A note on the first occurrence of strings

Ying Chao Hung, Robert W. Chen, Alan Zame, May Ru Chen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider the context of a three-person game in which each player selects strings over {0, 1} and observe a series of fair coin tosses. The winner of the game is the player whose selected string appears first. Recently, Chen et al. [4] showed that if the string length is greater and equal to three, two players can collude to attain an advantage by choosing the pair of strings 11...10 and 00...01. We call these two strings "complement strings", since each bit of one string is the complement bit of the corresponding bit of the other string. In this note, we further study the property of complement strings for three-person games. We prove that if the string length is greater than five and two players choose any pair of complement strings (except for the pair 11...10 and 00...01), then the third player can always attain an advantage by choosing a particular string.

Original languageEnglish (US)
Pages (from-to)1-8
Number of pages8
JournalElectronic Journal of Combinatorics
Volume17
Issue number1
DOIs
StatePublished - 2010

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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