Scoring formula for odds and probability

O

opc10

I have a scenario relating to betting odds which i'm trying to work ou
a
formula for, but i'm having some trouble...so here goes:

Lets assume a runner is 'even money' to win a race (IE: 1 to 1 odds).
His odds are displayed as $2.00 (This includes the $1 the punter ha
bet
on him, and the $1 profit the punter makes if the runner wins).

Now I give points to a runner depending where he finishes:
25 points for first
7.5 points for second
7.5 points for third.

Now Its easy to work out what a runners 'probabilty score' to WIN is:
EG: In the case of the $2.00 runner, its 12.5. (IE: He should wi
every
2nd race if he's even money so he'll get 25 points every 2 races.

But what i need is a formula to show what the 'probability point
score'
for a particular runner with the following criteria (Based on th
'Even
money' runner for the example):

His odds for running first are $2:00
His odds for running Either 1st, 2nd, or 3rd are $1.25 (1/4 of his odd
of
winning only).

I've deduced that the answer for the $2.00 runner is 14.75, because
out
of every 5 races he'll run 1st, 2nd, or 3rd, and every 2nd race he'l
win.

So over 10 races he runs 1st, 2nd , 3rd 8 times, and of these he win
5
times.
So its 5 x 25, plus 3 x 7.5 = 147.5/10 = 14.75.

To cut a long story short, how do i apply this logic/criteria to
runner
with any odds? (EG: $5.00 odds for a runner to win is $2.00 to ru
1st,
2nd, 3rd).

Hope i haven't over complicated things....thanks in advance
 

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