CFR without Unbiasedness: Deterministic Guarantees for Persistent Public-Chance Schedules

At a finite public-chance cut, counterfactual regret minimization (CFR) must choose how many outcomes to evaluate before each regret update. Exact evaluation processes the full cut at one strategy profile; persistent partial evaluation processes a fixed without-replacement order across evolving profiles. The latter covers every outcome once per epoch, yet its feedback is generally conditionally biased because earlier batches influence the profiles seen by later batches. We establish a deterministic target-transfer theorem for uniform, nonnested additive public cuts. The theorem bounds full-cut exploitability by regret on the delivered feedback and a public-debit term that couples prefix c...

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