# Equilibrium Approximation Quality of Current No-Limit Poker Bots

arXiv: https://arxiv.org/abs/1612.07547 · HTML: https://mlsanity.com/paper/1612.07547/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2016.

## Built on by (most cited first, 3 of 3)

- [Finding mixed-strategy equilibria of continuous-action games without gradients using randomized policy networks](https://mlsanity.com/paper/2211.15936/) (2022)
- [ApproxED: Approximate exploitability descent via learned best responses](https://mlsanity.com/paper/2301.08830/) (2023)
- [Beyond Outcome-Based Imperfect-Recall: Higher-Resolution Abstractions for Imperfect-Information Games](https://mlsanity.com/paper/2510.15094/) (2025)

## Abstract (arXiv)

Approximating a Nash equilibrium is currently the best performing approach for creating poker-playing programs. While for the simplest variants of the game, it is possible to evaluate the quality of the approximation by computing the value of the best response strategy, this is currently not computationally feasible for larger variants of the game, such as heads-up no-limit Texas hold'em. In this paper, we present a simple and computationally inexpensive Local Best Response method for computing an approximate lower bound on the value of the best response strategy. Using this method, we show that existing poker-playing programs, based on solving abstract games, are remarkably poor Nash equilibrium approximations.