# Outer-Learning Framework for Playing Multi-Player Trick-Taking Card Games: A Case Study in Skat

arXiv: https://arxiv.org/abs/2512.15435 · HTML: https://mlsanity.com/paper/2512.15435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Deep Counterfactual Regret Minimization](https://mlsanity.com/paper/1811.00164/) (2018)
- [The αμ Search Algorithm for the Game of Bridge](https://mlsanity.com/paper/1911.07960/) (2019)
- [Competitive Bridge Bidding with Deep Neural Networks](https://mlsanity.com/paper/1903.00900/) (2019)
- [Improving Search with Supervised Learning in Trick-Based Card Games](https://mlsanity.com/paper/1903.09604/) (2019)
- [Bidding in Spades](https://mlsanity.com/paper/1912.11323/) (2019)
- [Learning Policies from Human Data for Skat](https://mlsanity.com/paper/1905.10907/) (2019)
- [Policy Based Inference in Trick-Taking Card Games](https://mlsanity.com/paper/1905.10911/) (2019)
- [Can Large Language Models Master Complex Card Games?](https://mlsanity.com/paper/2509.01328/) (2025)
- [Building a Computer Mahjong Player via Deep Convolutional Neural Networks](https://mlsanity.com/paper/1906.02146/) (2019)
- [Set-Based Retrograde Analysis: Precomputing the Solution to 24-card Bridge Double Dummy Deals](https://mlsanity.com/paper/2411.09089/) (2024)
- [Transformer Based Planning in the Observation Space with Applications to Trick Taking Card Games](https://mlsanity.com/paper/2404.13150/) (2024)

## Abstract (arXiv)

In multi-player card games such as Skat or Bridge, the early stages of the game, such as bidding, game selection, and initial card selection, are often more critical to the success of the play than refined middle- and end-game play. At the current limits of computation, such early decision-making resorts to using statistical information derived from a large corpus of human expert games. In this paper, we derive and evaluate a general bootstrapping outer-learning framework that improves prediction accuracy by expanding the database of human games with millions of self-playing AI games to generate and merge statistics. We implement perfect feature hash functions to address compacted tables, producing a self-improving card game engine, where newly inferred knowledge is continuously improved during self-learning. The case study in Skat shows that the automated approach can be used to support various decisions in the game.