Monty Python and the Probability of Winning the Holy Grail

Many popular games that people play at home, such as board and card games, provide a basis for interesting problems that can be solved using combinatorial analysis. When thinking about activities such as choosing cards from a standard deck or drawing Scrabble tiles from a sack, we can calculate the probabilities of specific events associated with these activities by employing basic counting techniques. It is also useful to consider another game of chance—one that I encountered during a visit to a casino—in which players must choose cells from a rectangular grid to reveal symbols that are hidden in the cells. The cells that the player chooses determine which of several possible prizes the player will win. The number of cells that the player must choose to determine the prize is not known in advance.

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