I am having a mental block at the moment and wondered if someone could show me the quickest way to work out how to apply the sum of £10,000 to the following example for the maximum benefit:

Several years ago I noticed the following arbitrage opportunity on an England game (only after it was too late).

First Goalscorer - Owen:

BACK at local bookmaker at 7.0 (far higher than all other bookmakers who were offering around 4.0)

LAY on Betfair at around 4.0

Obviously, there is a difference of 3.0 and I would wish to BACK and LAY first goalscorer - Owen, using my available £10,000 to make the most from this arbitrage situation.

How can I work this out quickly?

Wolf,

I looked at laying odds some time ago but couldn

Grant,

Many thanks for your reply.

The odds were 6/1 (7.0) at the bookies to back, and the market was offering to back the selection at 3/1 (4.0) on Betfair.

I want to back and lay the same selection (basically buy and sell the bet and pocket the difference of 3.0)

How would I apportion my entire £10,000 most effectively to do that? What is the quickest formula.

Maybe I am asking a very simple question without realising but am just trying to understand the concept better.

Many thanks

Apologies if I get this wrong - I'm an FX trader full time, and a sports spread betting punter only when I fancy a bit of light entertainment, but I think it works as follows;

Best way conceptually imho to understand what to do is to imagine the two prices that you are seeing are at the same bookies, but at different times (rather than different bookies, same time - stay with me here).

So first price is 6-1. You think these apre pretty good odds so you take 'em for £5000.

Price then comes in a fair bit, as everyone piles in, so you decide to lay em. Basically the amount you can lay em for is such that your maximum downside is the same as the upside on the bet you made earlier.

If Owen scores, you make (including your original stake) £5k * 7 = £35k
So you could lay bets such that this is your downside. i.e. £35k / 4 = £8,750

So if I'm not mistaken your profit would be £3,750 regardless of whether Owen scores or not. Make sense?

I could be wrong on this one, so don't quote me, but that's what I think happens. However, that raises one serious problem. You probably need sufficient funding in your betfair account to cover £35k, NOT just £5k, so you need access to larger short term funds if you're going to be able to arb in your full account size. Otherwise, you probably need to tweak the formula a bit and your bet will inevitably be smaller. Works far better when the prices are changing over time rather than as an instantaneous arb for this precise reason.

Personally I reckon with a bit of thought you could easily build an Excel sheet with solver functions built in for this type of thing, but I don't have time to walk you through that if you don't know how to do it.

Shame - if that was really the prices that was a decent arb - good spot.

Good luck - hope I helped not hindered

GJ

Thanks GJ,

That has helped me solve the problem. The scenario did actualy occur, where one bookmaker had set the odds above the market at 6/1 instead of 3/1. Whether I would have been able to actualy lay it on betfair and profit, I don't know for sure.

I had a maximum available of £10k at the time, and looking back wondered how i could have used that to maximum advantage without exposing myself to risk - arbing it basically.

Your calculation has helped me see that I would need to do the lay side first, then back the other selection:

If Owen scores, you make (including your original stake) £5k * 7 = £35k
So you could lay bets such that this is your downside. i.e. £35k / 4 = £8,750

:. Lay £10k / 4 = £2.5k LAY FIRST
Amount to use to Back £2.5k / 7 = £357.14 THEN BACK (by dividing sum layed by odds)

Note : £7142.86 left over from available £10k - so I have only used £2857.14

Profit regardless of outcome: £2142.86

Is there a more optimal way of using the £10K. I can't find one.

I will try and design a spreadsheet in case this unlikely scenario ever happens again.

Cheers.

Hi,
here is the formula you looking for:

A:7/1
B:4/1
total investment:10000

stakeA=(B+1)*(10000)/A+B+2
StakeB=(A+1)*(10000)/A+B+2

SO IN YOUR EXAMPLE;
STAKE A=£3846
STAKE B=£6154
IF A WINS; YOU WIN =(3846*7)-(6154)=£20768
IF B WINS; YOU WIN =(6154*4)-(3846)=£20770

REGARDS,
SEARCHLIGHT

Nice work. That's what I was after.

Hang on , is that right? would it not cost more than £10k to do that (wouldn't the potential liability on the Lay side be higher)?

now thats weird! I had a look this afternoon and got a different answer to GJ, so I left it.

but I get:
if you have two possible outcomee, 6/1 and 3/1, you have 7 + 4 unit outcomes ( ^ + 1 + 3 + 1) = 11 units for 2 units risked.

thus, to maximise profits, you get:
7/11 * 10,000 = 6,363.64
4/11 * 10,000 = 3,636,36.

you bet 6,363 on the 3/1 shot, and 3,636 on the 7/1 shot.

if the 6/1 bet wins, you return (6363 * 4) = 25,455.
if the 3/1 bet wins, you return (3636 * 7) = 25,455.

EDIT: the above should say:
if the 6/1 bet wins, you return (3636 * 7) = 25,455.
if the 3/1 bet wins, you return (6363 * 4) = 25,455.
END EDIT

you have bet a total of 10,000, and optimal return = 25,455, resulting in a net profit of 15,455 irrespective which bet wins.

NB: in searchlights calcs, he is only subtracting the bet amount from the win, and not BOTH bets, one of which fails, so the subtracted value should be 10K in each case.
hope I am not confusing the issue - or should I get a job at Northern Rock?

Wolf, GJ, Searchlight, Trendie,

I despair at my own ignorance at times. You provide inspiration to rectify this. Well done, chaps.

Grant.

Hi Trendie,
if you subtract 10k, you should also add your initial bet to the return.
in your example;
if 6/1 bet wins your total return would be; 25455+6363=31818
if 3/1 bet wins your total return would be; 25455+3636=2909

regards,

searchlight