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First off, I feel it really important to mention that you shouldn't worry if these numbers don't make sense to you just yet, even as you read this. This article begins to describe arbitrage calculation formulas in depth. The numbers are here to solidify the legitimacy in how arbs work for the mathematically inclined. Professional arbers will tend to use specified software or calculators that do this work for them.
Playing with our fully featured and detailed Arbitrage Calculator will also probably help you to see how the mathematics works in a practical perspective. The calculator is built in such a way that it follows the directions listed below for calculating arb viability and return, so you can easily follow along with it.
There are several different ways to calculate arbs. The method described in this article however, will tell you how much you will need to invest in the arb to realise your specified return whilst also making it apparent to you if the pair of bets you intend to pair as an arb are legitimately profitable.
The steps here are intended for use if you were to find your arbs manually and are included for reference purposes, as professional arbers will often use specialised automatic alert service software.
Determing an arb is easy and involves these few simple steps:
Find your two best odds
Pick your total winnings
For this example we'll use a winnings amount of $1000 (although this is in an arbitrary amount - the higher the sum you pick, the larger the bets and the greater the profit).
Divide your chosen total winnings amount by each set of odds to get each respective bet amount. Add them together to get your total outlay.
In this example:
($1000 ÷ 1.20) + ($1000 ÷ 8.00) = your total outlay
$833.33 + $125.00 = $958.33
Calculating your profit is just as easy:
Winnings - Outlay = your total Profit
$1000 - $958.33 = $41.67
And finally, to calculate your return on investment you simply divide your profit by the initial amount invested: $41.67 ÷ $958.33 = 4.35%
All arbitrages are expressed as a percentage. Contrary to what you would usually expect, this percentage is not the same as your return on investment. The arbitrage percentage is calculated by dividing 1 by each set of odds and then adding them together.
1 ÷ 1.20 = 83.333%
1 ÷ 8.00 = 12.5%
83.333% + 12.5% = 95.833%
This percentage, 95.833%, indicates what portion your investment will take up of the total winnings.
In other words, if your winnings were to be $1000 as used in the example above, the two bets add up to $958.33, 95.83% of the total winnings. This means that 4.17% of the winnings was not invested, and is therefore left over as profit. Thus, when people refer to arbs as a '95.83% arb' or a '4.17% arb', they are talking about the same thing.
Notice that 4.17% is not the same as your return on investment (4.35%) because 4.17% is the percentage of the total winnings, not the percentage of the amount invested.