## Abstract

We consider a game with two piles in which two players take turns adding a or b chips, randomly and independently, to their respective piles. Here a, b are not necessarily positive. The player who collects at least n chips first wins the game. We derive general formulas for p_{n}, the probability of the second player winning the game by collecting n chips first, and give the calculation for the cases {a, b} = {−1, 1} and {−1, 2}. The latter case was considered by Wong and Xu. At the end, we derive a general formula for p_{n1},n_{2}, the probability of the second player winning the game by collecting n_{2} chips before the first player collects n_{1} chips.

Original language | English |
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Article number | 19.4.8 |

Journal | Journal of Integer Sequences |

Volume | 22 |

Issue number | 4 |

Publication status | Published - 2019 |

## Keywords

- Gosper’s algorithm
- Probability
- Take-away game

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics