On Thursday, February 14, 2013 6:05:23 PM UTC, Jussi Piitulainen wrote: > email@example.com writes: ... > > > > > > 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. >
No, the reciprocal of (X + Y)/ Y is Y/(X + Y) which is what I should have said. Ullrich wrongly said X/(X + Y). > > 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? > No, Y/(X + Y) is correct.
> > "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.