Dutching is backing two or more selections in one race or market, with stakes sized so that whichever of them wins, the return is the same. The stakes follow the implied probabilities, 1 / decimal odds, so a shorter price gets a bigger share. $100 dutched across illustrative prices of $3.00, $4.00 and $6.00 returns about $133.33 if any of the three wins, and nothing if anything else wins.
Dutching, also called dutch betting, turns several runners into one bet at one combined price. It changes how often you collect and how much, not whether the prices are good, and how betting odds work sets out the chances behind every price.
What is dutching, and how are the stakes worked out
Each selection gets the share of the total stake that its implied probability is of the whole set:
- implied probability = 1 / decimal odds, for each selection
- the dutch's book = the implied probabilities added up
- stake per runner = total stake x (1 / odds) / sum of (1 / odds)
- return if any of them wins = total stake / sum of (1 / odds)
The last line is also the dutch's combined price: 1 / sum of (1 / odds). Three runners whose implied chances add to 75% behave like one bet at 1 / 0.75 = $1.33, which wins whenever any of the three does. Implied probability explains the conversion, and the dutching calculator splits a stake across up to 10 selections.
A $100 dutch across $3.00, $4.00 and $6.00
With illustrative prices, the three implied probabilities add up to 1 / 3.00 + 1 / 4.00 + 1 / 6.00 = 0.75, a 75% book. Each runner's share of the $100 is its implied probability divided by 0.75:
| Runner | Price | Share: (1 / price) / 0.75 | Stake from $100 | Return if it wins |
|---|---|---|---|---|
| Runner A | $3.00 | (1 / 3.00) / 0.75 = 44.44% | $44.44 | 44.44 x 3.00 = $133.32 |
| Runner B | $4.00 | (1 / 4.00) / 0.75 = 33.33% | $33.33 | 33.33 x 4.00 = $133.32 |
| Runner C | $6.00 | (1 / 6.00) / 0.75 = 22.22% | $22.22 | 22.22 x 6.00 = $133.32 |
Rounded to the cent the stakes come to $99.99 and each winner pays $133.32. Unrounded, every winner pays 100 / 0.75 = $133.33. That gives the dutch its whole shape:
| Result | What comes back | Profit or loss on the $99.99 |
|---|---|---|
| Runner A, B or C wins | $133.32 | +$33.33 |
| Any other runner wins | Nothing | -$99.99 |
To aim at a set return instead, divide that return by each price. $200 back whichever wins needs 200 / 3.00 = $66.67, 200 / 4.00 = $50.00 and 200 / 6.00 = $33.33, an outlay of $150.00, which is 200 x 0.75; rounded to the cent, those stakes return between $199.98 and $200.01.
Dutching vs backing one runner
Say your own illustrative estimates give Runner A a 31% chance, Runner B 23% and Runner C 15%, so one of the three wins 69% of the time and another runner wins the other 31%. Set the dutch beside $100 on Runner A alone:
| Dutch A, B and C | $100 on Runner A alone | |
|---|---|---|
| Chance of a profit | 0.31 + 0.23 + 0.15 = 69% | 31% |
| Profit when it wins | +$33.33 | 100 x 3.00 - 100 = +$200.00 |
| Loss when it loses | -$99.99 | -$100.00 |
| Average result | 0.69 x 133.32 - 99.99 = -$8.00 | 0.31 x 300 - 100 = -$7.00 |
The dutch collects more than twice as often, but its average result is no better, because a dutch is the stake-weighted average of its parts. Runner A returns 0.31 x 3.00 = 0.93 per dollar, Runner B 0.23 x 4.00 = 0.92 and Runner C 0.15 x 6.00 = 0.90. Weighted by the stakes, 0.4444 x 0.93 + 0.3333 x 0.92 + 0.2222 x 0.90 = 0.92: an 8% average loss, built from the three runners' own losses of 7%, 8% and 10%.
If your estimates were 36%, 27% and 18% instead, each price would return 1.08 per dollar and so would the dutch. That is 0.81 x 133.33 = $108 back per $100 on average, an 8% edge that collects 81% of the time. Value betting explains how to check whether an estimate holds up.
So dutch when you rate two or three runners above their prices and want results that arrive more steadily. Back one runner when one carries your whole opinion, because adding runners you think are short only adds their margin.
Risk: Betting involves risk. A dutch that collects 81% of the time still loses its whole outlay the other 19%, the estimates behind any edge can be wrong, and there is no guarantee of profit. See responsible gambling for limits and support.
How many runners to cover
A dutch loses if none of your runners wins, and covering more runners does not remove that risk; it changes what a win pays. Add runners at illustrative prices of $8.00, $10.00 and $12.00 to the three above:
| Runners covered | Book | Return per $100 if one wins | Profit if one wins |
|---|---|---|---|
| A, B and C | 0.75 = 75.00% | 100 / 0.75 = $133.33 | +$33.33 |
| Add D at $8.00 | 0.75 + 0.125 = 87.50% | 100 / 0.875 = $114.29 | +$14.29 |
| Add E at $10.00 | 0.875 + 0.10 = 97.50% | 100 / 0.975 = $102.56 | +$2.56 |
| Add F at $12.00 | 0.975 + 0.0833 = 105.83% | 100 / 1.0583 = $94.49 | -$5.51 |
Each runner added raises the book and lowers what a winner returns. Past 100% the dutch loses money even when one of your runners wins. Cover a whole field at one bookmaker and the book is that market's full percentage, above 100% by its margin, so every result loses a little.
When a dutch becomes an arbitrage
A dutch's book says nothing about the runners you left out. Under 100% it only means your selections pay back more than they cost if one of them wins. A dutch is an arbitrage only when the selections cover every possible outcome and their implied chances still add to under 100%, which usually means taking each price from a different bookmaker.
Example: A two-player tennis market, with illustrative prices of $2.15 for Player 1 at Bookmaker A and $1.95 for Player 2 at Bookmaker B. The book is 1 / 2.15 + 1 / 1.95 = 0.4651 + 0.5128 = 0.9779, or 97.79%. Dutching $100 puts 100 x 0.4651 / 0.9779 = $47.56 on Player 1 and 100 x 0.5128 / 0.9779 = $52.44 on Player 2, and either result returns about 100 / 0.9779 = $102.26 ($102.25 on Player 1 once the stakes are rounded to the cent).
Both bookmakers have to accept both bets at those prices and settle the match the same way, which a retirement or a voided bet can break. Arbitrage betting covers those risks, and the arbitrage calculator does that sum on a market of two to four outcomes.
Risk: Betting involves risk. An arbitrage or a middle only works if every bet is accepted at the price shown, and bookmakers can limit stakes, void bets or close accounts. See responsible gambling for limits and support.
Spreading the bets across bookmakers, and on the tote
Taking each runner's price from whichever bookmaker offers the most lowers the book. At illustrative best prices of $3.20, $4.00 and $6.40, the book falls to 0.3125 + 0.25 + 0.15625 = 0.71875. Then $100 returns 100 / 0.71875 = $139.13 whichever of the three wins, $5.80 more than at $3.00, $4.00 and $6.00.
Spreading the bets brings edge cases with it:
- A refused or part-accepted bet leaves one runner short of its stake, so that runner pays less than the others. Re-work the split on what was actually accepted.
- A price that moves before your last bet breaks the balance, so each bet goes on at the price you actually get, not the one you planned.
- A late scratching of one of your runners gets its stake refunded, and the stewards' deduction, in cents in the dollar, comes off winning fixed-odds bets on the other runners struck before the scratching. For NSW on-course bookmakers that is BR 14 of Racing NSW's Rules of Betting; online bookmakers apply their own terms. Either way the returns are no longer level, as scratchings and deductions explains.
- On an exchange, commission comes off net winnings in the market, which lowers the profit but leaves the stake split where it was.
A tote dutch cannot be levelled in advance at all. A dividend is declared only after the result, from a pool that takes bets until betting closes, your own included; the Northern Territory's tote rules, for example, pay out the pool less refunds and commission. Stakes sized on approximates therefore pay unequal amounts, and tote dividends explains how a pool pays.
Risk: Betting involves risk. The extra $5.80 arrives only if each bookmaker accepts its bet at the price you planned, and a refused bet, a price move or a late scratching leaves the returns uneven. See responsible gambling for limits and support.
Mistakes that cost a dutch money
With the illustrative prices above:
| Mistake | What it costs | The fix |
|---|---|---|
| Expecting the dutch to add value | On prices you rate short, the dutch averages -8%, the stake-weighted average of its parts | Dutch only runners you rate above their price |
| Covering too many runners | Six runners from $3.00 to $12.00 make a 105.83% book, so a winner returns $94.49 per $100 | Check the book after each runner you add |
| Placing the bets one by one while prices move | If Runner C shortens to $5.00 before your last bet, it returns 22.22 x 5.00 = $111.10, a profit of $11.11 instead of $33.33 | Re-work the stakes on the prices you actually get |
| Reading the book as your chance of winning | The 75% book is the prices' view; on the estimates above the three win 69% of the time | Judge the dutch on your own chances |
Shopping runner prices on B337's Terminal
A dutch is only as good as the price on each runner, and the $5.80 gap above came from shopping three prices. On the Terminal each bookmaker has its own column, 40+ bookmakers across racing and sports, with the best available price on each runner picked out and exchange back and lay prices alongside. Its prices are collected on a cycle rather than tick by tick, so confirm each one in your bookmaker account and work the stakes on the prices you got. A free account opens a limited view of the Terminal with live odds.
Risk: Betting involves risk. Every leg of a dutch has to be accepted at the price shown, a dutch loses its whole outlay when none of its runners wins, and there is no guarantee of profit. See responsible gambling for limits and support.