The Mathematics
Convert each selected runner's price to decimal d, then calculate its reciprocal 1/d. Add those reciprocals to obtain Q. With total budget B, the stake on runner i is B × (1/d_i) ÷ Q. Every chosen runner then produces the same conditional gross return B ÷ Q if it is the sole winner. Conditional profit is B ÷ Q − B. A selected subset can have Q below one while still excluding the eventual winner.
Q = sum of 1 ÷ decimal odds for selected runners
Stake on runner i = total budget × (1 ÷ d_i) ÷ Q
Return if a selected runner wins = total budget ÷ Q
Conditional profit = conditional return − total budget
If an unbacked runner wins: return = £0
Worked Example
Allocate £50 between two selected horses at 3/1 and 5/1, or decimal 4.00 and 6.00. Q = 1/4 + 1/6 = 5/12. Stakes are exactly £30 and £20. Either backed sole winner returns £120, giving £70 profit after the full £50 outlay. If neither horse wins, return is £0 and loss is £50. Rounding Q to 0.417 before dividing would incorrectly produce £119.90.
How do I use the dutching inputs?
Enter the prices of the horses you intend to back, and enter one Total Stake for the entire allocation. The form starts with three rows; remove a row to follow the two-horse example or add rows for a larger selected group. Enter every chosen price, then read Individual Stakes as the amounts for the separate cash singles. These are not multiples and do not require several horses to win.
The shorter-priced selection receives the larger stake because each pound on it pays less. At decimal 4.00 and 6.00, the £30 allocation to the first horse and £20 to the second both produce £120 gross returns. The other stake loses when one wins, so subtract the whole £50 budget to measure profit. Do not subtract only the winning horse's individual stake from the equalized return.
What does the selected book percentage tell me?
The Implied Book percentage is 100 × Q for the selections entered. In the example it is 41.67%, not the percentage of the complete race market unless those are every possible winner. Q below one gives positive conditional profit on a selected winner. It does not establish a forty-one-percent actual group chance or guarantee that the excluded horses will lose.
If every outcome of an exhaustive mutually exclusive market is covered at executable fixed prices, Q below one represents an arithmetic underround before fees and settlement complications. If Q equals one, equalized returns merely recover the total budget. If Q exceeds one, even a covered winner leaves a loss. For two exhaustive outcomes both at 4/5, decimal 1.80, a £50 allocation splits £25 each and returns £45, losing £5 regardless of which wins.
How do rounding, limits and price movement affect dutching?
The calculated stakes are displayed to pennies, while the underlying arithmetic uses more precision. Rounding each line can leave the sum a penny above or below the intended budget and produce slightly unequal realized returns. Before placing anything, add the rounded stakes and multiply each by its executable price. Bookmaker minimum stakes or stake limits can prevent the exact allocation from being accepted.
Prices can change between calculating and placing the separate bets. If the £20 stake at decimal 6.00 is actually accepted at 5.50, its gross return becomes £110 rather than £120. The other £30 at 4.00 still returns £120. Recalculate from the accepted prices, not a previous screen quote, and avoid describing an allocation as locked until all relevant bets are accepted.
How is dutching different from accumulators and probability models?
Dutching is a stake allocation across alternatives, usually horses in one race. An accumulator combines outcomes across events and requires every leg to succeed. If you dutch two horses from unrelated races, both could win or both could lose, so the one-winner equal-return interpretation no longer describes all possible outcomes. The formula assumes mutually exclusive winning selections.
Equalizing payouts does not assess form or select the horses. The tool has no live odds feed, true probability model, commission field, Rule 4 control or non-runner processing. A withdrawn chosen runner may refund one stake while also changing payouts on remaining winners; a dead heat can change the ordinary full-price return. Use the relevant operator rules and the separate settlement tools to understand those adjustments, rather than treating the initial allocation as a guaranteed net profit.
Popular questions about this calculator
Does dutching guarantee a profit?
No. With only some runners covered, an unbacked winner loses all allocated stakes. Even a backed winner can leave a loss if the selected reciprocal sum exceeds one. Equalizing conditional returns is not the same as guaranteeing the outcome or eliminating betting risk.
How do I split £50 at 3/1 and 5/1?
Use £30 at 3/1 and £20 at 5/1. Either backed sole winner returns £120 including its stake, giving £70 profit after subtracting the entire £50 allocation. If an unbacked runner wins, the return is zero and the loss is £50.
Why does the favourite receive more of the dutching stake?
A shorter decimal price pays less per pound, so more stake is needed to reach the same return. Stakes are proportional to reciprocal prices. At decimal 4 and 6, the ratio is 1/4 to 1/6, or 3 to 2, giving a 60/40 split.
What does Implied Book mean for a selected subset?
It is the sum of the entered selections' reciprocal decimal prices, expressed as a percentage. It is not necessarily the complete market book and is not a measured group winning probability. Unentered runners may still win and cause the allocation to lose.
What happens when the dutching book exceeds 100%?
Equalized gross return falls below the total stake. For two exhaustive outcomes at decimal 1.80 and a £50 budget, stakes are £25 each and the covered winning return is £45, giving a £5 loss. No stake split can create profit at those complete-market prices.
Can I dutch every runner in a race?
The form can add rows, but covering every runner does not guarantee positive profit. A complete quoted book normally exceeds 100%, making equalized return less than the outlay. Fees, limits, withdrawals, price execution and dead heats also need separate checking.
Does dutching use singles or an accumulator?
Separate singles. Each selected horse receives its own stake and any one backed winner can trigger the conditional return. An accumulator is a different structure requiring all linked legs to succeed; horses in one outright race are not ordinary independent accumulator legs.
Do rounded dutching stakes always add up exactly?
Not necessarily. The displayed stakes are rounded to pennies, while the allocation uses unrounded values. Check their sum and each resulting return before using them. Minimum accepted stake increments can further prevent a perfect equal-return allocation.
Does the dutching calculator include commission?
No. It calculates gross fixed-price back-bet allocations. Exchange commission is usually based on net market winnings under account terms and may change the final profit. The tool also omits Rule 4, withdrawals and dead heats.
Can I use dutching prices as true win probabilities?
No. Reciprocal prices are allocation weights and odds-implied figures, not calibrated chances. The formula chooses stakes to equalize gross payout; it does not identify value, rank horses or establish the likelihood that one of your selections will win.
Official rules and further reading
These operator references explain bet structures and settlement rules. They are not endorsements, and the terms attached to your accepted bet take precedence. Worked amounts on this page are illustrative arithmetic, not live odds or promised outcomes. Only gamble money you can afford to lose; a returns tool does not make a bet safe.