Strongly Solving the Royal Game of Ur

We strongly solve three conjectured rule sets for the Royal Game of Ur: Finkel, Blitz, and Masters. For every reachable state, we compute the game-theoretic value, the first player’s probability of winning under optimal play, and an optimal move. From the initial position, these values are 51.54% for Finkel, 50.41% for Blitz, and 50.48% for Masters, implying a small first-player advantage in each variant. We obtain the solution maps using value iteration and the Bellman equations, verify them through convergence analysis and large-scale simulations, and describe practical optimizations that make the computation tractable. The same framework applies to other finite, enumerable variants, and the resulting maps are deployed on RoyalUr.net for optimal play, game review, and player feedback.