Re: Question for the Mathematicians


"Greg Neill" <gneillRE@xxxxxxxxxxxxxxxx> wrote:
Big LN wrote:
Seasons Greetings all,

I'm looking for a formula in regards to the following:

Suppose there is a four horse race with the odds of 2/10, 3/10,
4/10 and
5/10
and payments are awarded to the first three across the line. What
amount
should
I bet on each horse to get the same profit no matter which horse
comes 4th
and misses out on the payment?

Eg. If I bet $116 on the 2/10, $108 on the 3/10, $100 on the 4/10
and $92
on
the 5/10 then I'll make an overall profit of $2.40 if the 2/10 misses
out,
$1.20 if the 3/10 misses, $1.60 if the 4/10 misses or $3.60 if the
5/10
misses.

However, I want to make the *same* overall profit regardless of
which
horse
misses out.

Therefore, what amount do I need to bet on each horse to achieve
this
outcome
and what is the formula used to work out such a result?

Thanks in advance.

'Onya

Given bets b1, b2, b3, b4 on horses with odds h1, h2, h3, h4, write
the expression for the profit for each of the four cases in terms
of those variables (you've obviously got such expressions as you've
provided sample results).

Set each of them equal to a constant profit value, P. Solve the four
equations for unknowns b1,...b4.

Actually, I haven't got any expressions. I'm just trialling and erroring figures
to get the best result. I've managed to get closer to the result by putting
27.92% of my bank on the 2/10, 25.79% on the 3/10, 23.93% on the 4/10 and 22.35%
on the 5/10. Like I said, trial and error.
However, I'm looking for the exact answer and a formula on how to do it for
these (and any other) four odds?
Having not done any maths for over 20 years, I need the help of you guys.

'Onya
.

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