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We recall a combinatorial derivation of the functions generating the probability of winning for each of many participants of the Penney game and show a generalization of the Conway formula for this case.
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Penney’s game in didactics

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This paper describes, at elementary level, Penney‟s game using the example of two players and a symmetric coin. It also provides a generalization for an unlimited number of players and coins, as an example, not an intuitive aspect of the teaching probability theory.
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