Supplemental Material for Monte Carlo Sampling for Regret Minimization in Extensive Games

The supplementary material presented here first presents a detailed description of the MCCFR algorithm. We then give proofs to Theorems 3, 4, and 5 from the submission Monte Carlo Sampling for Regret Minimization in Extensive Games. We begin with some preliminaries, then prove a general result about all members of the MCCFR family of algorithms (Theorem 18 in Section 6). We then use that result to prove bounds for the MCCFR variants (Theorems 19 and 20 in Section 7). We finally prove the tightened bound for vanilla CFR (Theorem 21 in Section 8).