## Profitability math

aperr
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### Profitability math

Hi,

can someone help me with calculating the profitability of surebet between betting exchange only?
I am looking for a way to calculate for profitability from odds only.

I will use an example:

Commission on both sides is 5%
o1 (odd1) :1,5
o2 (odd2) : 3,5
s1 (stake1) : € 160,17
s2 (stake2): € 70,00
Profit: € 6,08
Profitability = Profit/(s1+s2) = 6,08 / 213,17 = 2,64%

Now, if I try to do the math from the odds only, here is what I would do (but it is not working):

Profitability = 1 - [1/(1+(1-5%)*(o1-1))] - [1/(1+(1-5%)*(o2-1))]= 2,57%

Can someone tell me where I am doing a mistake?
Best
aperr
Last edited by aperr on Mon Jun 09, 2014 5:17 pm, edited 1 time in total.
arbusers
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### Re: Profitability math

What is o1, o2, s1, s2?
aperr
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### Re: Profitability math

can you show me the formula?
qbet
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### Re: Profitability math

You formula is not correct. You also need to divide by the amount invested in order to get the arb percentage. Your formula reads as 1 - x where x is the amount invested in order to win 1. (without the stakes). 1 -x is just the profit. For percentage the correct one is  (1-x)/x.

(Use 0.05 instead and multiply by 100 in the end to get the %. )
Last edited by qbet on Mon Jun 09, 2014 6:50 pm, edited 1 time in total.
ppintaluba
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### Re: Profitability math

aperr wrote: Hi,

can someone help me with calculating the profitability of surebet between betting exchange only?
I am looking for a way to calculate for profitability from odds only.

I will use an example:

Commission on both sides is 5%
o1 (odd1) :1,5
o2 (odd2) : 3,5
s1 (stake1) : € 160,17
s2 (stake2): € 70,00
Profit: € 6,08
Profitability = Profit/(s1+s2) = 6,08 / 213,17 = 2,64%

Now, if I try to do the math from the odds only, here is what I would do (but it is not working):

Profitability = 1 - [1/(1+(1-5%)*(o1-1))] - [1/(1+(1-5%)*(o2-1))]= 2,57%

Can someone tell me where I am doing a mistake?
Best
aperr
Profit calculation without considering stake:

o1 = 1.5
o2 = 3.5
comm = 5%

You must adjust odds (with commission):
o1.1 = 1+(o1-1)*(1-comm) = 1+(1.5-1)*(0.95) = 1+(0.5*0.95) = 1+0.475 = 1.475
o2.1 = 1+(o2-1)*(1-comm) = 1+(3.5-1)*(0.95) = 1+(2.5*0.95) = 1+2.375 = 3.375
Then sum 1/o1.1 + 1/o2.1 = 1/1.475 + 1/3.375 = 0.9743 = P (less than 1 means arbitrage)
Your profit is (1-P)/P = (1-0.9743)/0.9743 = 0.026378 = 2.6378%
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aperr
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### Re: Profitability math

What if Matchboook is involved?

Let's say:

comm betfair 5%
o1 (odd betfair) :2,4
s1: € 70

comm matchbook 1%
o2 (odd matchbook) : 2,1
s2 (stake2): € 77,7

Profit= € 14,62
Profitability = 14,62 / (77,7+70) = 9,9%

How do I calculate the profitability from odds only?
qbet
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### Re: Profitability math

The previous (correct) formula is valid here too but Matchbook's commission in this example is 2%.
doncht
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### Re: Profitability math

I'd like to see please if there's a working formula for commission set to 5%
ppintaluba
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### Re: Profitability math

doncht wrote: I'd like to see please if there's a working formula for commission set to 5%
For matchbook or a normal exchange?
My previous post has a general formula for any commission (not for matchbook)
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