English

Probabilistic chip-collecting games with modulo winning conditions

Combinatorics 2022-10-06 v1

Abstract

Let aa, bb, and nn be integers with 0<a<b<n0<a<b<n. In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects aa chips or bb chips. If Alice collects aa chips, then Bob collects bb chips, and vice versa. A player is announced the winner when they have accumulated a number of chips that is a multiple of nn. In this paper, we settle two conjectures from the literature related to this game.

Keywords

Cite

@article{arxiv.2201.10506,
  title  = {Probabilistic chip-collecting games with modulo winning conditions},
  author = {Joshua Harrington and Xuwen Hua and Xufei Liu and Alex Nash and Rodrigo Rios and Tony W. H. Wong},
  journal= {arXiv preprint arXiv:2201.10506},
  year   = {2022}
}
R2 v1 2026-06-24T09:02:25.911Z