Paul
Posts:
492
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:
>
> > 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
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
|
|
