How Does a solver calculate the exact frequencies for each combo? - Poker Theory

Two Plus Two Forums Poker Strategy Poker Theory & GTO

How Does a solver calculate the exact frequencies for each combo?

Post Reply Subscribe

...

01-07-2022 , 02:25 AM

Philthy_Phish

newbie

Join Date: Aug 2021 Posts: 19

So I understand that the EV of betting a specific combo is the weighted sum of betting vs each combo in villain's range. But how does it calculate the exact frequency to bet each combo? I imagine calculating the weighted sum of betting 1% frequency, 2% frequency etc. for each combo would be exhaustive but I can't intuitively figure out how else it would find the optimal frequency.

EDIT: I forgot Alpha and Omega exist. My bad

Last edited by Philthy_Phish; 01-07-2022 at 02:34 AM.

Quote

01-07-2022 , 04:17 AM

tombos21

veteran

Join Date: Sep 2018 Posts: 2,120

It's not something you find with manual math. It's something you find with an iterative algorithm.

IP and OOP start with random strategies.
Now lock IP's strategy and let OOP exploit it.
Now lock OOP's new strategy and let IP exploit it.
Now lock IP's new strategy and let OOP exploit it.
Repeat until Nash.

This method slowly shifts frequencies towards something that is unexploitable. A solver is way more precise than a human. It will mix to avoid creating exploitable blocker weaknesses. It perfectly balances value, bluffs, calls and folds. It has good board coverage on different runouts. This is far too complex to solve manually.

The truth is that the way you mix one hand isn't really important. There are countless strategies that are extremely close to unexploitable using different mixtures. What actually matters is the overall range construction.

Last edited by tombos21; 01-07-2022 at 04:29 AM.

Quote

01-07-2022 , 09:22 AM

Brokenstars

Verified Coach NLHE

Join Date: Jul 2012 Posts: 16,323

Quote:

Originally Posted by tombos21

This is a great post.

Quote

01-07-2022 , 02:18 PM

Philthy_Phish

newbie

Join Date: Aug 2021 Posts: 19

Quote:

Originally Posted by tombos21

It's not something you find with manual math. It's something you find with an iterative algorithm.

IP and OOP start with random strategies.
Now lock IP's strategy and let OOP exploit it.
Now lock OOP's new strategy and let IP exploit it.
Now lock IP's new strategy and let OOP exploit it.
Repeat until Nash.

Ah I see, that makes perfect sense. Thanks a lot!

Quote

01-07-2022 , 03:12 PM

aner0

Verified Coach NLHE

Join Date: Oct 2013 Posts: 3,795

Quote:

Originally Posted by Philthy_Phish

It's an iterative process, not an equation. Basically the solver tries a bunch of different stuff until it doesn't lose much EV

Quote

Post Reply Subscribe

...