# Yield (ROI = Return Of Investment) formula question

#### r_ivica

##### Board Regular
The Calculation of simple yield:

The Return*
(Winnings)
__________ X 100= ROI (%)

Investment*
(Stakes)

so for example: I have 1000 bets with odds 2,00
500 of them are winning and 500 losing. So i am on 0 and my ROI is zero

Would like to get odds to have 15% yield,
How to calculate on what odds should i be to have ROI 15% ?
Because odds are not always 2,00 - they are different but i gave 2,00 as example...

Looks like very easy but can't figure it out!?

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#### Andrew Fergus

##### MrExcel MVP
Hi

If you gamble long enough then you will confirm to the 'odds'. In other words, whatever the take is from the totaliser agency / bookie - lets say that is 15%, then on average, over an extended period of time, you can expect to be down 15%. Expressed simply, your expected return will be -15%. Unless of course you have (or think you have) a system that can beat the odds!

Anyway, your question : what you have done is compress the top line into a single a number (i.e. \$1,000) which was actually 3 variables, being the number of bets x the winning percentage X the odds (i.e. 1000 bets x 50% winning percentage x 2:1 odds). So the variable you want to change is either the winning percentage or the odds or a combination of the two to give you are turn of 15% - take your pick...

The next question you may want to ask yourself is 15% a sufficiently high return for the risks I am taking? Or would I be better off putting my money into something else?

Good luck!
Andrew

#### r_ivica

##### Board Regular
Hi,
i am using betting exchanges mostly where can get much better odds than classic bookies (places where people bet against each other..) so it is pretty possible to get fair and valuable odds!

anyway, i received one answer on some other forum but not sure what it is all mean, and not sure how could i put it into excel formula, so hoping you could help me..
here it is:

Let p = 1/odds be the probability of success, and R = 2 be the amount you win on a success (as a multiple of the amount you put down). Suppose you play n games, where n is large (in your case n = 1000, but it doesn't really matter).

Expected winnings are npR, and expected cost is n. ROI is (npR - n)/n = pR - 1.

If you want ROI to be 0.15, just solve pR - 1 = 0.15. If R is fixed at 2.00, solve 2p - 1 = 0.15.

#### Andrew Fergus

##### MrExcel MVP
Hi

That is essentially the same answer that I provided. Nothing has changed from my previous post - to get a return of 15% either change the win % or change the odds. If the odds are fixed then change the win % to 57.5% or if the win % is fixed then change the odds to \$2.30. You may notice I increased both values by 15%. As I mentioned earlier you could change both variables instead.

If you aren't sure how to 'solve' an equation, then you may want to have a quick read of this algebra tutorial. To be successful at this kind of betting you may want to first invest a little time in understanding maths because that is what gambling is.

Good luck!
Andrew

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