Arbitrage Betting Examples
Work through the numbers before interpreting a result. All examples use a $100 CAD total stake and assume no fees.
Two-way arbitrage example: 2.10 and 2.10
P = 1/2.10 + 1/2.10 = 20/21 = 95.238095…%. Each ideal stake is $50.00. Both payouts are $105.00, leaving $5.00 net profit and 5.00% stake ROI. The implied-probability gap is 4.761905 percentage points; it is not the same number as stake ROI.
Three-way arbitrage example: 2.50, 3.50 and 3.50
Consider home win, draw and away win in the same regulation-time market. P = 2/5 + 2/7 + 2/7 = 34/35 = 97.142857…%. Ideal stakes are $41.176470…, $29.411764… and $29.411764…. The optimized cent stakes are $41.18, $29.41 and $29.41, summing to $100.00. Payouts are $102.95, $102.935 and $102.935 before settlement rounding. The smallest net profit is $2.935, displayed as $2.94; exact stake ROI is 2.935%, displayed as 2.94%. Theoretical ROI is 2.941176…%.
No arbitrage: 1.90 and 1.90
P = 20/19 = 105.263158…%. A $50.00 stake on each side returns $95.00 whichever outcome wins. Net profit is −$5.00 and ROI is −5.00%. Covering all outcomes alone does not create a positive return.
A small edge can disappear in cents
With decimal prices 2.01 and 2.01 and a total stake of $0.01, P is below 100%. You cannot split one cent across two outcomes. At least one outcome has a zero stake and zero payout, so the worst-case net result is −$0.01. The theoretical flag can be Yes while the practical profit flag is No.
Put the numbers into perspective.
Compare theoretical returns with a practical cent allocation.
Open the arbitrage calculator →