Penney's Game
In Penney's Game, Player 1 picks a sequence of three coin flip outcomes (e.g. HHT). Player 2, knowing Player 1's choice, picks their own sequence of three. The player whose sequence appears first in an infinite series of fair coin flips wins. For how many of the 8 possible sequences can Player 2 always find a sequence that wins with probability greater than 1/2?
Related problems & prerequisites
Worth solving first
- St. Petersburg Paradox 5.0/10
Source: Introduced by Walter Penney (1969). Statement written for AxiomIQ.