How to Calculate a Sure Bet (Step-by-Step)

Finding an arbitrage opportunity is only half the job. Here's the exact formula for splitting a stake so every outcome pays back the same amount — and where beginners get it wrong.

Last updated 2026-09-17

Finding an arbitrage opportunity is only half the job. If you split your stake incorrectly, you can turn a mathematically guaranteed profit into a guaranteed loss on whichever outcome actually happens. Here's the formula, broken down so there's no ambiguity.

Step 1: Convert odds to implied probability

If a bookmaker offers decimal odds of 2.50 on an outcome, the implied probability is:

1 ÷ 2.50 = 0.40, or 40%

Do this for every outcome you're planning to bet, using the best available odds for each one (which will usually come from different bookmakers).

Step 2: Add up the implied probabilities

Sum the implied probabilities across all outcomes. If the total is under 100%, you have an arbitrage opportunity. If it's 100% or more, there's no guaranteed profit available — walk away.

Example: Home 40% + Draw 28% + Away 25% = 93%. That's your arbitrage margin: 7%.

Step 3: Calculate your stake for each outcome

For a total bankroll you want to commit (say ₦100,000), the stake for each outcome is:

Stake for outcome = (Implied probability of that outcome ÷ Total implied probability) × Total stake

So:

• Home: (0.40 ÷ 0.93) × 100,000 = ₦43,011
• Draw: (0.28 ÷ 0.93) × 100,000 = ₦30,108
• Away: (0.25 ÷ 0.93) × 100,000 = ₦26,881

Total staked: ₦100,000 (allowing for rounding).

Step 4: Verify the payout

Multiply each stake by its own decimal odds to confirm the payout is identical (or very close) regardless of outcome:

• Home: ₦43,011 × 2.50 = ₦107,528
• Draw: ₦30,108 × 3.57 = ₦107,486
• Away: ₦26,881 × 4.00 = ₦107,524

Small differences come from rounding — in practice you round stakes to whole naira or to whatever increment your bookmaker allows, which slightly shifts the guaranteed payout between outcomes. This is where most beginner mistakes happen.

The rounding trap

Bookmakers don't accept infinitely precise stakes — you're rounding to the nearest naira, sometimes the nearest 100 naira depending on the platform. If your calculated stake is ₦30,108.47 and you round down to ₦30,100, that small shortfall reduces your payout on that specific outcome. On a thin-margin arb (say 1%), a rounding error of even half a percent can wipe out your entire profit or tip you into a loss on one leg.

The fix: always round in the direction that protects your worst-case outcome, and recheck the total payout after rounding — don't just trust the pre-rounding math.

A shortcut worth knowing

If you only care about your guaranteed profit percentage rather than exact stakes, it's:

Profit % = (1 ÷ Total implied probability) − 1

For the example above: (1 ÷ 0.93) − 1 = 0.0753, or about 7.5% profit on total stake — assuming perfect execution and no rounding loss.

Doing this math by hand for every match you're checking is exactly why manual arbitrage is slow. A scanner that runs this calculation automatically, live, across many bookmakers at once, removes the single biggest source of error — and lets you act while the window is still open.