The asymptotics of group Russian roulette
T van de Brug, W Kager, R Meester - arXiv preprint arXiv:1507.03805, 2015 - arxiv.org
T van de Brug, W Kager, R Meester
arXiv preprint arXiv:1507.03805, 2015•arxiv.orgWe 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\to\infty $, and
becomes asymptotically periodic and continuous on the $\log n $ scale, with period 1.
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\to\infty $, and
becomes asymptotically periodic and continuous on the $\log n $ scale, with period 1.
We study the group Russian roulette problem, also known as the shooting problem, defined as follows. We have 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 of having no survivors does not converge as , and becomes asymptotically periodic and continuous on the scale, with period 1.
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