The backwards induction method due to Bellman~\cite{bellman1952theory} is a popular approach to solving problems in optimiztion, optimal control, and many other areas of applied math. In this paper we analyze the backwords induction approach, under min/max conditions. We show that if the value function is has strictly positive derivatives of order 1-4 then the optimal strategy for the adversary is Brownian motion. Using that fact we analyze different potential functions and show that the Normal-Hedge potential is optimal.

翻译：Bellman ⁇ cite{bellman{bellman1952theory} 的后向上岗方法是一种解决优化、最佳控制和许多其他应用数学领域问题的流行方法。 在本文中,我们分析了在分钟/最大条件下的后文上岗方法。 我们显示,如果价值函数具有第1-4号命令的绝对正衍生物,那么对手的最佳策略就是布朗运动。 我们利用这一事实分析不同的潜在功能,并显示正常- 隐藏潜力是最佳的。