Re: Incoherent Odds?

matt271829-news@xxxxxxxxxxx wrote:
Protoman wrote:
What are "incoherent odds"; I've only heard of them in an unfair
wagering system called a "Dutch book".

I confess I'd never heard of the term, but you might find some relevant
info at
http://en.wikipedia.org/wiki/Coherence_%28philosophical_gambling_strategy%29

And what's the difference
between "odds" and "probability"? And how do you calculate the
probability of odds like "3:2 against"; Is it the same as "4:1
against", just take the decimal odds (5) and take the reciprocal of
that (.20)? Thanks!!!!!

Probability is a measurement of the likelihood of an event happenning.
If you carry out n identical trials, and let s be the number of times
that the event occurs, then the probability of the event happening is
the limit of the ratio s/n, as n becomes indefinitely large. "Odds" are
just a practical system designed to make it easy(ier) to work out how
much to pay as winnings (in the old days, before calculators and
computers).

.... oh, and, in amongst all my other waffle, I forgot to mention here
that, while probability is the ratio of successes to total number of
trials, odds (against) are the ratio of failures to successes (where
"success" means the event happens, and "failure" means it doesn't).

So, for example, a probability of 1/5 means that out of five trials you
get, "on average", one success. (Fair) odds of 4:1 mean that on average
you get four failures for every one success; therefore in five trials
you get on average four failures and one success, meaning a ratio of
successes to trials of 1/5 - i.e. a probability of 1/5 as before.

Similarly, (fair) odds of 3:2 mean that you expect three failures for
every two successes. So, out of five trials you get "on average" three
failures and two successes, making a probability of 2/5. This sort of
working results in the same conversion formula that I quoted later in
the post.

You can also imagine "laying odds" as meaning literally laying your
money on the table. If I offer you odds of 4:1 then I put down $4 for
every $1 of yours (hence "four to one"), and the winner takes all. If
the odds are fair then on average, over five games, you win once
netting you 1 x $4, and I win four times, netting me 4 x $1. So we're
all square.

.

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