Companion

Default learning rate from the EXP4 regret analysis: sqrt(ln(N) / (T * K)) collapsed to a horizon-free form using T = 1 as a starting heuristic.

Default exploration mix min(1, eta).

min(1, K * eta) is the textbook rule only while eta still carries the 1/T horizon term. With the horizon-free defaultEta above it works out to sqrt(K * ln N), at least 1.177 for any real configuration, so it would clamp to exactly 1.0 and leave playDistribution uniform. Pass gamma = 1.0 explicitly for pure uniform sampling.