We study a type of generalized recursive game introduced by Castronova, Chen, and Zumbrun featuring increasing stakes, with an emphasis on continuous guts poker and $1$ v. $n$ coalitions. Our main results are to develop practical numerical algorithms with rigorous underlying theory for the approximation of optimal mutiplayer strategies, and to use these to obtain a number of interesting observations about guts. Outcomes are a striking 2-strategy optimum for $n$-player coalitions, with asymptotic advantage approximately $16\%$; convergence of Fictitious Play to symmetric Nash equilibrium; and a malevolent interactive $n$-player "bot" for demonstration.

翻译：我们研究的是卡斯特罗诺瓦、陈和宗布伦引入的一种普遍循环游戏,其特点是赌注不断增加,重点是连续的赌博和1美元对美元联盟。 我们的主要成果是开发实用的数字算法,其基础理论严格,以近似最佳的穆提亚战略,并用这些算法获得一些关于胆量的有趣观察。 结果对美元玩家联盟来说是惊人的2种最佳策略,无药可救的优势约为16美元;折叠游戏与对称纳什平衡的结合;以及一个用于示范的邪恶互动型美元玩家“机器人 ” ( 机器人 $n-player ) 。