```Date: Feb 14, 2013 11:20 AM
Author: Paul
Subject: Re: probability question about the dice game

On Thursday, February 14, 2013 4:17:50 PM UTC, peps...@gmail.com wrote:> On Thursday, February 14, 2013 3:09:37 PM UTC, Jussi Piitulainen wrote:> > > David C. Ullrich writes:> > > > > > > > > > > > > On 14 Feb 2013 15:50:27 +0200, Jussi Piitulainen wrote:> > > > > > > > > > > > > > >starwayinc@gmail.com writes:> > > > > > > >> > > > > > > >> two players Ann and Bob roll the dice. each rolls twice, Ann wins if> > > > > > > >> her higher score of the two rolls is higher than Bobs, other wise> > > > > > > >> Bob wins. please give the analyse about what is the probability that> > > > > > > >> Ann will win the game> > > > > > > >>   > > > > > > > >> > > > > > > > Because> > > > > > > >> > > > > > > >   >>> from itertools import product> > > > > > > >   >>> die = {1,2,3,4,5,6}> > > > > > > >   >>> dice = set(product(die, die, die, die))> > > > > > > >   >>> sum(int(max(a,b) > max(c,d)) for a,b,c,d in dice)> > > > > > > >   505> > > > > > > >   >>> sum(int(max(a,b) <= max(c,d)) for a,b,c,d in dice)> > > > > > > >   791> > > > > > > > > > > > > > Cool.> > > > > > > > > > > > > > > I'd say her odds are 505 for and 791 against. I hope my gambling> > > > > > > > vocabulary is not too far off.> > > > > > > > > > > > > > The terminology would be "her odds of winning are 505 to 791".> > > > > > > > > > > > Thanks, that looks familiar. I'm sure I've also seen "for" (or maybe> > > > > > "on") and "against" _somewhere_ in such expressions.> > > > David Ullrich is wrong. "X to Y" means that the probability of winning is > > (X + Y)/Y.> > "X to Y against" means that the probability of winning is (X + Y)/Y and X is larger than Y.> > "X to Y on" means that the probability of winning is (X + Y)/Y and X is less than Y.  > > > > In this context "on" and "against" are redundant.  However, these words enable useful abbreviations as follows.  "Twos on" means " 1 to 2 " "Twos against" means "2 to 1".  You can also write a slash "/" instead of the word "to".> > > > Paul EpsteinSorry, I stated the reciprocals of the probabilities instead of the probabilities.  My previous posting becomes correct if you exchange the word "probability" with "the reciprocal of the probability".Paul Epstein
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