Mathematics – Probability
Scientific paper
2009-06-08
The Mathematical Intelligencer 32 (2010) (4) 44-48
Mathematics
Probability
5 pages; slight revision of original
Scientific paper
It was widely reported in the media that, on 23 May 2009, at the Borgata Hotel Casino & Spa in Atlantic City, Patricia DeMauro, playing craps for only the second time, rolled the dice for four hours and 18 minutes, finally sevening out at the 154th roll, a world record. Initial estimates of the probability of this event were erroneous, but consensus was reached within days: one chance in 5.6 billion. More generally, what is P(L \ge n), where the random variable L denotes the length of the shooter's hand (154 in Ms. DeMauro's case) and n is a positive integer? It is well known that these probabilities can be derived recursively or by Markov chain methods. Our aim here is to give an explicit closed-form expression for them, showing that the distribution of L is a linear combination (not a convex combination) of four geometric distributions.
Ethier S. N.
Hoppe Fred M.
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