Paul
Posts:
719
Registered:
7/12/10


Re: probability question about the dice game
Posted:
Feb 14, 2013 11:17 AM


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

