```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); probabilitiesneed to be between 0 and 1. But then it seems to me that Ullrich saysthe 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 thatthe 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 notationwhen 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 acollection of I.J. Good and the posthumous E.T. Jaynes volume.
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