Date: Feb 14, 2013 1:05 PM
Author: Jussi Piitulainen
Subject: Re: probability question about the dice game

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.