Simple Arbitrage Calculation

[THE WOLF2222]

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?

 

[grantx]

Wolf,

I looked at laying odds some time ago but couldn’t see much advantage.

I assume the odds you quote are the same as 7-1 and 3-1. If not, what follows can be ignored.

Essentially, you need to take the opposite side of each bet.

If you lay either bet, the best outcome (doesn’t score) for both is 1 (ie, the “1” in 7-1, 3-1); the best losing bet is -3 (3-1). So, you’ll either win a max of 1 or lose a min of -3. If all this wrong, it perhaps explains why I couldn’t get anything out of laying odds.

From my experience, if I remember correctly, summing all the lay sides of odds in a horserace was below the minimum bet payout, hence no arbitrage. For example, six horses in a race, all bets at 7-1. Lay all bets to gain 6 but lose 7 on the winner for a net –1.

Grant.

 

[THE WOLF2222]

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

 

[THE WOLF2222]

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.

 

[searchlight]

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?

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

 

[THE WOLF2222]

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)?

 

[trendie]

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?

 

[grantx]

Wolf, GJ, Searchlight, Trendie,

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

Grant.

 

[searchlight]

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?

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

 

[trendie]

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

its frightening that we trade the markets isnt it!

hope you have a good trading day.

 

[THE WOLF2222]

Hi folks, and thanks again for your persistence. However, I thinks we have strayed from the objective a bit, although some worthwhile angles have been explored.

I am still trying figure it out myself.

Just to confirm:

My maximum available cash (no credit allowed) is £10,000.

To benefit from the arbitrage I need to BACK the bet offered at 6/1 and
LAY the bet offered at 3/1. This is 3/1 to back it, so I will be accepting the liability on someone backing at 3/1.

There is a clear arbitrage opportunity presented by the difference in odds offered for the same bet.
I need to deposit any, and the full, potential loss on each bet.

Searchlight: I have just noticed that your formula is to be used in the case of apportioning the cash to BACKING both selections as opposed to BACKING and LAYING to benefit from the arbitrage. But the formula is still useful for that purpose in the future. Thanks.

I think in all honesty I have overcomplicated a straightforward problem.

GJ: I have been working from your example:

If Owen scores, you make (including your original stake) £5k * 7 = £10k
So you could lay bets such that this is your downside. i.e. £35k / 4 = £8,750

Hence: £10k / 7 = £1429 stake to back with
(£10k-£1429) / 3 = £2857 offer to lay a bet of this size - potential liability 3* £2857 = £8521

£1429 + £8521 = £10,000

Note: Divide by 3 not 4 as backer stake counts as 1. I’m liable for 3. (Hence 3/1)

Still trying....confusing myself further..... how can I lock in a profit?? I'm going for a beer.

 

[searchlight]

Hi folks, and thanks again for your persistence. However, I thinks we have strayed from the objective a bit, although some worthwhile angles have been explored.

I am still trying figure it out myself.

Just to confirm:

My maximum available cash (no credit allowed) is £10,000.

To benefit from the arbitrage I need to BACK the bet offered at 6/1 and
LAY the bet offered at 3/1. This is 3/1 to back it, so I will be accepting the liability on someone backing at 3/1.

There is a clear arbitrage opportunity presented by the difference in odds offered for the same bet.
I need to deposit any, and the full, potential loss on each bet.

Searchlight: I have just noticed that your formula is to be used in the case of apportioning the cash to BACKING both selections as opposed to BACKING and LAYING to benefit from the arbitrage. But the formula is still useful for that purpose in the future. Thanks.

I think in all honesty I have overcomplicated a straightforward problem.

GJ: I have been working from your example:

If Owen scores, you make (including your original stake) £5k * 7 = £10k
So you could lay bets such that this is your downside. i.e. £35k / 4 = £8,750

Hence: £10k / 7 = £1429 stake to back with
(£10k-£1429) / 3 = £2857 offer to lay a bet of this size - potential liability 3* £2857 = £8521

£1429 + £8521 = £10,000

Note: Divide by 3 not 4 as backer stake counts as 1. I’m liable for 3. (Hence 3/1)

Still trying....confusing myself further..... how can I lock in a profit?? I'm going for a beer.

Hi The wolf2222,
You think you confused? you have to see the state I am in. LOL
Now anything i say should be taken with the handful of salt.
Yes you are correct about the formula I gave. it has to be two opposing outcomes of a event in order to make a guaranteed profit. I don't know why, but i was thinking Owen scoring, not scoring kind of a scenario.
Although I am not familiar with the laying bets, but as i understand it; you(the layer)
name the odds... right?
if so why you are trying the copy the odd of somebody? create one for yourself. 2/1 for example.:cheesy:
What really I am trying to say is , if you can lay bets, you can always create a arbitrage by offering lower odds than you saw elsewhere.I stress the lower. that way you can raise the money to bet on the higher odd you saw elsewhere.Practically you would be betting with other people's money, zero risk to you. I bet you, the guy who layed 4/1 was raising money to bet on 7/1.

EXAMPLE: you layed 4/1 and collected £1000 put that money on 7/1 (owen scoring)
IF Owen scores you make a profit £3000
IF not you had a fun.
If you believe you can find somebody to take your odds while there is a tens of better odds elsewhere you should do this for a living. And believe you me there is a around over 75000 people in this forum alone will follow you.
Last suggestion; To increase the likelihood of you winning offer and put your money on Owen not scoring.

Regards,

searchlight

 

[trendie]

Just to confirm:

My maximum available cash (no credit allowed) is £10,000.

To benefit from the arbitrage I need to BACK the bet offered at 6/1 and
LAY the bet offered at 3/1. This is 3/1 to back it, so I will be accepting the liability on someone backing at 3/1.

There is a clear arbitrage opportunity presented by the difference in odds offered for the same bet.
I need to deposit any, and the full, potential loss on each bet.

I think I understand this laying bit!

you get odds of 6/1.
you offer odds of 3/1 to others. I am assuming this is same as betting 1/3 for it to lose.

odds: 6/1 and 1/3.
normalise, ie, get same "denominator".
18/3 and 1/3. total units = (18 + 3 + 1 + 3) = 25 units.

(18 + 3) = 21 / 25 * 10,000 = 8,400.
(1 + 3) = 4 / 25 * 10,000 = 1,600.

you are betting 1,600 for horse to win.
you are betting 1/3 for horse to lose.
you offer 8,400 as potential winnings to others by offering 3/1.
you can therefore "collect" 2,800 in winnings (others bettors stakes) if horse loses. (8,400 / 3).

if horse wins: you collect (1,600 * 7) = 11,200.
if horse loses: you collect (8,400 * 4/3); ie, your deposited risk comes back, PLUS the bets of 2,800 = 11,200.

you risked 10,000 to collect 11,200; net result = 1,200.

this had better be right! I will finally get some sleep.

 

[searchlight]

I think I understand this laying bit!

you get odds of 6/1.
you offer odds of 3/1 to others. I am assuming this is same as betting 1/3 for it to lose.

odds: 6/1 and 1/3.
normalise, ie, get same "denominator".
18/3 and 1/3. total units = (18 + 3 + 1 + 3) = 25 units.

(18 + 3) = 21 / 25 * 10,000 = 8,400.
(1 + 3) = 4 / 25 * 10,000 = 1,600.

you are betting 1,600 for horse to win.
you are betting 1/3 for horse to lose.
you offer 8,400 as potential winnings to others by offering 3/1.
you can therefore "collect" 2,800 in winnings (others bettors stakes) if horse loses. (8,400 / 3).

if horse wins: you collect (1,600 * 7) = 11,200.
if horse loses: you collect (8,400 * 4/3); ie, your deposited risk comes back, PLUS the bets of 2,800 = 11,200.

you risked 10,000 to collect 11,200; net result = 1,200.

this had better be right! I will finally get some sleep.

Hi Trendie,
if he has collected 2800 0n 3/1 his liability is 8400+2800=11200
he has to borrow £1200 to cover it let alone bet on the 7/1.
regards,
searchlight

 

[THE WOLF2222]

'Hi Trendie,
if he has collected 2800 0n 3/1 his liability is 8400+2800=11200
he has to borrow £1200 to cover it let alone bet on the 7/1.
regards,
searchlight'

The 'backer' has to deposit £2,800 as the stake. I would have to deposit £8400 to cover my potential liability (his potential profit)

I would then have a remainder of £1600 to back the selection at 6/1

 

[searchlight]

'Hi Trendie,
if he has collected 2800 0n 3/1 his liability is 8400+2800=11200
he has to borrow £1200 to cover it let alone bet on the 7/1.
regards,
searchlight'

The 'backer' has to deposit £2,800 as the stake. I would have to deposit £8400 to cover my potential liability (his potential profit)

I would then have a remainder of £1600 to back the selection at 6/1

Hi,
Yes, absolutely right. Now first thing in the morning I will apply for a job at the Northern Rock. I think I am better qualified then Trendie.
Regards,
Searchlight