoker39 commented 10 months ago

Thanks for the project, I ran the solver using the default configs in README, and it output the following:

...
Iter: 81
player 0 exploitability 6.5465393
player 1 exploitability -6.1164308
Total exploitability 0.43010855 precent
time used: 299.299
...

As you can see, the exploitability of player 1 is negative. What does that mean? Thanks in advance.

bupticybee commented 10 months ago

because in this case, the best exploitibility you can get is negetive, for player1, but for all player, it sums to be positive for sure.

aipoker39 commented 10 months ago

What's the definition of exploitability? My understanding is that it indicates the distance between the strategy and nash equilibrium. How can the distance be a negative number?

bupticybee commented 10 months ago

What's the definition of exploitability? My understanding is that it indicates the distance between the strategy and nash equilibrium. How can the distance be a negative number?

In the above log,

player 0 exploitability means how much you can get from p0 if your strategy is optimal player 1 exploitability means how much you can get from p1 if your strategy is optimal

So it can be negative, because even if your strategy is optimal, you can still have a negative ev against a single player.

Since you can never know what a nash equilibrium is when running cfr , you can't calculate what you describe "the distance between stratgy and nash".

aipoker39 commented 10 months ago

Thank you for the prompt and clear explanation; it has greatly helped my understanding. As I delve deeper into this repository and the codebase, having comprehensive documentation on the code and its underlying algorithms would be immensely beneficial. Regardless, I truly appreciate your efforts and contributions. Thanks again!

bupticybee commented 10 months ago

Thanks. Closing since the issue is resolved. Reopen if necessary.