A repository for sharing mater's work in the related research in game AI. English is recommended for the readme file.
Pluribus does not use neural network: it completely uses CPU
It uses a tabular method to train. To cope with large state space, information abstraction is needed.
The use of CFR:
- Calculate the "blueprint" strategy: the exact strategy given by linear CFR
- Also used in depth-limited search. Authors assume each player can take on 4 prespecified strategies. But it's unclear whether they are randomly looking ahead or tree-searching.
Other details: The use of baffling: sample all possible hand (in the view of opponents), policy sould not differ too much on these hands
Same authors as Pluribus. Amricans really like Texas hold'em!
Similar techniques. CFR is in ramdom look ahead style.
Continual resolving: CFR-style look ahead and replace leaf node value with neural network evaluation A value function network tries to mimic the solved regret (AlphaZero style training)
Regret Minimization in Games with Incomplete Information
Prove CFR converges into
Convergence of Monte Carlo Tree Search in Simultaneous Move Games This proves certain forms of MCTS converges into approximate-Nash equilibrium.
Non-Asymptotic Analysis of Monte Carlo Tree Search The work show that MCTS, combined with nearest neighbor supervised learning, acts as a “policy improvement” operator
Information Set Monte Carlo Tree Search The work presents a very clever algorithm that combines sampling (determinization in their term) with tree search.
- Klaverjas.pdf: 一种流行于德语区的扑克游戏，按墩打，拣正分，只用 4x8=32 张牌，某些情况下要求必须要出比之前大的牌（这有点像斗地主）。这是一本书太长没必要看，只要看 Springer 上他们自己写的简介就够了 https://link.springer.com/chapter/10.1007/978-3-030-31978-6_9 。
- shuffle: 关于洗牌的一些研究，这是纯粹的概率论，但我觉得很有趣
- bayer92.pdf: 最主要的一篇文章，他论证了用 dovetail （燕尾，一种洗牌方法，最常见的分成两堆然后左右交错的洗法） 要洗8次才能洗匀，用石聚最喜欢的从中间抽出一部分放到最上面的方法要大约10000次，用桥牌比赛时摊开在桌子上揉的方法要好几分钟。他还描述了一种类似于相变的现象：在洗到七八次的时候牌的混乱程度（文章中有定义）突然就有一个上升。但是文章我有好几处看不懂，第二章那个魔术怎么变也就是他要引入的基础概念没看懂，定理3也没看懂。Youtube 上有文章作者亲身讲解，还挺清楚的 The Best (and Worst) Ways to Shuffle Cards - Numberphile。
- aldous86.pdf、0501401.pdf: 另外两篇与洗牌相关的文章，但我没看。
- 我想洗牌方面有两个自然的推广，第一是他们都没有考虑 (S13)^4 的对称群，这会让8次才能匀的结果降低。第二是将之应用于麻将机，麻将机要洗多久一直是各大厂家争论不休的问题，我们可以给出建议的值，最好还能演示洗牌时间不够+无穷好的记忆力可以明显提高胜率。