Bet Calculation Problem?

Question

If i wish to place 2 bets......of which only one can win.....

1 at a probable payout of $2.25, and the other at a probable payout of $2.95

How much do I have to bet on each of these so that the one winner (which will eliminate the other) will give me a profit of $100.00 AFTER covering the cost of both bets?

What is the formula for figuring this out?

What type betting calculator can compute this?

Thank you.

Answer 1

You set up two simultaneous equations:

On the one with a payout of 2.25 we bet A, on the other we bet B. Our total return therefore needs to be:

A + B + 100

If A wins:

A + B + 100 = A * 2.25 (eq 1)

If B wins:

A + B + 100 = B * 2.95 (eq 2)

Subtract eq 2 from eq 1 and we get:

A + B + 100 = A * 2.25 (eq 1)
A + B + 100 = B * 2.95 (eq 2)
----------------------------------------------------
0 = 2.25A - 2.95B
or
2.25A=2.95B
A = (2.95/2.25)B (eq 3)

Add eq 1 and eq 2 and we get:

A + B + 100 = A * 2.25 (eq 1)
A + B + 100 = B * 2.95 (eq 2)
----------------------------------------------------
2A +2B +200 = 2.25A + 2.95B

Substitute in eq 3:

2(2.95/2.25)B + 2B + 200 = 2.25(2.95/2.25)B +2.95B
200 = 2.95B + 2.95B - 2.62B - 2B
200 = 1.28B

B = 156.50

Substituting back into eq 3:

A = 205.19

Therefore we bet a total of 361.69. Either Bet (A or B) will payout 461.68.

Answer 2

1. If I understand correctly you want to end up with 100 dollars more than you started with.

2. I am not familiar with "payout of 2.25" and assume that it means you will get 2.25 for each dollar you bet and likewise for the 2.95.

Assume you have T dollars to begin with
Then you want to end up with T+100

If you bet N dollars on 2.25 then:
T + 100 = 2.25N

And also (T - N) is the remainder of your money:
T + 100 = 2.95(T - N)

Solve:
(T + 100)/ 2.25 = N
(T + 100)/2.95 = T - N

Add them:
(T + 100)/ 2.25 + (T + 100)/2.95 = T
(2.25 T + 225 + 2.95T + 295 = 6.6375T
520 = 1.4375T
T = 361.74
N = 205.22

So bet 205.22 at 2.25 and 156.62 at 2.95

You start with 361.74 and, if either bet wins, you will have 461.74 or a profit of 100 dollars. For other payouts just substitute them into those first equations and then work it out.

Answer 3

If you could find this out, a lot of horse race track bettors would be very happy.