Probabilities of Winning a Certain Carnival Game

Abstract

A carnival game is described in which a player rolls eight dice or eight marbles into holes. To win, the player must obtain a favorable outcome on a number of plays. The probability distribution for the outcome of a single play is discussed. The distribution of a winning combination of outcomes is discussed and approximated. These probabilities show that the game is essentially unbeatable.

Key Words:

• Carnival games
• Win probabilities
• Sums of random variables
• Markov chains