May the Best Bot Win: Variance and Sample Efficiency Across Poker Formats

How much simulation is required to distinguish poker agents depends strongly on the format being played. We benchmark matched agent evaluation across seven poker environments and ask both how large the simulation burden becomes and how much of it can be removed through variance reduction. At a common operational target of 1 BB/100 and 80% power, median played-hand requirements range from roughly 0.34 million for 4-max All-in-or-Fold to 20.5 million for NLHE Bomb Pot, with 4-max and 6-max NLHE requiring about 4.3 to 4.4 million. These are conditional benchmark requirements, not intrinsic difficulty rankings of the games.

The cost differences are associated with highly concentrated matched payoff distributions. Across the 100BB environments, blocks containing a pot of at least one starting stack account for 79 to 97% of squared deviation. Controlled NLHE interventions show that simulation burden also depends on stack depth, table size and the chosen effect-size scale.

Variance reduction can materially change the cost, but not uniformly. Exact all-in EV removes about 90% of variance in 8BB All-in-or-Fold, 28% at 20BB NLHE and 12% at 100BB NLHE. At 100BB, fitted AIVAT removes about 42%, but its approximately 1.72 times sample-efficiency gain is offset by an approximately 1.86 times simulation slowdown in our implementation.