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Dutching Calculator

Split one stake across several selections so you collect the same amount whichever one wins.

This sizes a split across selections you have already picked and prints the hit rate it needs, not how likely those selections are, which is the half that decides whether it pays.

Profit if one of the 3 wins

+$19.23stake $50.00 → collect $69.23

1. Build the split

Every odds field reads a decimal price (2.50). Switch the format above to enter prices the way your book quotes them, or open the odds converter to see one price in all of them.

2. Every lane finishes level

  1. Selection 1. Stake $23.08 (46%)Return $69.23

  2. Selection 2. Stake $15.38 (31%)Return $69.23

  3. Selection 3. Stake $11.54 (23%)Return $69.23

StakeComes back if it winsTotal outlay

The outlay

Book %

72.2%

Total outlay

$50.00

Book is 72.2%, and that is the break-even hit rate: your 3 selections have to win 72.2% of the time between them before the split pays for itself. A book under 100% is an arbitrage only when the selections cover every outcome in the event. Here, anything else winning takes the whole outlay.

Against the full field

Add up the implied probability (1 divided by decimal odds) of every outcome in the market, not just your selections, and enter that total here as a percentage. This reads your selections against the market’s own proportional view of them, the same arithmetic the FAQ below walks through by hand.

Your selections’ book72.2%

Market’s reading, once the full field’s book is entered–

Share this scenario

A link to this page opens the calculator on the same selections, prices, stake or target return, manual split (if any), and full-field book (if entered) shown here. It carries those inputs and nothing else: nothing is stored, and nothing in it identifies you.

Written and reviewed by Alexander Korsager · last reviewed September 28, 2026 · corrections

The idea

What this tool shows

Dutching is backing more than one outcome in the same event, sized so the return is identical no matter which of your selections comes in. It turns several individual prices into one combined position, useful when you can narrow a race to two or three live contenders but cannot separate them.

  1. Each selection's share of the stake is proportional to its implied probability (one divided by its decimal odds), so shorter prices get more of the stake. Add those implied probabilities up and you have the book for your selections, and the return whichever one wins is your total stake divided by that book. The book is also the number that says what the split has to do, because it is the break-even hit rate: at a 72.2% book your selections have to win 72.2% of the time between them before the split pays for itself.

  2. A book under 100% is not an arbitrage, and that is the most common misreading of this page's central number.It is an arbitrage only when your selections cover every outcome in the event. Back three runners in a twelve-runner field and their book will often sit well below 100% simply because they are short prices, while the other nine still win their share of the time and take the whole outlay when they do. A book above 100% is the clearer case: break-even would sit past certainty, so the split loses on average at those prices however likely the selections really are.

  3. It is worth being precise about what the split changes, because it is less than it looks.Where a market spreads its margin proportionally across the field, dutching a group of selections carries the same expected loss per dollar staked as backing one of them on its own. The margin does not compound across selections the way it does across the legs of a parlay, and it does not shrink either. What the split buys is a narrower range of outcomes, not a better price. The one place it does move the price is the favorite-longshot bias: betting markets are generally found to load more margin onto long prices than short ones, so a split made of favorites tends to pay less than the market's headline margin and one made of longshots more.

  4. None of that makes a dutch a safe position, and the equal payout can make it feel like one.Every selection in the split can lose, the whole outlay goes when they all do, and each extra name you add makes the payout smaller. Stake only money you have set aside for betting and can afford to lose.

FAQ

Questions players ask

What does the book percentage tell me?

It is the sum of the implied probabilities of the selections you backed, and it is the hit rate they have to reach between them for the split to break even. At a 90% book they need to win 9 times in 10 between them. At a 105% book break-even sits past certainty, so the split loses on average at those prices whatever the true chances are. What it is not is a rate of profit or loss: the amount below or above 100% is not what you make or lose on average, because the book of a subset of the field says nothing about how likely those particular selections are.

Is a book under 100% an arbitrage?

Only if your selections cover every outcome in the event, which is what the arbitrage calculator is for and is rare inside a single bookmaker's market. Across a subset of the field a book under 100% is ordinary: it happens as soon as your prices are short enough. It means the break-even hit rate is below certainty, not that the profit is locked in. Everything you did not back still wins its share of the time and takes the whole outlay when it wins.

When is dutching better than a single bet or a parlay?

When you have a strong opinion on a small group of outcomes rather than one. Dutching two selections at 3.0 and 4.0 gives a smoother result than picking one and being wrong half the time, at the cost of a lower payout when you are right. Against a parlay the difference is structural rather than a matter of taste: a parlay pays the bookmaker's margin on every leg it stacks, while a dutch pays it once, on one event. That makes the split cheaper than a parlay of the same names, not cheaper than backing one of them.

Can I dutch to a target return instead of a fixed stake?

Yes. Switch the mode to target return and enter the amount you want back; the calculator sizes each stake to hit it and shows the total outlay required. The book does not change with the mode, so neither does the hit rate the selections have to reach.

How do I tell whether the break-even hit rate is beatable?

Measure it against what the market itself says those selections are worth. Add up the implied probability of every outcome in the market, not just the ones you backed, and enter that total as the full field's book below the calculator: it divides your selections' book by it for you. That strips the margin out proportionally and leaves the market's own combined chance for your group. On the three prices this page ships with, 3.0, 4.5 and 6.0, your book is 72.2%, so break-even needs 72.2%. If the whole field prices out at 112%, the market's fair reading of those same three is 72.2 divided by 1.12, or 64.5%. You need 7.7 points more than the market is giving them, and the same gap counted as money is 1 divided by 1.12 less 1, a loss of 10.7 cents per dollar staked. Notice what that last figure does not contain: any term for which three selections you chose. It is the market's margin and nothing else, which is the arithmetic behind this page saying the split cannot improve the price. What the comparison gives you is the size of the disagreement you are taking on, not a reason to take it. The market's number is still the market's, and the split only pays if your own reading of those selections is the better one. Proportional removal is also the roughest of the three methods on the no-vig calculator, because it assumes the margin sits evenly across the field, which the favorite-longshot bias says it does not: where that bias holds, this arithmetic is pessimistic about a split made of short prices and optimistic about one made of long ones.

What if I want more on one selection than an even split gives it?

Switch the mode to manual stakes and type a stake beside each price. A box left blank reads as zero rather than as missing, so that selection stays in the book and its row shows the whole outlay going when it is the one that lands. The calculator stops sizing anything and prices what you entered: one profit per outcome instead of the single repeated figure an even split produces, with the stake an even split of the same total outlay would have put on each selection printed alongside. It leads with the worst of your outcomes and how far that sits below the even split's flat profit, because that gap is what favoring a pick costs when the one you backed least is the one that lands. The book is the same either way, so the hit rate your selections have to reach between them does not move.

What does the full-field book box below the calculator do?

It runs the FAQ answer above for you. Enter the sum of every outcome's implied probability in the market, not just your selections, as a percentage, and the page divides your selections' book by it to show the market's own proportional reading of your group, the point gap between the two, and what backing any subset of a field margined this way costs per dollar staked on average. Leave it blank and nothing changes: it only ever reads what you type into it, and a number smaller than your own selections' book gets flagged rather than priced, since a real market cannot produce one.

Methodology

How this is calculated

Each price becomes an implied probability (1 divided by the decimal odds), and those add up to the book for your selections. The return whichever selection wins is your total stake divided by that book, and each selection's stake is that return divided by its own odds, which is what makes every winner pay the same amount.

Target-return mode runs the same arithmetic backwards: the outlay is the return you asked for multiplied by the book.

The book is also the break-even reading, because a stake of return times book comes back as the return when the group hits, so the split is only positive expected value when the true combined chance of your selections is higher than the book.

Manual-stakes mode sizes nothing: it adds the stakes you type for the outlay and prices each outcome on its own, as that selection's stake times its odds less the whole outlay. The even split of the same outlay is priced beside it, and the gap between your worst outcome and its flat profit is what the uneven split costs.

That gap can never run the other way: if every outcome collected more than the even split's return, the stakes would have to add to more than the outlay they came from, which they cannot.

An optional full-field book, entered below the split, is divided into your selections' own book (marketComparison in math.ts) to give the market's proportional reading of your group, the point gap against it, and the per-dollar cost of a proportionally margined field, live rather than worked by hand.

Common misreadings5
  • A book under 100% is not an arbitrage unless the selections cover every outcome in the event. Across a subset it only means break-even sits below certainty, and everything unbacked still takes the whole outlay when it wins.
  • The profit shown is what lands if one of your selections wins. It is not an expected result, and staking up on it treats a conditional payout as a return.
  • Adding selections is not the same as adding safety. Each one raises the book, which lowers the payout and raises the hit rate the group has to reach, and a selection carrying more margin than the rest pulls the whole split's expected value down with it.
  • An equal payout across several names can read as a hedged or locked-in position. Nothing here is hedged: every leg is a back bet on the same event, and they lose together.
  • The best figure in manual-stakes mode is one outcome out of several, not what the split is worth. Exactly one outcome happens, the worst of them is on the same panel, and every selection losing takes the whole outlay.
Assumptions6
  • Every odds field reads whichever format the odds format control is set to, and only that one. The control exists, rather than a field that takes anything, because 150 is a real decimal price as well as the American price +150: a field reading both would have to guess which you meant on exactly the input where guessing wrong is invisible, since a wrong price of that kind still prints a complete and correctly formatted panel. A price that does not read in the selected format shows nothing rather than a figure, and the page names the format it would read in when there is one. Switching the format rewrites the prices already entered, so a field never holds a number in a format the page is no longer reading, and a fractional price is rewritten to the closest fraction with a denominator of 100 or less.
  • In manual-stakes mode a blank stake reads as zero rather than as missing, so that selection stays in the split: it still counts toward the book, it is still priced in the even-split comparison, and the outcome where it wins prints the loss of the whole outlay. Declining to back one of the names you are pricing is a real opinion, which is why it is priced rather than ignored, but an empty box is a decision here and not a gap. A stake that is not a number, or is negative, is the other case entirely: the whole split reports itself unsolvable, because quietly dropping that selection would change the outlay every other figure on the panel is computed from. A price that does not parse drops its selection in every mode, and any stake typed beside it goes with it.
  • Every price entered is available at the same moment and at the stake sizes shown. A split assembled from prices captured minutes apart, or at a limit smaller than its stake, does not return what this prints.
  • The selections are all in the same event and only one of them can win. Backing outcomes that can both land is a different position, and the equal-payout arithmetic here does not describe it.
  • Stakes go on exactly as sized. Rounding each one to a whole dollar or to a minimum bet unit tilts the payout slightly toward whichever selections rounded up. Manual-stakes mode holds cents, so it treats a gap smaller than cent rounding on your prices can produce as the even split rather than as a pick you favored.
  • The full-field book you enter is a figure you gathered yourself, from the rest of the market's own prices at the same moment as your selections. The comparison it produces is only as current as that figure: a market that has moved since you added it up compares your selections against a field that no longer exists.
Limits7
  • The book of a subset of the field is the rate your selections need to hit, not the rate they will hit. This page has no way to estimate the second, and the gap between the two is the entire bet. Dividing your book by the full field's, as the FAQ does, gets you a baseline rather than an answer: it recovers the market's estimate of your selections, which is the number you are disagreeing with, not a check on whether the disagreement is right.
  • The shortfall below 100%, or the excess above it, is not a rate of profit or loss. That reading only holds for a book covering every outcome in a market, which a dutch by definition does not.
  • Where a market spreads its margin proportionally, dutching carries the same expected loss per dollar staked as backing one of the selections alone. The split narrows the range of outcomes, it does not improve the price.
  • Betting markets are generally found to load more margin onto long prices than short ones, so a split made of favorites tends to pay less than the market's headline margin and one made of longshots more. The direction is well documented in racetrack betting; the size of it in the market you are pricing is not something this page can measure.
  • Dutching needs no lay side, so this page is the least exchange-dependent of the tools it sits with, and the honest version of the limit is narrower rather than absent. What two-sided prices change is how often a split is worth pricing at all: the tightest numbers in a market are usually the ones with a lay side quoted against them, and a subset whose required hit rate looks beatable at scale is generally found by having those prices in front of you. That is ordinary in the UK and Australia and uneven in the US, where a two-sided price is more likely to come from a federally regulated prediction market than from a state-licensed sportsbook exchange. Nothing on this page stops working without one. The supply of splits worth making is what thins.
  • The cost of favoring a pick is measured against an even split of the same total outlay, not against not betting at all. It says what an uneven split gives up when the selection you backed least is the one that lands, and nothing about whether either split is worth making.
  • The full-field comparison assumes the market's margin sits proportionally across every outcome, which the favorite-longshot bias says it usually does not: it is pessimistic about a split made of short prices and optimistic about one made of long ones. It also assumes the full-field figure you entered is complete and current, and it is never computed for you from the individual prices in the rest of the market, only from the single total you provide.
Evidence

The arithmetic is the definition of the book. Implied probability is 1 divided by decimal odds, and a stake of collect divided by odds returns the collect figure on any winner, so a total outlay of collect times book pays collect when the group hits and nothing when it does not.

Break-even at the book follows directly from that. announce.test.ts pins the payout as conditional and pins the break-even line in both directions, including the reading this page got wrong until 2026-09-09 (issue #342), when a book under 100% across part of a field was described as an arbitrage.

Manual-stakes mode is the same arithmetic read per outcome, and math.test.ts checks its one non-obvious claim over a grid of prices and weightings rather than asserting it: the worst outcome of an uneven split never beats the even split's flat profit, so the cost printed is never a gain in disguise.

The comparison against the full field above is the same proportional removal the no-vig, EV and CLV calculators use, applied to a group of selections instead of to one side of a two-way market: dividing every implied probability by the full book leaves the subset's fair combined chance as its own book divided by the full one, so a stake that collects outlay divided by subset book returns, on average, outlay divided by full book, and the expected result per dollar staked is 1 divided by the full book less 1.

That expression carries no term for the selections, which is the derivation behind this page's statement that a proportionally margined market charges the same for a split as for a single bet.

The worked figures in that answer are that arithmetic on the prices the page ships with, and the 112% full-field book in it is an illustration rather than a measurement of any particular market.

It is also, since this pass, a live figure: marketComparison in math.ts takes the selections' own book and the full-field percentage typed into the optional field below the calculator and returns the same three figures the FAQ answer walks through by hand, pinned in math.test.ts against that exact worked example (72.2% against 112%, giving 64.5%, a 7.7-point gap and a 10.7-cent loss per dollar) plus the boundary case where the entered full-field figure is smaller than the selections' own book, which a real market cannot produce and the function flags rather than prices.

The favorite-longshot bias referred to above is an empirical regularity rather than a fixed quantity, documented most thoroughly in parimutuel racetrack betting and surveyed there by R. H. Thaler and W. T.

Ziemba, Anomalies: Parimutuel Betting Markets: Racetracks and Lotteries, Journal of Economic Perspectives 2 (1988), number 2, pages 161 to 174. It is stated on this page as a direction only, and the size of it in any particular market is not something this tool measures.

Gambling can cause serious harm. The National Problem Gambling Helpline is free, confidential and open 24/7, call or text 1-800-MY-RESET (1-800-697-3738), or chat at ncpgambling.org/chat.

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