The Asymptotics of Group Russian Roulette

W. Kager, T. van de Brug, R.W.J. Meester

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We study the group Russian roulette problem, also known as the
shooting problem, defined as follows. We have n armed people in a room. At
each chime of a clock, everyone shoots a random other person. The persons shot
fall dead and the survivors shoot again at the next chime. Eventually, either
everyone is dead or there is a single survivor. We prove that the probability p_n
of having no survivors does not converge as n → ∞, and becomes asymptotically
periodic and continuous on the log n scale, with period 1.
Original languageEnglish
Pages (from-to)35-66
Number of pages32
JournalMarkov Processes and Related Fields
Issue number1
Publication statusPublished - 2017


  • group Russian roulette
  • shooting problem
  • non-convergence
  • coupling
  • asymptotic periodicity and continuity


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