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:
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> > David C. Ullrich writes:
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> > > On 14 Feb 2013 15:50:27 +0200, Jussi Piitulainen wrote:
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> > > >starwayinc@gmail.com writes:
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> > > >> two players Ann and Bob roll the dice. each rolls twice, Ann wins if
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> > > >> her higher score of the two rolls is higher than Bobs, other wise
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> > > >> Bob wins. please give the analyse about what is the probability that
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> > > >> Ann will win the game
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> > > >>
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> > > > Because
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> > > > >>> from itertools import product
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> > > > >>> die = {1,2,3,4,5,6}
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> > > > >>> dice = set(product(die, die, die, die))
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> > > > >>> sum(int(max(a,b) > max(c,d)) for a,b,c,d in dice)
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> > > > 505
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> > > > >>> sum(int(max(a,b) <= max(c,d)) for a,b,c,d in dice)
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> > > > 791
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> > > Cool.
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> > > > I'd say her odds are 505 for and 791 against. I hope my gambling
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> > > > vocabulary is not too far off.
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> > > The terminology would be "her odds of winning are 505 to 791".
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> > Thanks, that looks familiar. I'm sure I've also seen "for" (or maybe
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> > "on") and "against" _somewhere_ in such expressions.
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> David Ullrich is wrong. "X to Y" means that the probability of winning is
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> (X + Y)/Y.
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> "X to Y against" means that the probability of winning is (X + Y)/Y and X is larger than Y.
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> "X to Y on" means that the probability of winning is (X + Y)/Y and X is less than Y.
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> 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".
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> Paul Epstein


Sorry, 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