# Adapting Beyond the Depth Limit: Counter Strategies in Large Imperfect Information Games

arXiv: https://arxiv.org/abs/2501.10464 · HTML: https://mlsanity.com/paper/2501.10464/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 12 references that are in the map.
- First posted on arXiv 15 Jan 2025.

## Builds on (most cited first, 3 of 3)

- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Solving Imperfect Information Games Using Decomposition](https://mlsanity.com/paper/1303.4441/) (2013)
- [Complexity and Algorithms for Exploiting Quantal Opponents in Large Two-Player Games](https://mlsanity.com/paper/2009.14521/) (2020)

## Built on by (most cited first, 2 of 2)

- [Agents That Certify Their Own Exploits: Confidence-Scheduled Restricted Responses for Safe Opponent Exploitation](https://mlsanity.com/paper/2607.28520/) (2026)
- [Look-ahead Reasoning with a Learned Model in Imperfect Information Games](https://mlsanity.com/paper/2510.05048/) (2025)

## Abstract (arXiv)

We study the problem of adapting to a known sub-rational opponent during online play while remaining robust to rational opponents. We focus on large imperfect-information (zero-sum) games, which makes it impossible to inspect the whole game tree at once and necessitates the use of depth-limited search. However, all existing methods assume rational play beyond the depth-limit, which only allows them to adapt a very limited portion of the opponent's behaviour. We propose an algorithm Adapting Beyond Depth-limit (ABD) that uses a strategy-portfolio approach - which we refer to as matrix-valued states - for depth-limited search. This allows the algorithm to fully utilise all information about the opponent model, making it the first robust-adaptation method to be able to do so in large imperfect-information games. As an additional benefit, the use of matrix-valued states makes the algorithm simpler than traditional methods based on optimal value functions. Our experimental results in poker and battleship show that ABD yields more than a twofold increase in utility when facing opponents who make mistakes beyond the depth limit and also delivers significant improvements in utility and safety against randomly generated opponents.