Arbitrage & value
Dutching calculator
Dutching splits a single total stake across several selections in the same market, at the same bookmaker, in proportion to their implied probabilities. The result is that whichever of your selections wins, the return is the same amount — the outcome of the bet no longer depends on which one of them comes in.
This is the same allocation arithmetic as an arbitrage, and it is worth being clear about why the two are not the same thing. An arbitrage takes the best available price on every outcome from several bookmakers, so the complete set sums below 100% and some result always pays. Dutching takes prices from one bookmaker on a subset of the market: the subset can sum below 100% only because outcomes have been left out. If none of the selections you backed wins, the whole stake is lost.
Inputs
All selections must come from the same market, so that at most one of them can win.
The amount split across all selections together, not the amount on each one.
Result
- Stake on selection 1 (at 3.50)Returns €163.73 if it wins
- €46.78
- Stake on selection 2 (at 5.00)Returns €163.75 if it wins
- €32.75
- Stake on selection 3 (at 8.00)Returns €163.76 if it wins
- €20.47
- Total stakedSplit across the selections above, with the rounding remainder allocated so the total matches exactly
- €100.00
- Combined percentage of the selections backedUnder 100%, so a winning selection returns more than the total stake. This is not an arbitrage unless these prices cover every outcome of the market and came from different bookmakers.
- 61.07%
- Return on the total stake if a selection winsBefore stakes are rounded to whole cents
- +63.74%
- Profit if one of your selections winsWorst of the backed legs after rounding — 63.73% of the €100.00 staked
- €63.73
- If none of your selections winsEvery outcome of the market you have not backed is uncovered
- The full €100.00 stake is lost
These figures are the arithmetic of the prices entered, not a forecast. Placing several legs at one bookmaker takes time and the price on a later leg can shorten before it is matched; stakes can be limited or rejected; a non-runner, void selection, dead heat or Rule 4 deduction changes the return on legs already placed; and accounts can be restricted. Above all, the profit line applies only if one of the selections you backed wins.
How this is calculated
stake_i = total x (1 / odds_i) / sum(1 / odds_j)
Invert each price to its implied probability (1 / odds), add those together, and give each selection the share of the total stake that its implied probability represents. To check the result by hand, multiply each stake by its own price: every leg should come back to roughly the same return, and that return is the total stake divided by the sum of the implied probabilities. The sum is the number that decides everything. Below 1, a winning selection returns more than the total stake; at or above 1, every selection returns less than the total stake and the set loses on any result. At a single bookmaker the complete market always sums above 1 — 2.10, 3.60 and 3.80 on a football match is 101.71% — so a dutching set can only fall below 100% by leaving outcomes out, and the outcomes it leaves out are exactly the risk. Stakes are then rounded to whole cents, with the remainder given to the legs whose discarded fraction was largest, so the total staked equals the amount you asked for rather than drifting a cent or two below it.
Worked example
Three runners in one race, all priced at the same bookmaker, with EUR 100 to be split between them.
- 01Prices at one bookmaker: 3.50, 5.00 and 8.00 on the three runners you want to back.
- 02Implied probabilities: 1/3.50 = 0.2857, 1/5.00 = 0.2000, 1/8.00 = 0.1250. They total 0.6107, i.e. the three selections cover 61.07% of the book.
- 03Split EUR 100 in those proportions: 100 x 0.2857 / 0.6107 = EUR 46.78 at 3.50, EUR 32.75 at 5.00, and EUR 20.47 at 8.00.
- 04Check the legs: 46.78 x 3.50 = EUR 163.73, 32.75 x 5.00 = EUR 163.75, 20.47 x 8.00 = EUR 163.76. The calculator reports the smallest of the three, so the figure shown is EUR 63.73 above the EUR 100 staked.
- 05That 61.07% is not an arbitrage. Every other runner in the race is unbacked, and if one of them wins the EUR 100 is lost in full — which is the trade dutching makes: a narrower range of results in exchange for still needing one of your selections to win.
Questions
What is the difference between dutching and arbitrage?
The stake allocation is identical — both split a stake so that every leg returns the same amount. The difference is where the prices come from and what they cover. An arbitrage uses the best price on every outcome of the market, taken from several bookmakers, so the complete set can sum below 100% and one of your legs must win. Dutching uses one bookmaker and usually a subset of the market, so a sum below 100% only reflects the outcomes you left out.
Is dutching risk-free?
No. Equalising the legs removes the question of which of your selections wins, not whether one of them does. If the market settles on an outcome you did not back, the entire stake is lost. Dutching a complete market at a single bookmaker is not an escape either: the prices sum above 100%, so every result returns less than you staked.
Why do the legs not all return exactly the same amount?
Stakes have to be whole cents, so the ideal proportions cannot usually be placed exactly. The calculator rounds the stakes, recomputes each leg from the rounded figure, and reports the smallest return rather than the largest — the number you are shown is the one that holds regardless of which of your selections comes in.
Why might the real result differ from the figure shown?
The legs are placed one after another at the same bookmaker, so a price can shorten before the later stakes are matched, and the set no longer equalises. Maximum stake limits can cap a leg. In racing, a non-runner triggers a Rule 4 deduction that cuts the return on bets already struck; a dead heat pays a reduced amount; a void selection returns its stake and unbalances the rest. Bonus or free-bet funds that do not return the stake also change the maths. Recalculate with the prices you actually got rather than the ones you planned on.
Related calculators
These calculators are information tools. They describe the arithmetic of the prices you enter — they are not advice, and they do not predict outcomes. Betting involves risk. 18+ only. If gambling is causing you harm, support is available from Peluuri.