
Re: probability question about the dice game
Posted:
Feb 14, 2013 1:05 PM


pepstein5@gmail.com writes: > 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: > > > > > > > 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.
Which you later corrected to the reciprocal X/(X + Y); probabilities need to be between 0 and 1. But then it seems to me that Ullrich says the same, and that's also what I meant.
My expression above is still off. I appreciate the input. Thanks.
> "X to Y against" means that the probability of winning is (X + Y)/Y > and X is larger than Y.
The probability should be X/(X + Y). Also, X _smaller_ than Y, so that the odds are against one who bets on the outcome associated with X, right?
> "X to Y on" means that the probability of winning is (X + Y)/Y and X > is less than Y.
Similarly, X/(X + Y) but now X _larger_ than Y, right?
> 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".
Odds are treated as the numerical fractions suggested by the notation when one calculates things like log odds. Would X/Y be read "X to Y" in that context?
Some day I'll dig up the books where I've seen these used. Mainly a collection of I.J. Good and the posthumous E.T. Jaynes volume.

