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

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Paul

Posts: 401
Registered: 7/12/10
Re: probability question about the dice game
Posted: Feb 14, 2013 11:17 AM
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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 Epstein



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