### 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 language | English (US) |
---|---|

Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Electronic Journal of Combinatorics |

Volume | 17 |

Issue number | 1 |

State | Published - Aug 20 2010 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Geometry and Topology
- Theoretical Computer Science

### Cite this

*Electronic Journal of Combinatorics*,

*17*(1), 1-8.

**A note on the first occurrence of strings.** / Hung, Ying Chao; Chen, Robert W.; Zame, Alan; Chen, May R.

Research output: Contribution to journal › Article

*Electronic Journal of Combinatorics*, vol. 17, no. 1, pp. 1-8.

}

TY - JOUR

T1 - A note on the first occurrence of strings

AU - Hung, Ying Chao

AU - Chen, Robert W.

AU - Zame, Alan

AU - Chen, May R.

PY - 2010/8/20

Y1 - 2010/8/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77955635140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955635140&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77955635140

VL - 17

SP - 1

EP - 8

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1

ER -