Dutching Calculator: Split One Stake So Any Winner Pays the Same

How to use the dutching calculator

1. Choose the odds format you will type in: decimal, fractional or American.
2. Set the number of selections, from two to six.
3. Type the price of each selection in the rows that appear.
4. Enter the total stake you want to spread across them.
5. Read the results: the combined odds, the return if any selection wins, the profit, and the implied chance that one of them wins.
6. Use the table to place each bet. It lists every selection with its odds, its stake and its return. Round each stake to the penny, or to the smallest unit the site accepts.

The dutching formula

Each price is first turned into an implied probability, one divided by the decimal odds. For selections with decimal odds o1, o2 and so on, and a total stake T:

• Sum of implied probabilities: P = 1/o1 + 1/o2 + … + 1/on
• Combined odds: 1 / P
• Return if any selection wins: T / P
• Stake on selection i: T × (1/oi) / P
• Profit: T / P − T

The stake on each selection is proportional to its implied probability. A selection at 5.00 implies 20%, one at 10.00 implies 10%, so the first takes twice as much of the stake as the second. Multiply any stake by its own odds and you get the same figure, T / P, which is the whole point. The dutching calculator runs exactly these steps after converting fractional or American prices to decimal.

Worked example: three horses at 5.0, 7.0 and 9.0

Three horses at 5.00, 7.00 and 9.00 (4/1, 6/1 and 8/1), with a total stake of 50.

The implied probabilities are 0.20000, 0.14286 and 0.11111. Their sum is 0.45397, so the group has an implied chance of 45.4%. The combined odds are 1 / 0.45397 = 2.20, which is 6/5 in fractions. The return is 50 / 0.45397 = 110.14.

The exact return is 110.14 on each horse. Once the stakes are rounded to the penny, the returns land between 110.11 and 110.16, a spread of a few pence that no one will notice. If any of the three wins, the profit is 60.14. If the race goes to one of the other nine runners, the loss is 50.

Dutching in correct-score football betting

Correct score is where a dutching calculator earns its keep in football. The market is split into dozens of outcomes, none of them likely on its own, so a single correct-score bet is a long shot almost by definition. Many bettors hold a view on the shape of a match rather than on the exact score: a narrow home win, a low-scoring game, both sides scoring.

Take a narrow home win and three scores at illustrative prices, not quotes from any site: 1–0 at 7.50, 2–1 at 9.00 and 2–0 at 10.00, with 30 to stake. The implied chances add up to 34.4%, the combined odds are 2.90, and the stakes come out at 11.61, 9.68 and 8.71. Any of those three scores returns 87.10, a profit of 57.10.

Widen it to six scores at 7.00, 8.00, 9.00, 11.00, 13.00 and 15.00 with 60 staked and the implied chance rises to 61.3%. The combined odds fall to 1.63, the return to 97.80 and the profit to 37.80. Every score you add makes a return more likely and smaller. The draws, the away wins and the 3–0 outside the group still lose the full stake. Correct-score markets also carry a heavier margin than the match result, so the combined price usually flatters the real chance. How football markets are priced is set out on the football betting hub.

When dutching makes sense

Dutching suits a view that covers a range of outcomes rather than one. Typical cases:

• Racing fields with a few genuine contenders. Handicaps and big-field races often come down to three or four horses on form, with long prices on each. The horse racing guide explains how those prices are formed.
• Correct-score and scorer markets. Many outcomes, none likely on its own, and a view that fits several of them.
• Outrights. A golf event or a tournament winner market where you rate a handful of names and cannot pick between them.
• Best prices from different sites. The dutching calculator does not care where each price comes from, so you can take the best available odds for each selection and dutch them across sites.

In each case the test is the same. The combined odds have to pay enough to make up for the outcomes you left out. If your own estimate of the group's chance is higher than the implied chance the calculator shows, the dutch has value by your numbers. If it is lower, splitting the stake only spreads a poor bet more thinly.

When the combined odds are too short

Every selection you add shortens the price of the group. Add a 2.50 favourite to the horses at 5.00 and 7.00 and the implied chance jumps to 74.3%. The combined odds fall to 1.35 and 50 staked returns 67.31, a profit of 17.31 for covering three quarters of the race on paper.

Push further and the bet stops making sense at all. Four horses at 2.50, 4.00, 5.00 and 6.00 have implied chances that add up to 101.7%. Dutch 50 across them and the return is 49.18: you lose 0.82 even when one of your horses wins, and you lose 50 when none of them does.

The reason is the margin. Every price on a sportsbook already contains a slice of the bookmaker's overround, so every selection you add to a dutch brings its slice with it. Dutch the whole field and your loss is exactly the bookmaker's margin. The odds calculator measures that margin for any market.

Our view: once the group's implied chance passes about two thirds, the profit left is thin enough that one price drifting before you place the last bet can take most of it. Fewer, better selections beat a wide net.

Dutching versus arbitrage

Dutching and arbitrage use the same formula: stakes in proportion to implied probabilities, the same return on every covered outcome. The difference is what they cover.

Arbitrage needs prices from several sites that together add up to less than 100% across the whole market. It is rare, the gaps are small, and sites tend to limit accounts that chase them. Dutching is a betting opinion expressed across several selections. The arbitrage version of this tool, which checks whether a set of prices covers every outcome at a profit, is the arbitrage calculator.

What the calculator does not include

The dutching calculator works with the prices and the stake you type and nothing else. It does not account for:

• Exchange commission. On a betting exchange the winnings are reduced by commission, so the real return is lower than shown.
• Withdrawn runners. When a horse is pulled out late, British racing applies a Rule 4 deduction to winning bets in that race, which cuts the returns.
• Dead heats. A dead heat halves the stake that counts, or more with a three-way tie, and breaks the equal return.
• Price changes. The stakes are right only at the prices entered. If one price moves before you place every bet, recalculate.
• Each-way terms, stake limits and minimum stakes, which vary from site to site.

For accumulators, full-cover bets and each-way returns, use the bet calculator.

Sportsbooks that take these bets with only an email and a wallet are ranked among the non-KYC sportsbooks we have read.

Next to read: Hedge bet calculator, Kelly calculator and all betting calculators.

Bitcasino.ioSportsbook

US$2,500When ID can be asked

Open