Penney's game, named after its inventor Walter Penney, is a binary (head/tail) sequence generating game between two players. At the start of the game, the two players agree on the length of the sequences to be generated. This length is usually taken to be three, but can be any larger number. Player A then selects a sequence of heads and tails of the required length, and shows this sequence to player B. Player B then selects another sequence of heads and tails of the same length. Subsequently, a fair coin is tossed until either player A's or player B's sequence appears as a consecutive subsequence of the coin toss outcomes. The player whose sequence appears first wins.
Provided sequences of at least length three are used, the second player (B) has an edge over the starting player (A). This is because the game is nontransitive such that for any given sequence of length three or longer one can find another sequence that has higher probability of occurring first.
Famous quotes containing the word game:
“Neighboring farmers and visitors at White Sulphur drove out occasionally to watch those funny Scotchmen with amused superiority; when one member imported clubs from Scotland, they were held for three weeks by customs officials who could not believe that any game could be played with such elongated blackjacks or implements of murder.”
—For the State of West Virginia, U.S. public relief program (1935-1943)