On the Duration of the Problem of the Points.

Abstract

We consider an r-player version of the famous problem of the points which was the stimulus for the correspondence between Pascal and Fermat in the seventeenth century. At each play of a game, exactly one of the players wins a point - player i winning with probability p sub i. The game ends the first time a player has accumulated his required number of points - this requirement being n sub i for player i. Our main result is to show that N, the total number of plays, is an increasing failure rate random variable. In addition, we prove some Schur convexity results regarding P(n < or = k) as a function of p (for n sub i = n) and as a function of n (for p sub i = 1/r). (Author)

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1978
Accession Number
ADA066563

Entities

People

  • Gideon Weiss
  • Mehrdad Shahshahani
  • Sheldon M. Ross

Organizations

  • University of California, Berkeley

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  • Materials and Manufacturing Processes

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