Dutching: how to split your stake across several outcomes (with examples)

Often an idea does not fit in a single outcome: "the home side wins by one goal", "it ends 1-0, 2-0 or 2-1". Backing the same amount on each one gives a different result depending on which comes in. Dutching solves this: it splits the amount so that the result is the same whichever of the selections wins.

The formula

The idea is to back each selection in proportion to the inverse of its odds. Start from the sum of the inverses:

The group of selections behaves like a single bet with equivalent odds of 1/W.

Back example: three correct scores

You want to cover 1-0 at 7.00, 2-0 at 9.00 and 2-1 at 11.00 with 20 euros in total. W = 0.1429 + 0.1111 + 0.0909 = 0.3449, so the equivalent odds are 2.90.

Whichever of the three comes in, you win about 38 euros gross (about 36.26 net with 4.5% commission); if none of them does, you lose the 19.99 euros staked. Stakes are rounded to the cent, which is why the total is 19.99 and the results differ by one cent.

When stakes go in fixed steps

Some exchanges only accept stakes in fixed steps: on the Betflag exchange, for example, the minimum is 0.50 euros and stakes go up 0.50 at a time. The stakes become 8.50, 6.50 and 5.00 and the results are no longer identical: +39.50, +38.50 and +35.00 gross. No problem, as long as you know it beforehand: the maths must be redone with the real stakes.

Lay example: maximum liability

Dutching works when laying too. Here you usually don't choose the total laid but the maximum liability, that is how much you are willing to lose if one of the selections comes in. The total to lay is:

Example: you lay the draw at 3.50 and the away win at 4.00, losing 30 euros at most. W = 0.2857 + 0.25 = 0.5357, the total to lay is 34.61 euros: 18.46 on the draw and 16.15 on the away win.

• if it's a draw or an away win: −30 euros;
• if the home side wins: +34.61 euros gross (+33.05 net with 4.5%).

Does dutching create value?

No: it changes the shape of the risk, not its substance. The group of selections has its own equivalent odds, and it only pays off if the probability that one of the outcomes comes in is higher than 1 divided by those odds, net of commission. In the back example the equivalent odds are 2.90: you need a combined probability above roughly 34.5%, a little more to cover commission. For the value maths, see fair odds and expected ROI.

Dutching and cashing out a single outcome

Once a dutch is open, one of the outcomes may suddenly become more likely, for example after a goal. You can close that one only, leaving the others as they are: we explain how in the article on cashing out a single outcome.

In the OraGol PRO Exchange extension this maths is automatic: click the prices, the bet slip lists them one under another and with "Dutching" you type a single amount, total or maximum liability, which is split in steps the exchange accepts.