Dutching Calculator — Equal-Profit Stakes for Any Selection
Split your stake across multiple selections so every winner returns the same profit. Enter your total stake and the odds for 2–10 selections to instantly see how much to bet on each and what you make if one of them wins.
Odds format
Saved for all betting calculators
Amount you want to spread across all selections
e.g. -110 or +150
e.g. -110 or +150
Return if any selection wins
$136.36
Same profit whichever selection wins
| Selection | Odds | Stake | Return if Wins |
|---|---|---|---|
| Selection 1 | +200 | $45.45 | $136.36 |
| Selection 2 | +150 | $54.55 | $136.36 |
Total Profit / Loss
+$36.36
Implied Probability Sum
73.33%
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How to Use the Dutching Calculator
The dutching calculator divides a single total stake across multiple competing selections so that whichever selection wins, you receive the same total return. This technique is called dutching and is widely used in horse racing, football, and any market with three or more outcomes.
To use the calculator:
- Enter your total stake — the combined amount you want to spread across all selections.
- Choose the number of selections (2 to 10).
- Enter the odds for each selection. Use the odds available at the same bookmaker, or mix odds from different books for an arbitrage dutch.
The calculator shows the exact stake for each selection, the return if any of those selections wins, and whether the combined implied probability is below 100% — then that return exceeds your stake. It is a true arbitrage only when your selections cover every possible outcome; otherwise you lose the whole stake if something you did not select wins.
Type the odds in the format you picked with the Odds format switch — 3.50 decimal, 5/2 fractional and +250 American are the same price. Odds of 2.00 (+100) represent even money; shorter odds represent the favourite.
The Formula
Dutching mathematics relies on the concept of implied probability — the probability implied by a set of odds. Here is the full derivation:
- Implied probability of each selection:
p_i = 1 / O_i
where O_i is the decimal odds for selection i. - Total overround (implied probability sum):
Overround = Σ p_i = Σ (1 / O_i)
When using a single bookmaker, this number is typically above 1.0 (above 100%), reflecting the book's built-in margin. When shopping across books, you can sometimes find a combination below 1.0, creating an arbitrage opportunity. - Stake for each selection:
Stake_i = S × (p_i / Overround) = S × (1/O_i) / Σ(1/O_j)
This distributes your total stake S proportionally to each selection's implied probability. - Return if any selection wins (the same for each):
Return = Stake_i × O_i = S × (1/O_i / Overround) × O_i = S / Overround
Notice the O_i cancels, confirming the return is identical regardless of which selection wins. - Profit if any selection wins:
Profit = Return − S = S / Overround − S = S × (1/Overround − 1)
Positive when Overround < 1 — an arb only if the selections cover every outcome. Negative when Overround > 1 (book edge).
Practical Examples
Example 1 — Three-Way Football Market (No Arb)
A bookmaker offers Home Win at 2.40, Draw at 3.40, and Away Win at 2.90. You want to dutch all three outcomes with a $100 total stake.
- Implied probs: 1/2.40 + 1/3.40 + 1/2.90 ≈ 0.4167 + 0.2941 + 0.3448 = 1.0556
- Overround: 105.56% — book has a 5.56% edge
- Home Win stake: $100 × (0.4167 / 1.0556) ≈ $39.47
- Draw stake: $100 × (0.2941 / 1.0556) ≈ $27.86
- Away Win stake: $100 × (0.3448 / 1.0556) ≈ $32.67
- Guaranteed return: $100 / 1.0556 ≈ $94.73 (a guaranteed −$5.27 result)
Even without an arb, dutching is useful here: you guarantee seeing any outcome return $94.73. You have covered the entire market and your maximum loss is capped at $5.27 — identical to the book's built-in margin of 5.27%.
Example 2 — Two-Selection Arbitrage Dutch (Arb)
Book A offers Team X to win at 2.10. Book B offers Team Y to win at 2.10 (in a two-outcome market). You dutch both with $200.
- Implied probs: 1/2.10 + 1/2.10 ≈ 0.476 + 0.476 = 0.952
- Overround: 95.24% — arb exists!
- Stake on each: $200 × (0.476 / 0.952) = $200 × 0.5 = $100 each
- Guaranteed return: $200 / 0.952 ≈ $210
- Guaranteed profit: +$10 (5% ROI)
This is a classic sports arbitrage: the same event is priced at 2.10 on both outcomes at two different books, creating a risk-free $10 profit on a $200 investment.
Example 3 — Horse Racing (4 Selections)
A horse race has four realistic contenders at odds: 3.50, 4.00, 5.00, and 6.00. Total stake: $120.
- Implied probs: 0.2857 + 0.25 + 0.20 + 0.1667 ≈ 0.9024
- Overround: 90.24% — under 100% only because the four do not cover the field, so this is not an arbitrage
- Return if one of the four wins: $120 / 0.9024 ≈ $132.98
- Profit if one of the four wins: +$12.98; if any other runner wins, you lose the $120
This situation arises in larger fields where the runners you leave out carry the rest of the probability. Covering the top four contenders at the best available prices gives the same profit whichever of them wins — the risk is a longer-priced runner winning instead.
Frequently Asked Questions
Dutching is a betting strategy where you spread a single total stake across multiple selections in the same event so that whichever selection wins, you receive the same return. Named after Al Capone's accountant Dutch Schultz, who reportedly used the technique to cover multiple race outcomes, it is widely used in horse racing, football, and any market where you want to back several runners without the return depending on which specific one wins.
Both strategies spread bets across multiple outcomes, but with different intent. Arbitrage (arbing) specifically refers to situations where the combined implied probabilities across all outcomes are below 100%, guaranteeing a profit regardless of the result. Dutching is the broader technique of equalising returns across selections — it can be done whether an arb exists or not. When you dutch in a market with no arb, you still equalise your return across your chosen selections, but your total return is less than your total stake (a controlled loss instead of a random one).
Dutching opportunities with guaranteed profit (true arbs) require the sum of 1/odds across your chosen selections to be below 1.0 (100% implied probability). This rarely happens within a single bookmaker. Instead, use odds from multiple bookmakers: check Book A for the best price on Selection 1, Book B for Selection 2, and so on. Odds comparison sites and arb-finding software can automate this search. In horse racing, each-way dutching across top-3 or top-4 selections is popular even without a strict arb.
Yes, and this is very common. In an 18-runner horse race you might dutch just the three horses you think are realistic contenders, accepting that if a longshot wins you lose everything. The calculator handles this automatically — simply enter the odds of only the selections you want to cover. The return shown applies only when one of your chosen selections wins. If any other outcome occurs (e.g. a horse you did not dutch wins), you lose your entire stake.
If the implied probability sum of your selections is above 100% (overround greater than 1), there is no arbitrage and your return will be less than your total stake. This is the bookmaker's built-in margin working against you. You are still reducing variance — instead of winning big on one outcome and losing on others, you guarantee a consistent (small) loss equal to the book's edge. To find opportunities with guaranteed profit, you need the combined implied probability from all your chosen selections (ideally sourced from different bookmakers) to be below 100%.
Implied probability is the probability of an outcome that is implied by its odds: implied probability = 1 / decimal odds. Odds of 2.00 imply a 50% probability; odds of 4.00 imply 25%. A bookmaker prices a two-outcome market so that both implied probabilities sum to more than 100% (e.g. 105%), with the excess representing the vig. When dutching, you distribute your stake in proportion to each selection's implied probability. Lower implied probability (longer odds) gets a smaller absolute stake, but the same return if it wins — that is the mathematical elegance of dutching.
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