What is dutching?
Dutching is the practice of distributing a wager across multiple options in the same market, in proportions that produce the same return regardless of which of the selected options wins. Unlike a standard bet on a single option, dutching allows a player to cover several possible outcomes while controlling the risk and the return.
The term originates from the gambling strategies attributed to the American organized crime figure Arthur Flegenheimer, known as Dutch Schultz, who reportedly used this method in horse racing in the 1920s and 1930s.
How dutching works
Suppose a market has four options, and a player believes that options 1 and 2 are both likely to win, but is uncertain about which one. Rather than choosing one, the player can dutch options 1 and 2 by distributing his total stake in inverse proportion to their odds, so that the total return is the same if either option wins.
The stake for each option is calculated as:
S: total amount to wager
dₖ: decimal odd of option k
sₖ: stake on option k
sₖ = S · (1/dₖ) / Σ(1/dⱼ)
Where the sum Σ(1/dⱼ) is taken over all options included in the dutch.
For example, a player wants to dutch options 1 and 2 with a total stake of ¤100:
Option 1: decimal odd 2.50
Option 2: decimal odd 4.00
Σ(1/dⱼ) = 1/2.50 + 1/4.00 = .40 + .25 = .65
s₁ = ¤100 · .40 / .65 ≈ ¤61.54
s₂ = ¤100 · .25 / .65 ≈ ¤38.46
Verification:
If option 1 wins: ¤61.54 · 2.50 = ¤153.85
If option 2 wins: ¤38.46 · 4.00 = ¤153.84
The return is approximately ¤153.85 in either case, producing a profit of approximately ¤53.85 on the ¤100 wagered. The minor difference is due to rounding.
The combined odd and implied probability
A dutch bet effectively creates a combined odd. The combined odd of a dutch across selected options is:
Combined odd = 1 / Σ(1/dⱼ)
In the example above:
Combined odd = 1 / .65 ≈ 1.538
This combined odd can be interpreted just like any individual odd: it implies a probability (1 / 1.538 ≈ 65%), it has an associated expected value, and its profitability depends on whether the actual combined probability of the selected options exceeds the combined implied probability.
Expected value of a dutch
A dutch bet has positive expected value if and only if the sum of the actual probabilities of the selected options exceeds the sum of their implied probabilities. Let w₁ and w₂ be the estimated actual probabilities of options 1 and 2:
Combined actual probability = w₁ + w₂
Combined implied probability = Σ(1/dⱼ) = 1/d₁ + 1/d₂
If the combined actual probability exceeds the combined implied probability, the dutch has positive expected value. Otherwise, it does not.
For instance, if the player estimates w₁ = .45 and w₂ = .25:
Combined actual probability = .45 + .25 = .70
Combined implied probability = .40 + .25 = .65
Since .70 > .65, the dutch has positive expected value. The expected value per unit wagered is:
e = (w₁ + w₂) · (combined odd − 1) − (1 − w₁ − w₂)
e = .70 · (1.538 − 1) − .30
e = .70 · .538 − .30
e = .377 − .30
e = .077 = 7.7%
Dutching versus arbitrage
Dutching and arbitrage are related but distinct concepts. Arbitrage involves covering all options in a market, using odds from different bookmakers, to guarantee a profit regardless of the outcome. Dutching involves covering a subset of options, typically at the same bookmaker, and does not guarantee a profit — it only guarantees the same return if any of the selected options wins, but produces a total loss if none of them wins.
Dutching can be combined with odds comparison: the player could select the best available odd for each option across different bookmakers, and then dutch those options at their respective bookmakers. This maximizes the combined odd and therefore the expected value of the dutch.
When dutching is useful
Dutching is useful when a player has reason to believe that more than one option in a market has positive expected value, or when the player's analysis suggests a high combined probability for a group of options but is unable to determine which specific option will win.
In horse racing, for example, a player might estimate that three of twelve horses have a combined probability of 60% of winning, while the sum of their implied probabilities is only 50%. Dutching these three horses produces a bet with positive expected value, without requiring the player to predict which of the three will win.
In a three-option head to head market, a player might dutch local and draw if he believes the visit team is substantially less likely to win than the odds imply, even if he is uncertain whether the home team will win or the match will end in a draw.