OK, here goes....
We want to make £10 after 5% deduction.
x * 0.95 = 10
so
x = 10 / .95
rounded this makes x = £10.53 and this is the profit target.
Step 1 - Back a selection
==========================
In my first post I gave an example of backing at 5.0, so lets use this.
B is the amount I am backing for, giving rise to P as the potential profit should the selection win.
On Betfair you have to subtract 1 to get the true odds; e.g. 2/1 = 3.0 on Betfair
P = B * (5.0 - 1)
So if B = 100, P = 100 * (5.0 - 1) = 400
Step 2 - Lay a selection at lower odds
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In my first post I gave an example of laying at 4.0, so lets use this.
L is the amount I am laying for, giving rise to M as the liability should the selection win.
M = L * (4.0 - 1)
So if L = 100, M = 100 * (4.0 - 1) = 300
I now in the situation that if the selection wins I win P but lose M; that is I win 400 and lose 300, a 100 profit.
If the selection loses, I lose B but win L; that is I lose 100 and win 100, no profit and no loss.
Step 3 - green up
======================================
Now I divide my potential profit (P - M) by the Lay odds and Lay at this value. Note that this time we
DO NOT subtract 1 from the lay odds.
G = Potential Profit / 4.0
So, I have a potential profit of 100, I am Laying at 4.0 in this example, so G = 100 / 4 = 25
This generates an additional liability of 25 * (4.0 - 1), that is 75.00.
So the selections wins, I win 400, and lose 2 lay bets of 100 * (4.0 - 1) and 25 * (4.0 - 1) or 375, a profit of 25.
If the selection loses I lose my back stake (100) but win the Lay stakes of 100 + 25, a profit of 25.
Greened up nicely!
So, back to the original problem....
=====================================
What stakes should i use to return a profit target? Using 100 gave 25 profit, and I only wanted 10.53.
So if I divide 10.53 by 25 and multiply this by 100, I should get the stakes I am after.
10.53/25*100 = 42.12
let's see if this works:
P = 42.12 * 4 = 168.48
M = 42.12 * 3 = 126.36
Potential profit is 42.12
G = 42.12 / 4 = 10.53
Liability on G = 10.53 * 3 = 31.59
Selection wins, I win 168.48 but lose 126.36 + 31.59 = 10.53
Selection loses, I lose 42.12 but win 42.12 + 10.53 = 10.53
Woo Hoo.
So my solution is going to look something like this:
======================================================
Let X be my profit target
Let OB be the backing odds (as shown on Betfair)
Let OL be the laying odds (as shown on Betfair)
The Back Stake ( B ) will be
(X/0.95)/(((100*(OB-1))-(100*(OL-1)))/OL)*100
The Lay stake will be
=B+(((B*(OB-1))-(B*(OL-1)))/OL)
Let's check this
X = 10, OB = 5 and OL = 4
Back Stake = (10/0.95)/(((100*(5-1))-(100*(4-1)))/4)*100 = 42.11
Lay stake = 42.11+(((42.11*(5-1))-(42.11*(4-1)))/4) = 52.64
Win = (42.11 * 4) - (52.64 * 3) = 10.51
Lose = -42.11 + 52.64 = 10.53
Looks like a winner!
One more worked example just to make sure
X = 20, OB = 2.2 and OL = 1.23
Back Stake = (20/0.95)/(((100*(2.2-1))-(100*(1.23-1)))/1.23)*100 = 26.70
Lay stake = 26.70+(((26.70*(2.2-1))-(26.70*(1.23-1)))/1.23) = 47.76
Win = (26.70 * 1.2) - (47.76 * 0.23) = 21.06
Lose = -42.11 + 52.64 = 21.06
and 5% of £21.06 is £20.01
TA DA
Easy in the end....erm