Rummy is a family of melding games whose enduring appeal lies in the tension between probabilistic uncertainty and combinational structure. Each hand asks players to transform a noisy, partially observed state into ordered sets and runs, using draws, discards, and memory to maximize expected value. Theoretical analysis begins with the deck’s entropy: hidden information is concentrated in opponents’ hands and the stock, while mutual information grows through discard signals. Optimal play balances exploitation of immediate meld opportunities with exploration that preserves flexible “live” cards, a dynamic akin to frontiers in reinforcement learning. From a combinatorial viewpoint, a hand okrummy can be modeled as a dynamic partition problem under stochastic arrivals. Feasible partitions correspond to meld covers