Rock-Paper-Scissors with Stakes
Two players play rock-paper-scissors once. The loser pays the winner an amount that depends on the winning hand: rock beating scissors is worth 1, paper beating rock is worth 2, and scissors beating paper is worth 3. Equal hands give 0. In the (unique) optimal mixed strategy, with what probability does a player throw rock? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- A Three-by-Three Value 6.0/10
- Making the Other Side Indifferent 6.0/10
- Hawk-Dove 6.0/10
Source: Weighted rock-paper-scissors is a standard variant in game-theory courses; stakes chosen for AxiomIQ. Statement written for AxiomIQ.