Functions
defaultEta
Horizon-free default eta = sqrt(ln(K) / K).
defaultGamma
Horizon-free default exploration mix min(1, eta).
The textbook mixing rule min(1, K * eta) holds only when eta is the horizon-scaled sqrt(ln K / (K T)). Against the horizon-free eta above, K * eta is sqrt(K * ln K), at least 1.177 for every K >= 2, so it would clamp to exactly 1.0 at every arm count and collapse playDistribution to uniform. Using eta itself keeps the same "explore less as evidence per arm grows" shape and tops out at 0.59 for two arms, so it cannot saturate. Pass gamma = 1.0 explicitly for pure uniform sampling.