A probabilistic two-pile game

Ho Hon Leung, Thotsaporn Aek Thanatipanonda

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 pn, 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 pn1,n2, the probability of the second player winning the game by collecting n2 chips before the first player collects n1 chips.

Original languageEnglish
Article number19.4.8
JournalJournal of Integer Sequences
Volume22
Issue number4
Publication statusPublished - 2019

Keywords

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Fingerprint

Dive into the research topics of 'A probabilistic two-pile game'. Together they form a unique fingerprint.

Cite this