Paul
Posts:
258
Registered:
7/12/10
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Re: probability question about the dice game
Posted:
Feb 14, 2013 4:34 PM
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On Thursday, February 14, 2013 6:05:23 PM UTC, Jussi Piitulainen wrote:
> pepstein5@gmail.com writes:
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> >
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> > David Ullrich is wrong. "X to Y" means that the probability of
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> > winning is (X + Y)/Y.
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> Which you later corrected to the reciprocal X/(X + Y); probabilities
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> need to be between 0 and 1. But then it seems to me that Ullrich says
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> the same, and that's also what I meant.
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No, the reciprocal of (X + Y)/ Y is Y/(X + Y) which is what I should have said.
Ullrich wrongly said X/(X + Y).
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> My expression above is still off. I appreciate the input. Thanks.
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> > "X to Y against" means that the probability of winning is (X + Y)/Y
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> > and X is larger than Y.
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> The probability should be X/(X + Y). Also, X _smaller_ than Y, so that
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> the odds are against one who bets on the outcome associated with X,
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> right?
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No, Y/(X + Y) is correct.
> > "X to Y on" means that the probability of winning is (X + Y)/Y and X
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> > is less than Y.
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> Similarly, X/(X + Y) but now X _larger_ than Y, right?
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> > In this context "on" and "against" are redundant. However, these
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> > words enable useful abbreviations as follows. "Twos on" means " 1
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> > to 2 " "Twos against" means "2 to 1". You can also write a slash
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> > "/" instead of the word "to".
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> Odds are treated as the numerical fractions suggested by the notation
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> when one calculates things like log odds. Would X/Y be read "X to Y"
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> in that context?
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> Some day I'll dig up the books where I've seen these used. Mainly a
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> collection of I.J. Good and the posthumous E.T. Jaynes volume.
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