(eng): Ultimate Game serves for extensive studies of various aspects of human decision making. The current paper contribute to them by designing proposer optimising its policy using Markov-decision-process (MDP) framework combined with recursive Bayesian learning of responder’s model. Its foreseen use: i) standardises experimental conditions for studying rationality and emotion-influenced decision making of human responders; ii) replaces the classical game-theoretical design of the players’ policies by an adaptive MDP, which is more realistic with respect to the knowledge available to individual players and decreases player’s deliberation effort; iii) reveals the need for approximate learning and dynamic programming inevitable for coping with the curse of dimensionality; iv) demonstrates the influence of the fairness attitude of the proposer on the game course; v) prepares the test case for inspecting exploration-exploitation dichotomy.