Advanced Calculations

When you have the total arb percentage, as shown on the previous page, it is easy to calculate how much you will profit from any given total trade, as
well as how much to trade from any given winnings. For example, you could decide that you want to place a $1000 trade, or you could decide you want your winnings to be
$1000…

$1000 Trade $1000 Winnings
95.833% x Winnings = $1000 95.833% x $1000 = Initial
Winnings = $1043.48 Initial = $958.33
Profit = $43.48 Profit = $41.77

 

However, neither of these examples tell you how much each individual bet needs to be. In order to calculate that, you need to know what percentage of
the outlay each set of odds make up. To find this we need to divide each of the bet percentages by the total arb percentage:

  • 83.33% / 95.833% = 86.95%
  • 12.5% / 95.8333% = 13.05%

These two new percentages, 86.95% and 13.05%, are the percentages of the total arb percentage that each bet makes up. They are also the percentage of the
total trade that needs to be bet on their respective odds. That is, 86.95% of the total trade needs to be bet on 1.20, and the remaining 13.04% on 8.00.

With these percentages, you can calculate the two wagers from a desired total trade, you can calculated the two wagers from a desired total winnings,
and you can even choose a desired wager and calculate the second wager, thereby giving you the total trade and winnings in the process. Let us just cover all of those
examples so you can see how each of these are done:

Example 1

Desired total trade of $500
86.95% x $500 = $434.75
13.05% x $500 = $65.25
Easy to verify: $434.75 + $65.25 = $500.00
$434.75 x 1.2 = $521.70
$65.25 x 8.00 = $522.00
$500 / 95.833% = $521.70

Example 2

Desired total winnings of $750
95.833% x $750 = $718.75
86.95% x $718.75 = $624.95
13.05% x $718.75 = $93.80
Easy to verify: $624.95 + $93.80 = $718.75
$624.95 x 1.20 = $749.95
$93.80 x 8.00 = $750.40

Example 3

$305 Limit on 1.20 bet
86.95% x trade = $305.00
trade = $350.78
13.05% x $350.78 = $45.78
Easy to verify: $305 + $45.78 = $350.78
$305 x 1.20 = $366.00
$45.78 x 8.00 = $366.24
95.833% x $366.24 = $350.98

 

Example 1 shows $434.75 being bet on the favourite (1.20) and $65.25 being bet on the underdog (8.00) to come to a total trade of $500.00 (as desired)
with an eventual profit of either $21.70 or $22.

Example 2 shows $624.95 being bet on the favourite (1.20) and $93.80 being bet on the underdog (8.00), coming to a total outlay of $718.75. The
desired winnings of $750.0 is closely approximated with actual winnings of $749.95 (favourite) or $750.40 (underdog). Total profit will therefore be $31.20 or $31.65.

Example 3 shows $305 (our limit) being bet on the favourite (1.20), forcing us to match with a $45.78 bet on the underdog (8.00)resulting in a
total trade of $350.78 with a profit of either $15.22 or $15.46.

When you understand completely how these calculations work, you will be able to easily calculate exactly how much money you will need to place on either
side of an arbitrage trade, while also being quicker to know how much you can hedge either side.

More Complicated Arbitrage Calculations

3-way, 1×2, Home-Draw-Away

A 3-way arbitrage is similar to a 2-way arb, just with three possible outcomes that need to be calculated. 3-way arbs are most commonly found on Soccer
games where odds are offered on the draw (the ‘x’ in ’1×2′), but can also be found in 3-ball golf and any other scenario where a third option is required to cover a last
potential outcome.

Using the same method as above, we divide 1 by each of the odds and add them together to determine the arbitrage %.

  • (1 / 1.30) + (1 / 7.00) + (1 / 17) = 97.09%

In the same way that was used above, the amounts can be calculated and then the corresponding bet amounts worked out.

  1. Calculate the bet percentages:
  • 1 / 1.30 = 76.92%
  • 1 / 7.00 = 14.29%
  • 1 / 17 = 5.88%

2. Divide those % values by the total arb percentage:

 

Just like in the 2-way example above, we can use these 3 bet percentages and the total arb percentage to calculate any element of the arb that we want:

Example 1

Desired total trade of $500
79.22% x $500 = $396.10
14.72% x $500 = $73.60
6.06% x $500 = $30.30
Verify: $396.10 + $73.60 + $30.30 = $500
$396.10 x 1.3 = $514.93
$73.60 x 7 = $515.20
$30.30 x 17 = $515.10

Example 2

Desired total winnings of $750
$500 / 97.09% = $514.99
97.09% x $750 = $728.18
79.22% x $728.18 = $576.86
14.72% x $728.18 = $107.19
6.06% x $728.18 = $44.13
Verify: $576.86 + $107.19 + $44.13 = $728.18$576.86 x 1.3 = $749.92
$107.79 x 7 = $754.53
$44.13 x 17 = $750.21

Example 3

$305 limit on 1.30 bet
79.22% x trade = $305.00
trade = $385.00
14.72% x $385.00 = $56.67
6.06% x $385.00 = $23.33
Verify: $305.00 + $56.67 + $23.33 = $385.00
$305.00 x 1.3 = $396.50
$56.67 x 7 = $396.69
$23.33 x 17 = $396.61

Home – Draw – Double Handicap Arbs, 1×2(+0.25)

This Example will be added shortly (eventually).

Additional Reading

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