Finding the optimum odds to close a position.

i think, as with the constipated mathematician, you need to work it out with a pencil :-)

I did this a while back, and it went along these lines. Assuming two runners, profit of p1 for runner 1 winning, stake of s1 on runner 1, at odds1 etc, and backing only (cos it's simpler for the example) you can say:

p1 = s1 * (odds1 - 1) - s2 winnings if runner 1 wins
p2 = s2 * (odds2 - 1) - s1

To green up, p1 = p2 ==>
s1 * (odds1 - 1) - s2 = s2 * (odds2 - 1) - s1

s1 * odds1 = s2 * odds2

given you have s1, odds1, odds2 you work out s2.

So it gets a bit more complicated when you want to lay instead. But i think it follows through much the same way.

Or am i teaching you grandmothers to suck eggs here?

I divide the potential profit by the latest price...here is my (C#) code

If I have an opening back position (the size is 'stakeToRecover'), I place a lay bet of size stakeAdjustment:
stakeAdjustment = CalcStake(averageBetBackPrice, currentLayPrice, stakeToRecover);

If I have an opening back position, I place a backbet of size stakeAdjustment:
stakeAdjustment = CalcStake(averageBetLayPrice, currentBackPrice, stakeToRecover);

private static double CalcStake(double price1, double price2, double originalStake)
{
double profit = CalcProfit(price1, price2, originalStake);

double adjustedStake = Math.Round(originalStake + (profit / price2), 2);

if (adjustedStake < MinStake)
{
adjustedStake = MinStake;
}

return adjustedStake;
}

private static double CalcProfit(double price1, double price2, double originalStake)
{
double profit = Math.Round((price1 - price2) * originalStake, 2);

return profit;
}

Does that make sense?! Theres probably a more efficient way of doing it, but this does the job for me.

OK, if you are looking for a margin of m on an original stake of S at a price P, the formulas you need are:

New Price, P' = (P-m)/(1+m)
Stake to Lay, S' = (1+m)S

So in your example the new price would be :
P' = (1.5 - 0.05) / (1 + 0.05) = 1.45 / 1.05 = 1.3809
And the stake you are laying would be:
S' = (1 + 0.05) x £3.00 = 1.05 x £3.00 = £3.15

HTH

If you know the price you are going to get out at (odds2), then yes it's easy
stake2 = stake1 * odds1 / odds2

We're trying to find the target odds.

First we need to work out the target profit.
If we want to lock in min 5%, then stake2 must be at least stake1 * 1.05

In the example:
stake1 = £3
So stake2 must be at least £3 * 1.05 = £3.15

Now work out the target odds:
odds2 = odds1 * stake1 / stake2
odds2 = 1.5 * 3 / 3.15 = 1.4286

We now need to move to a valid tick
As we backed first, we need to move down to a valid tick - if we had layed first, we would move up, but otherwise all the maths is the same - denp's nice new library code will get you there

So move down to 1.42
So stake2 needs adjusting
stake2 = stake1 * odds1 / odds2
stake2 = 3 * 1.5 / 1.42 = 3.169

So the bet is 3.17 at 1.42, locking in 17p profit, or 5.67%

EDIT: confused - I reckon you can be 26p green if you back at 1.5 and lay at 1.38 - what's happened?
Looks like the quick way to work out the target odds is:
Back first: Odds2 = odds1 / 1.05, and then move down to nearest tick (1.42) - back £3, lay £3.17, 17p green
Lay first: Odds2 = odds1 * 1.05, and then move up to nearest tick (1.58) - lay £3, back £2.85, 15p green

Peteb, I think the confusion arises because your method just breaks even if the horse wins - Inksmithy was specifically after a formula to give an equal green outcome regardless of result.

Arrgh - sorry Peteb, I was working on gross returns, not net - obviously if the horse wins, you make a profit equal to the difference in stakes (which is what we want). I'll extract my head from my arse and try again:

Original bet is a stake of S at price P, and required margin is m

New Price, P' = P/(1+m)
Stake to Lay, S' = (1+m)S

(which is what everyone else was saying anyway)

Obviously, if P' isn't a valid price, go to the next shorter valid price, say P". In this case, the stake to lay will become:

Revised Stake to Lay, S" = SP/P" , rounded to the nearest penny, giving a revised margin of:
Revised margin, m" = (S"-S)/S , or equivalently m" = (P-P")/P"

Sorry to have added confusion with my earlier posts, too many years working with bookmakers' prices:-)

myrddin - yes that looks right to me - your maths is much better than mine - I can only think in excel formulae, not maths equations - yours is very neat and clear once I had figured out your notation!

Can I just check though - do we reckon the get-out price is 1.42 for 17p green?? Hope so, as that is obviously going to be easier to match than 1.38!

Yep, that's what I got (eventually)

Original bet is a stake of S at price P, and required margin is m
So S = £3.00 P = 1.5 m = 0.05

New Price, P' = P/(1+m) = 1.5/(1.05) = 1.4285714

P' isn't a valid price, go to the next shorter valid price, so P" = 1.42

Revised Stake to Lay, S" = SP/P" = (£3.00 x 1.5)/1.42 = £3.169014 = £3.17
(rounded to the nearest penny), giving a revised margin of:

Revised margin, m" = (S"-S)/S = (£3.17 - £3.00)/ £3.00 = 0.0567