# PokaiTrainer: Scaling Equilibrium Search to Competitive Pok'emon VGC

arXiv: https://arxiv.org/abs/2608.29197 · HTML: https://mlsanity.com/paper/2608.29197/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Mastering the Game of Stratego with Model-Free Multiagent Reinforcement Learning](https://mlsanity.com/paper/2206.15378/) (2022)
- [Combining Deep Reinforcement Learning and Search for Imperfect-Information Games](https://mlsanity.com/paper/2007.13544/) (2020)
- [Solving Imperfect-Information Games via Discounted Regret Minimization](https://mlsanity.com/paper/1809.04040/) (2018)
- [Safe and Nested Subgame Solving for Imperfect-Information Games](https://mlsanity.com/paper/1705.02955/) (2017)
- [Human-Level Performance in No-Press Diplomacy via Equilibrium Search](https://mlsanity.com/paper/2010.02923/) (2020)
- [PokeLLMon: A Human-Parity Agent for Pokemon Battles with Large Language Models](https://mlsanity.com/paper/2402.01118/) (2024)
- [Student of Games: A unified learning algorithm for both perfect and imperfect information games](https://mlsanity.com/paper/2112.03178/) (2021)
- [Pok'eChamp: an Expert-level Minimax Language Agent](https://mlsanity.com/paper/2503.04094/) (2025)
- [Human-Level Competitive Pok'emon via Scalable Offline Reinforcement Learning with Transformers](https://mlsanity.com/paper/2504.04395/) (2025)
- [VGC-Bench: Towards Mastering Diverse Team Strategies in Competitive Pok'emon](https://mlsanity.com/paper/2506.10326/) (2025)
- [Convergence of Monte Carlo Tree Search in Simultaneous Move Games](https://mlsanity.com/paper/1310.8613/) (2013)

## Abstract (arXiv)

Decision-time equilibrium search carried poker to superhuman play, but it has so far relied on tractable subgames: a handful of actions per decision, chance confined to card deals, one player moving at a time. Competitive Pok'emon in its official doubles format (VGC) breaks all three assumptions at once. Both players act simultaneously from joint menus in the hundreds, each joint action resolves to hundreds of stochastic outcomes, and the opponent's reserves and stat allocations are hidden. No prior Pok'emon agent performs equilibrium search, and whether it scales to this regime was open; we show that it does, and report what it took. PokaiEngine, our Rust battle engine, enumerates a joint action's full weighted outcome distribution in one pass, at ~99% parity with Pok'emon Showdown and a fraction of the cost of sampling it. PokaiTrainer adapts Student of Games to this scale and trains it by self-play over hundreds of human teams. Each decision is solved by counterfactual regret minimization as a Bayesian matrix game over public belief states, subgames grow under an explicit compute budget, and value targets are harvested from the interior of every solve and grounded by realized outcomes. The strength is in the search. The network's policy alone loses even to a shallow heuristic search. PokaiTrainer is, to our knowledge, the first VGC agent rated on the live Showdown ladder. Under open team sheets it wins 59% of 150 best-of-three sets against a human field averaging ~1320 Elo, holds a 1350-1400 Elo band, and at its peak reached 1492 Elo, entering the format's top 500.