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The math. Divide one by each odd and sum: 1/odd₁ + 1/oddₓ + 1/odd₂. If the sum is less than 1, an opportunity exists. The difference from 1 is your profit. In the industry this sum is called the overround or vig.

Why opportunities arise. Every bookmaker builds its own profit into its odds, so within that bookmaker the sum is always greater than 1 — you can never get an arbitrage within a single bookmaker.

Here's an illustrative example of margins for the bookmakers we track (statistical sample from football matches, full-time result — **not live data**):

The opportunity only appears when you take the best odds from each bookmaker separately. If two bookmakers disagree enough in their estimates, the sum of those best odds drops below 1 and the difference is yours. That’s why opportunities are more common between domestic and international bookmakers than between two domestic ones — big global bookmakers operate with just 2–3% margin, so even a tiny divergence opens a window.

It doesn’t always have to be three outcomes. Tennis and basketball have only two, so the math is simpler. The same applies to double chance: “1X at one, 2 at another” covers everything just as well as the classic three.

Why it’s harder in practice than on paper:

• You need an open and funded account at every bookmaker in the combination, otherwise you can’t close the loop.
• Odds change while you’re placing. If you place the first two tickets and the third moves, you’re left uncovered — and that’s no longer arbitrage, just an ordinary bet.
• Some bookmakers have minimum stakes higher than what the formula demands, so the distribution won’t match.
• If you repeatedly play only safe combinations, the bookmaker notices and reduces your maximum stake.

The math. margin = 1 − (1/odd₁ + 1/oddₓ + 1/odd₂), expressed as a percentage. The number you see in the table is exactly that.

Why 2% is already very good. Bookmakers watch each other and correct within minutes. If one held odds that gave others 5% guaranteed profit for long, it would lose money on every such match — so it simply doesn’t last. What remains are small, short-lived differences in estimates.

What the math doesn’t tell you. The shown margin assumes you stake exactly what the distribution requires. In reality you round to whole numbers, some places have a minimum stake limit, sometimes the odds drop while you’re typing — and from 2% you easily end up at 1.4%. That’s why opportunities below 1% are rarely worth the effort in practice, even when they show positive.

When the margin looks too good. Anything over 10% is almost never a real opportunity — it’s stale odds: a player withdrew, the match was postponed, the bookmaker didn’t react to news in time. Such combinations are usually rejected at placement or voided afterwards. That’s why we flag them, not hide them — so you can see why you shouldn’t chase them.

The math. stake for outcome = (1/odds of that outcome) ÷ sum of all 1/odds × total budget. This way every outcome returns the same amount, so your profit is identical no matter how the match ends.

Rounding. If you place 336.42 EUR as 336, and 257.19 as 257, you no longer have a perfectly even exit — one outcome now returns slightly less than another. On 1000 EUR that’s a few dozen cents and not a big deal; on small stakes it can eat more of the margin than expected.

Placement order. If you have to choose where to start, begin with the bookmaker that changes odds fastest and the outcome with the highest odds — that’s the hardest to recover if it moves. What you place first is what’s locked in.

When the distribution won’t work. Sometimes the formula asks for 4 EUR on one outcome, but the bookmaker won’t accept less than 5. Either raise the total budget until the smallest portion clears their threshold, or skip that opportunity — topping up “by feel” ruins the whole idea.

Bookmakers don't all work the same way. Roughly, they fall into two groups, and that difference is exactly why opportunities appear at all.

Sharp bookmakers (e.g. Pinnacle) run on a small margin, accept large stakes and don't restrict winning players. They adjust their odds quickly to the money coming in, so their odds are the closest to the true probability of an outcome.

Soft bookmakers (most local brands and the big recreational ones) carry a higher margin and move their odds more slowly, often on their own judgment rather than the market. That's where an out-of-line price shows up most often, but they are also the ones that restrict accounts that keep winning.

That's why it helps to have accounts at several bookmakers: an opportunity almost always needs two or three different ones, and if one limits your stake you can still bet with the others. Before you deposit, check that the bookmaker is licensed where you live.

We have no conflict of interest: we don't take your money, we don't handle deposits and we don't earn a commission from any bookmaker. Odds are shown exactly as they are.

True probability. We take the sharp market's odds for every outcome of the match and remove the margin: for each outcome we calculate 1/odds, then divide each part by their sum. Example: odds of 1.95 and 1.95 give 51.3% and 51.3%, 102.6% in total; without the margin that's 50% and 50%.

Expected value: odds × true probability − 1. If another bookmaker offers 2.20 on the same outcome and the true probability is 50%, that's 2.20 × 0.50 − 1 = 10%. That is what you would earn on average per 100 staked across many such bets, and only if the probability estimate is right.

Quarter Kelly. The Kelly formula says what share of your budget to stake: (odds × probability − 1) ÷ (odds − 1). For the example above that's 0.10 ÷ 1.20, about 8.3% of the budget. We recommend a quarter of that, about 2%, because no estimate is perfect and a smaller stake survives a bad run more easily.

Closing line value (CLV). Whether an opportunity was real shows best not in whether the bet won, but in where the odds went before kick-off. If by the start they dropped below the price you took, the market moved toward our estimate. If that doesn't happen regularly, the estimate is off, however many lucky wins come along the way.

Variance. At odds of 2.20 with a true probability of 50% you lose roughly every other bet, and a run of 5 or 6 losses in a row is nothing unusual. Even with a real 10% edge there is still roughly a one-in-five chance of being down after 100 such bets. The edge only shows reliably over several hundred bets.