- Formula: stake_i = S × (1 ÷ odds_i) ÷ Σ(1 ÷ odds_j); the payout is S ÷ Σ.
- Verified examples: with odds 2.10 and 3.40 and S = 100, stakes of 61.82 and 38.18, payout 129.82.
- If Σ exceeds 1: there is a guaranteed loss (the margin), and it is not a surebet.
The dutching formula
Dutching has a single formula.
With it you can split any number of selections.
We show it first and then use it in three examples.
stake_i = S × (1 / odds_i) ÷ Σ(1 / odds_j)
S is the total stake you want to split.
odds_i are the odds of selection i.
Σ(1 / odds_j) is the sum of the inverses of all the odds you cover.
Once you have calculated the stake for each selection, the payout is the same on all of them.
Payout = S ÷ Σ(1 / odds).
And the profit is the payout minus S.
All the numbers are examples with fictional data, verified with code.
Dutching does not remove the risk of the outcomes you do not cover.
Betting is for adults 18 and over only.
Why the formula works
Each stake is chosen so that stake × odds is the same on every selection.
In other words, the payout is the same whichever one wins.
For that, the stake has to be inversely proportional to the odds.
If one set of odds is double another, its stake is half.
That is why 1 ÷ odds appears in the formula.
The sum Σ only serves to make the stakes add up to the total S.
Substituting, the payout becomes S ÷ Σ.
You can check it with any example.
We do that now.
How to calculate dutching step by step
Example 1 · Two selections: home win and draw (example)
Match: Liverpool against Manchester United.
You cover “Liverpool win” at 2.10 and “draw” at 3.40.
Total stake S = 100.
| Step | Calculation | Result |
|---|---|---|
| 1 ÷ 2.10 | 1 ÷ 2.10 | 0.4762 |
| 1 ÷ 3.40 | 1 ÷ 3.40 | 0.2941 |
| Σ | 0.4762 + 0.2941 | 0.7703 |
| Liverpool stake | 100 × 0.4762 ÷ 0.7703 | 61.82 |
| Draw stake | 100 × 0.2941 ÷ 0.7703 | 38.18 |
| Payout | 100 ÷ 0.7703 | 129.82 |
| Profit | 129.82 − 100 | +29.82 |
Check the payout.
If Liverpool win, 61.82 × 2.10 = 129.82.
If it is a draw, 38.18 × 3.40 = 129.82.
If Manchester United win, you lose the 100.
That is why the profit of 29.82 only holds if one of the two covered outcomes happens.
It is not a guaranteed result.
When is it worth it? The break-even point
The covered set of outcomes needs to happen with a probability higher than Σ.
In this example, Σ = 0.7703, that is, 77.03%.
If you believe it happens more often, it has positive expected value.
| Real probability of the covered outcomes (example) | Calculation | Expected value |
|---|---|---|
| 80% | 0.80 × 129.82 − 100 | +3.86 |
| 77.03% | 0.7703 × 129.82 − 100 | 0.00 |
| 70% | 0.70 × 129.82 − 100 | −9.13 |
If you estimate that probability wrong, the expected value changes a lot.
See the expected value calculator and implied probability.
Example 2 · Three selections: exact score (example)
Match: Flamengo against Palmeiras.
You cover three scorelines: 1-0 at 6.50, 1-1 at 6.00 and 2-1 at 9.00.
Total stake S = 100.
| Scoreline (example) | Odds | Stake | Payout |
|---|---|---|---|
| 1-0 | 6.50 | 35.64 | 231.68 |
| 1-1 | 6.00 | 38.61 | 231.68 |
| 2-1 | 9.00 | 25.74 | 231.68 |
| Total | — | 100.00 | 231.68 |
Σ = 1/6.5 + 1/6 + 1/9 = 0.4316.
Payout = 100 ÷ 0.4316 = 231.68.
Profit = 231.68 − 100 = +131.68.
It looks like a lot.
But the break-even is 43.16%.
If it ends 0-0, 2-0, 0-1 or anything else, you lose the 100.
Example 3 · Σ above 1: when there is no profit
Now you cover all three outcomes of the Liverpool against Manchester United 1X2.
The example odds are 2.10, 3.40 and 3.60.
Total stake S = 100.
| Outcome (example) | Odds | 1 ÷ odds | Stake |
|---|---|---|---|
| Liverpool | 2.10 | 0.4762 | 45.43 |
| Draw | 3.40 | 0.2941 | 28.06 |
| Manchester United | 3.60 | 0.2778 | 26.50 |
| Total | — | 1.0481 | 100.00 |
Payout = 100 ÷ 1.0481 = 95.41.
Profit = 95.41 − 100 = −4.59.
You lose 4.59 whoever wins.
Σ is above 1, and the excess is the bookmaker's margin.
1.0481 means a 4.81% margin over the probabilities.
The guaranteed loss on your stake is 4.59%.
When Σ is above 1, dutching across all outcomes loses money.
It is not a way to win.
It only spreads the loss evenly.
How to tell dutching from a surebet
In a surebet, the odds come from several bookmakers.
You cover all outcomes and Σ comes out below 1.
There the profit does not depend on which outcome happens.
Example with two outcomes.
One bookmaker pays 2.20 for one and another 2.10 for the other.
Σ = 0.4545 + 0.4762 = 0.9307.
| Data (example) | Value |
|---|---|
| Σ | 0.9307 |
| Stake at 2.20 | 48.84 |
| Stake at 2.10 | 51.16 |
| Payout | 107.44 |
| Profit | +7.44 |
That is a surebet.
It is very rare, it does not last long and it carries practical risks.
You can read more in surebets and in sports trading.
Dutching, on the other hand, covers only some outcomes.
The formula is the same, but the risk is different.
Use the formula as a calculator, not as a guarantee.
The dutching calculator in Excel
You build the sheet once and reuse it.
The formulas are written for English-language Excel; in Spanish Excel, SUM is SUMA, IF is SI and the argument separator is a semicolon.
The table has three selections.
| Cell | Content | Example |
|---|---|---|
| B1 | Total stake S | 100 |
| A3:A5 | Odds of each selection | 6.50 / 6.00 / 9.00 |
| B3 | =1/A3 (copy down to B5) | 0.1538 |
| B6 | =SUM(B3:B5) | 0.4316 |
| C3 | =$B$1*B3/$B$6 (copy down to C5) | 35.64 |
| C6 | =SUM(C3:C5) | 100.00 |
| D3 | =C3*A3 (copy down to D5) | 231.68 |
| D6 | =D3-$B$1 | 131.68 |
Add a cell that warns you about the problem.
For example =IF(B6>1,"Σ above 1: no profit","Σ below 1").
That way you do not forget to look at the sum.
Rounding stakes
Bookmakers accept few decimals.
With 62 and 38 in example 1, the payout is 130.20 if Liverpool win and 129.20 if it is a draw.
The profit ends up between 29.20 and 30.20.
Rounding changes the split, but not by much.
When the stakes are small, the effect is bigger.
That is why it is better to use stakes with two decimals when you can.
Common mistakes when calculating dutching
- Forgetting the margin: if Σ is above 1, there is no profit.
- Believing you cannot lose: the uncovered outcome loses the whole stake.
- Using outdated odds: they change fast and break the split.
- Ignoring commission: on exchanges it is deducted from the net winnings.
- Betting too much because you are covered: covering is no reason to raise the stake.
What to read next
If you want the concept without the math, go back to dutching: what it is and how to do it.
If your question is about cost, see what is the bookmaker's margin.
To keep a record of what you bet, use the Excel control template.
And set your limits with the limits spreadsheet.
The background guide is AI for betting: the complete guide.
Calculate the expected value of a set of odds
Frequently asked questions
What is the dutching formula?
stake_i = S × (1 ÷ odds_i) ÷ Σ(1 ÷ odds_j).
S is the total stake and Σ is the sum of the inverses of the odds.
The payout is S ÷ Σ on whichever selection wins.
How is the money split with two selections?
With odds 2.10 and 3.40 and S = 100: stakes of 61.82 and 38.18.
The payout is 129.82 if either one wins, a profit of 29.82.
If a third outcome happens, you lose the 100.
What happens if the sum of inverses is above 1?
There is no profit.
With odds 2.10, 3.40 and 3.60, Σ is 1.0481 and you collect 95.41 for every 100 staked.
That excess is the bookmaker's margin.
How much profit does dutching give?
Profit = S × (1 − Σ) ÷ Σ.
With Σ = 0.7703 and S = 100 it is 29.82, but only if a covered outcome happens.
If another one happens, you lose the whole stake.
Is dutching the same as a surebet?
No.
A surebet covers every outcome and Σ is below 1.
Dutching covers some of them and does not guarantee a profit, even though it uses the same formula.
How do I calculate dutching in Excel?
Put the odds in a column and calculate =1/odds next to them.
Add up the inverses and calculate each stake with =S*inverse/sum.
The payout is =stake*odds and it must come out equal on all of them.