Dutching explained for betting — Statometrics Academy

In one sentence

Dutching is spreading one total stake across several selections, sized so that the profit is the same whichever of them wins.

How it works

Suppose you fancy three scorelines in a Correct Score market but cannot split them. Rather than backing one, you back all three with stakes weighted towards the shorter prices. Shorter prices get bigger stakes, longer ones smaller stakes, so every winner pays back the same amount.

In effect you are creating a new bet: "one of these three wins". The odds of that combined bet come from adding up the implied probabilities of the three prices.

Dutching does not create value. If each selection is poor value, the combined bet is poor value too. It simply reshapes the risk so you get one outcome instead of several.

The maths

S_i = T \times \frac{1 / O_i}{\sum_{j} 1 / O_j}

O_{\text{dutch}} = \frac{1}{\sum_{j} 1 / O_j}

S i: the stake on selection i.
T: your total stake across all selections.
O i: the decimal odds of selection i.
The sum runs over every selection you are dutching.
O dutch: the combined odds for "one of these wins".

In plain English: stake each selection in proportion to its implied probability, and your combined odds are one over the total implied probability.

Worked betting example

Correct Score on Betfair (illustrative prices). You dutch 1-0 at 7.00, 1-1 at 8.00 and 2-1 at 9.00 with a £100 total stake and 2% commission.

Implied chances: 0.1429, 0.1250 and 0.1111. Total = 0.3790.
Combined odds = 1 ÷ 0.3790 = 2.639.
Stakes: £100 × 0.1429 ÷ 0.3790 = £37.70; £100 × 0.1250 ÷ 0.3790 = £32.98; £100 × 0.1111 ÷ 0.3790 = £29.32.
Check: £37.70 + £32.98 + £29.32 = £100.00.
Return if it finishes 1-0: £37.70 × 7.00 = £263.90. If 1-1: £32.98 × 8.00 = £263.84. If 2-1: £29.32 × 9.00 = £263.88.
Profit before commission: about £163.87 whichever wins.
Betfair charges commission on net market winnings, so 2% of £163.87 = £3.28. Profit after commission: about £160.60.
If the score is anything else, you lose £100.

For this to be worth doing you need the three scorelines together to land more than 1 ÷ (1 + 1.6387 × 0.98), about 38.4% of the time.

Where it's good

Correct Score, where you think two or three scorelines are overpriced but cannot separate them.
Match Odds: backing the draw and the underdog together against a short favourite.
In-play trading, spreading a position across several outcomes.
Turning several small edges into one position with a single outcome.
Laying the field in reverse: "dutch laying" several scorelines you think are too short.

Limitations and pitfalls

Value does not add up magically. Dutching three poor-value prices gives one poor-value bet.
Each selection pays the market margin, so dutching in high-overround bookmaker markets is expensive.
Rounding stakes to pennies and minimum stakes shift the returns slightly; check the table.

How to build it

A few lines of Python or a spreadsheet; betfairlightweight to place all legs through the Betfair API quickly.
Data: live back prices for each selection.
Practical tip: calculate the break-even combined win chance after commission before you place anything, and only dutch if your model puts the group comfortably above it.

Arbitrage: dutching every outcome at a book under 100% is an arb.
Overround: the margin you pay on each dutched selection.
Back-lay hedging: the same equal-profit idea using lays.
Expected value: judging whether the combined bet is worth it.
Commission-adjusted EV: building commission into the break-even.