Nash equilibria

I see that SNGWIZ has a "Send to Nash Equilibrium Calculator" button now. I presume it's been there a while and I have just not noticed it.

I'm wondering anyone know how the Nash Equilibrium is calculated for each hand? The FAQ just says it's based on fictitious play, but offers no formulas.

As I understand it, fictitious play means they start with a random range for Player 1, determines the optimal range for Player 2 given Player 1's random range, then determines the optimal range for Player 1 given Player 2's range, then the optimal range for Player 2 given Player 1's new range (which will be different than Player 2's previous range), and so on until the ranges stop changing. Nash's Theorem says that the strategies obtained this way are going to be optimal for all the players. As you can see there's no way to write down a "formula" it's just the result of lots of computation.

Yeah I'd assume it's much easier to find the ranges that way, having found nash ranges for various stack sizes hu the other way.

Makes sense. I wonder how the evaluation process is so quick on HoldemResources.net: ICM Nash Calculator. I was thinking lookup tables, but is says this when I run it;

Runtime: 66ms [300 Iterations]