Two-way arbitrage: when the best prices add up to less than 100%
Concepts
2.10 at one bookmaker and 2.05 on the other side at another imply 96.40% in total. Staking 49.40 and 50.60 returns 3.73% more than the 100 staked, whichever side wins.
- 3.73%locked-in return
- 96.40%implied total
The Core Mechanism
A two-way arbitrage occurs when the sum of implied probabilities for opposing outcomes falls below the baseline. The key figures show an implied total under that threshold. This gap represents the locked-in return. The table below details the specific odds and stakes required to capture this difference. By backing both sides of a binary event at different venues, the bettor ensures a payout regardless of which outcome occurs. The mechanism relies entirely on the mathematical discrepancy between the two prices. If the sum equals the baseline exactly, no profit exists. Only when the total is lower does a guaranteed margin emerge for the player.
| Side | Odds | Stake |
|---|---|---|
| A | 2.10 | 49.40 |
| B | 2.05 | 50.60 |
Splitting the Stakes
Equal stakes do not maximize returns in this scenario. The higher odds require a larger portion of the total capital to balance the payout. As the table above illustrates, the stake on the side with higher odds is smaller than the stake on the side with lower odds. This inverse relationship ensures that the return is identical regardless of which side wins. The larger stake compensates for the lower payout multiplier. The smaller stake balances the higher multiplier. This precise division locks in the return shown in the key figures. Without this adjustment, one outcome would yield less than the other, reducing the guaranteed profit.
Practical Execution Risks
Arbitrage opportunities are fleeting. Prices change rapidly as other bettors place wagers. A delay between placing the first bet and the second can eliminate the margin. If the second price moves unfavorably, the guaranteed profit may vanish or turn into a loss. Furthermore, bookmakers often limit stakes for successful arbitrageurs. A large initial stake might be accepted, but subsequent bets could be capped at a lower amount. This limits the total profit potential. Voided bets also pose a risk. If one side is voided due to an event cancellation, the remaining bet may not cover the initial outlay. Timing and account limits are critical factors.
Understanding the Margin
The margin is the difference between the total implied probability and the baseline. In this example, the margin matches the locked-in return shown in the key figures. This figure represents the average profit per unit staked. It is not a guarantee of immediate wealth but a mathematical certainty over many iterations. Short-term results can vary due to the factors mentioned above. The margin ensures that, on average, the bettor recovers more than they wagered. However, this edge is small. It requires high volume to generate significant returns. The calculation is straightforward: divide the stake by the odds to find the implied probability, then sum these values. If the sum is low, the arbitrage exists.
Questions
Why do stakes differ between the two sides?
Stakes are inversely proportional to the odds. The side with lower odds requires a larger stake to match the payout from the side with higher odds. This balances the return across both outcomes.
What happens if one bet is voided?
If one bet is voided, the arbitrage structure breaks. The remaining bet may not cover the initial cost, leading to a loss. This risk highlights the importance of checking event status before placing bets.
Does a larger margin always mean better profit?
A larger margin means a higher percentage return per bet. However, it does not guarantee a larger absolute profit if the stake size is limited by the bookmaker. Volume and limits both matter.
Where can I find help with gambling habits?
If gambling stops being fun, free help is available. Visit help and support for resources on managing time and money effectively.
Every figure on this page is computed by code from exact fractions for odds, margins and parlays, and closed-form Kelly growth, each checked by a seeded simulation. See the methodology.