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Topic: probability question about the dice game
Replies: 21   Last Post: Feb 18, 2013 2:47 PM

 Messages: [ Previous | Next ]
 Paul Posts: 780 Registered: 7/12/10
Re: probability question about the dice game
Posted: Feb 14, 2013 11:20 AM

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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> > > >
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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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> > > >
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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

Date Subject Author
2/14/13 Jussi Piitulainen
2/14/13 David C. Ullrich
2/14/13 Jussi Piitulainen
2/14/13 Paul
2/14/13 Paul
2/14/13 Jussi Piitulainen
2/14/13 Paul
2/14/13 quasi
2/15/13 David C. Ullrich
2/15/13 Paul
2/15/13 Paul
2/15/13 David C. Ullrich
2/14/13 bacle
2/18/13 Bacle H
2/14/13 RGVickson@shaw.ca
2/14/13 Jussi Piitulainen
2/14/13 RGVickson@shaw.ca
2/14/13 Jussi Piitulainen
2/14/13 quasi
2/15/13 Frederick Williams
2/14/13 RGVickson@shaw.ca