At Least Two of Three
Three players agree on a strategy, after which each receives a hat that is red or blue, chosen independently by a fair coin. Each player sees the other two hats but not their own, and no communication is allowed once the hats are on. Simultaneously and silently, each player must guess the colour of their own hat (passing is not allowed). The team wins if at least two of the three guesses are correct. What is the largest possible probability of winning? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- One Hundred Hats 7.0/10
- Two Players, Five Colours 6.0/10
Source: Variant of the classic three-player hat-guessing game; original problem written for AxiomIQ.