Matching the stake amounts does not match the result.
A $10 stake on each of two outcomes at decimal odds of 2.00 and 3.00 risks $20 in total. The first outcome returns $20, producing zero profit; the second returns $30, producing $10 profit.
Equal profit requires larger stakes on shorter odds and smaller stakes on longer odds. Even then, “equal” does not mean profitable: the shared result may be positive, break-even, or negative. For decimal odds, add the inverse of each price—1 ÷ odds. A total below 1 allows positive equalized profit; exactly 1 breaks even; above 1 locks in an equal loss.
A valid split requires outcomes that are mutually exclusive and collectively exhaustive: only one can win, and every possible result must be covered. A two-way football split, for example, is incomplete if a draw is possible but omitted.
Check the market definitions before entering any odds:
Pre-event dutching divides a new total stake across all outcomes at once. Using another bet to hedge an open wager is different: the original stake and potential return are already fixed, so both must be included in the calculation.
Even matching outcome names may hide incompatible rules. If one bookmaker includes overtime and another settles on regulation time, the bets do not form a clean split.
Decimal odds put every possible return on the same basis: total payout per unit staked, including the returned stake.
Use these conversions:
a/b: decimal = 1 + a/b+A: decimal = 1 + A/100-A: decimal = 1 + 100/|A|For example, 5/2, +250, and decimal 3.50 all represent the same gross return. American -200 converts to 1.50.
The calculation should use executable prices, not headline or recently displayed quotes. Check that the stake can actually be placed at the stated odds and within any size limits. Commission, taxes, exchange fees, or payout deductions must also be reflected where relevant.
If an exchange charges commission rate c only on winnings, a practical net decimal price is:
net decimal = 1 + (quoted decimal - 1) × (1 - c)
Thus, decimal 2.00 with 5% commission becomes 1.95. Using gross odds would overstate the achievable profit.
For each decimal price, calculate its inverse by dividing 1 by the odds. Then add every result:
Inverse-odds sum = (1 ÷ odds A) + (1 ÷ odds B) + …
For two outcomes priced at 2.10 and 2.05:
Interpret the total as follows:
For a sub-1 total, the theoretical profit rate is (1 ÷ total) − 1. With 0.9640, that is about 3.73%. This check fits naturally into an arbitrage calculator workflow.
The figure is only theoretical until every wager is accepted and settled as expected. Odds may move, stake limits may apply, markets can suspend, and bookmakers may use different void or result rules. Those execution and settlement risks can erase an apparent margin.
Let B be the total bankroll, dᵢ the decimal odds for outcome i, and Q the inverse-odds total:
Q = Σ(1 / dᵢ)
For every winner to produce the same gross return R, each stake sᵢ must satisfy:
sᵢ × dᵢ = R
Therefore, sᵢ = R / dᵢ. Because all stakes must add up to the bankroll:
B = Σsᵢ = R × Σ(1 / dᵢ) = RQ
Rearranging gives the equal gross return:
R = B / Q
Substituting that result back into the stake equation produces the bankroll-allocation formula:
stakeᵢ = B × (1 / dᵢ) / Q
In plain terms, each outcome receives its inverse odds as a share of the total inverse-odds sum. Shorter-priced outcomes receive larger stakes because they need more money to reach the same payout.
The equal profit after recovering the full bankroll is:
P = R − B = B(1 / Q − 1)
For example, with a £100 bankroll and Q = 0.9640, the balanced gross return is about £100 / 0.9640 = £103.73, leaving an equal theoretical profit of £3.73 whichever outcome wins. Actual stakes may need minor rounding to match permitted bet increments.
Start with a £100 total stake and decimal odds of 2.10 and 2.05. First, calculate each inverse price without rounding:
1 ÷ 2.10 = 0.47619047621 ÷ 2.05 = 0.48780487800.4761904762 + 0.4878048780 = 0.9639953542Each stake is its inverse-odds share divided by that sum, then multiplied by £100:
£100 × 0.4761904762 ÷ 0.9639953542 = £49.39759036£100 × 0.4878048780 ÷ 0.9639953542 = £50.60240964The full-precision stakes add to exactly £100. In practice, they must usually be placed to the nearest penny, giving £49.40 at 2.10 and £50.60 at 2.05.
If Outcome A wins:
£49.40 × 2.10 = £103.74
If Outcome B wins:
£50.60 × 2.05 = £103.73
The one-penny difference comes from stake rounding. Before rounding, either outcome returns:
£100 ÷ 0.9639953542 = £103.73493976
That produces a theoretical profit of £3.73493976, commonly stated as approximately £3.74. The profit exists because the inverse-odds sum is below 1: the two stakes cost £100, while the balanced gross return is about £103.735. Actual settled profit is £3.74 or £3.73 here, depending on which rounded stake wins.
A phone calculator works for a quick split: calculate each reciprocal, add them to obtain Q, then use stake = budget × (1 ÷ odds) ÷ Q for every outcome. Keep full precision until the final stakes are rounded. The broader guide to sports betting tools can help when choosing between simple calculators and reusable sheets.
For a spreadsheet, place decimal odds in A2:A3 and the total budget in E1:
| Column | Formula in row 2 |
|---|---|
| Inverse odds | =1/A2 |
| Normalized share | =B2/SUM($B$2:$B$3) |
| Allocated stake | =$E$1*C2 |
| Projected return | =A2*D2 |
Copy the formulas down, then round the stake cells to the permitted betting increment. Before placing anything, verify three points:
Any mismatch should be corrected in the stake cells, then checked again—not hidden by formatting.
The calculated stakes are only a starting point. Minimum and maximum stakes, permitted increments, and account limits may make the exact amounts impossible to place. Round deliberately—sometimes adjusting one stake upward and the other downward gives closer net results than rounding both conventionally.
Always compare net profit by outcome, not headline returns. Deduct exchange commission, payment or currency-conversion costs, and any outcome-specific charges before judging equality.
Settlement terms also matter:
Prices can move between calculation and placement. If any odds change, rerun the entire split using the new executable prices; changing only one stake preserves neither the budget nor equal profit. After rounding, recalculate every outcome from the actual accepted stakes and settlement rules.
Record the currently available odds, not an earlier screenshot or estimate.
Use amounts the bookmaker or exchange will actually accept.
Confirm every leg meets minimums, maximums, and available-balance requirements.
Subtract commission, fees, taxes, and any expected slippage from the balanced result.
Proceed only when every stake is executable at its quoted price and the post-cost return remains acceptable.
If one price moves or one stake is rejected, stop and calculate the entire split again.
Equal-profit arithmetic is only a plan until every leg can be placed. A complete, executable, post-cost result is the threshold for proceeding; anything less is a no-go.
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