Odds are multiplicative in the following sense, useful in some types of
betting arrangements.
If the odds of one bet are 4 to 3 and of the next bet 3 to 2 then the odds
of both bets are the product 4*3 to 3*2 or 2 to 1. This is useful in some
horse racing bets where the second (and even more) bets are made
sequentially provided the earlier bets are winners for the gambler (placed
with the bookmaker).
Odds have a cultural history that seems to be lost. They were the common
form of gambling until quite recently, when even odds bets with point
spreads became common for such sports as basketball and football. Odds
require a strong facility with arithmetic when there are multiple results,
such as in a horse race. There, as always, the odds are constrained by the
usual requirement that the corresponding probabilities must still add to
one, at least for fair bets. Imposing this requirement "on the fly" when a
bookmaker changes the odds on a horse seems difficult unless there were some
quick simple rules of thumb that were part of bookmakers' lore. Those rules
of thumb would have included the profit margin for the bookie automatically,
making all the bets slightly, but fairly evenly, unfair for the bettor. If
anyone knows of such rules I would appreciate hearing them.
Regards,
David
David W. Smith, Ph.D., M.P.H.
(518) 439-6421
45 The Crosway
Delmar, NY 12054
[EMAIL PROTECTED]
----- Original Message -----
From: "Brad Branford" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Saturday, February 23, 2002 9:49 AM
Subject: Re: odds vs probabilities
> probabilities. I know that probs have a problem in that they don't
> make multiplicative sense:
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