Dutching is one of the less commonly known betting strategies out there. That is because it contradicts the usual approach of choosing which option offers the most value and instead, spreading your risk across several outcomes. What is dutching and how does dutching work? Read on to find out.
Typically, the process of placing a bet is straightforward: there is an event with multiple possible outcomes and odds are attributed to each of them. A bettor would choose the outcome for which they think there is an edge (or simply the one they fancy), and place their bets.
There it is, article finished!
Well, there are some cases in which there isn’t just one outcome that is preferred to bet on. Maybe the bettor wants to spread their risk over several outcomes, bet against a particular outcome, or hedge their position on a previous bet. Dutching is a technique used to place bets on multiple outcomes at the same time, such that the pay-off from any of these outcomes is the same. By dutching, the probability of winning a bet is increased, but this comes at the cost of lower potential returns, as the stake has to be split up over all the outcomes.
How does dutching work?
Say there is a four-horse race with each horse having odds of 10.0, 6.0, 3.0, and 2.2 respectively. The first thing a bettor should check is if there are any better odds elsewhere – as perhaps the horse with odds of 10.0 is being offered at odds of 12.0 elsewhere. That small bit of research could go a long way in terms of your potential profit.
Next, the bettor can check if there is an arbitrage opportunity using the best odds of 12.0, 6.0, 3.0 and 2.2. If the odds are too high, a risk-free profit can be made. In practice, however, finding an arbitrage opportunity is unlikely as trading bots will be quick to pick it up if it exists.
Thereafter, the decimal odds can be translated into implied probabilities by finding their inverse. For example, the horse with odds of 3.0 has an implied probability of a one third chance of winning. The sum of implied probabilities is generally higher than 100%, with the excess probabilities defined as the margin or the overround. In this example, the margin is 3.79%, and hence there are no arbitrage opportunities.
Say the bettor would like to place a bet on the two outsiders – that is the horses with odds of 12.0 and 6.0. If the bettor bets €1 on each horse, they would make a profit if either of the horses wins, but make more if the horse with odds of 12.0 wins.
The question is, how much should they bet on each horse in order to receive the same payoff irrespective of which one of the two wins? In this case, it is simple to note that the stake on the horse with odds of 6.0 should be double that of the horse with odds of 12.0 - since stakes of €1 and €2 on the horses with odds of 12.0 and 6.0 will return €12 in winnings and €12 minus €1 minus €2 equals €9 in profit if any of these two horses win.
The cases we tend to have at hand do not tend to be this simple, but thankfully we can use a simple equation to calculate how to split your stakes to achieve the same effect.
Dutching: How to calculate your stake
The proportion of total stake should be the ratio of the implied probability of each outcome to the sum of implied probabilities of the dutching portfolio. That’s a mouthful, so let’s go for it step by step.
- Decide which outcomes will be included in the portfolio.
- Find the implied probability of each of these outcomes.
- Sum the probabilities.
- The ratio of the total stake is the implied probability of each outcome to the sum from step three.
- If one is creating a dutching portfolio placing bets on the horses with odds of 12.0, 6.0 and 2.2;
- The implied probabilities are 1 in 12, 1 in 6, and 1 in 2.2 respectively;
- The sum of implied probabilities is 0.7046;
- The proportion of the stake to be placed on each horse are (1 / 12) / 0.7046 = 11.83%, (1 / 6) / 0.7046 = 23.66% and 64.52%.
In this case, if the total stake is €10, then €1.18, €2.36, and €6.45 can be bet on each horse and should any of these three win, the bettor would receive around €14.19, which is just above €4 in profit.
One should note that a dutching portfolio is not possible if the sum of implied probabilities is over one for the outcomes dutched. In this case, even if one of the outcomes occurs and one of the bets are won, the bettor only gets back part of their stake, making a guaranteed loss.
Alternatively, one can use the quick calculator we created to create a dutching portfolio below. Note that the app can deal with a dutching portfolio of up to five outcomes and automatically excludes odds that are zero or lower (as they are not possible and should not occur in any real-life setting).
What about alternatives to dutching?
If the selections within the dutching portfolio include all outcomes bar one, then one might consider laying the outcome on a betting exchange as a simpler alternative. Laying is the action of betting against an event, essentially acting as a bookmaker. The process of placing a lay bet typically includes a commission on any winnings by the betting exchange.
Assuming a standard commission of 5% and lay odds of 3.75 on the outstanding horse (with odds of 3.0 on the rest of the market)*, then the dutching portfolio is better than the lay option. (Note: the lay odds must be higher or equal to the back odds, or there is an arbitrage opportunity, as my co-author and I show in an academic paper available for those with a subscription.)
In order to earn €4.19 post-commission, the bettor would need to risk €12.39 (4.19 / (1 - 0.05) × (3.7 - 1)) on the lay bet, which is higher than the €10 from the dutching selection. Indeed, it seems that the only way that the positions would be equal is if the bettor can lay at odds of 3.27 ((10 ÷ 4.19 / (1 - 0.05)) +1). This may not be available to match in the market at all.
The mathematics of this section is not the focus of the article but calculations for the example are shown below. The aim is, however, to point out that laying is not always the best option and dutching might be better - especially if the bookmaker has low margins or the betting exchange has high commissions.
Dutching as a hedging tool
In a recent academic paper, my co-author and I show the mathematics behind hedging a bet through a dutching portfolio or a lay bet on an exchange. Pinnacle is thanked for sponsoring the Open Access fee for this paper which makes it available to all, rather than the publication being behind a pay-wall or only accessible to academics.
It is important to ensure that dutching technique guarantees a profit.
To show a simple example, let us again consider the same four-horse race (best odds: 12.0, 6.0, 3.0, and 2.2). You placed a bet of €10 at odds of 3.0 – receiving a potential pay-out of €30 should that horse win (a profit of €20). The odds have now changed and this horse is now the favourite, with the odds on the four horses now being 20.0, 10.0, 1.5, and 3.0. Now you can set bets on the other three horses, such that you will have a total profit regardless of which of the horses actually win.
We make a number of propositions in the paper, but the chief proposition related to this article is that a profit is only possible if the difference in implied probability for the outcome that was bet on is higher than the current market spread.
As usual, it is easier to explain using a simple example - the interested reader can see Proposition X in our paper for the general case. The odds on the bet we made changed from 3.0 to 1.5, meaning that the implied probabilities changed from 33.33% to 66.67% (the inverse of 3 and 1.5). That is a change of 33.33%.
The new market spread is ((1 ÷ 20) + (1 ÷ 10) + (1 ÷ 1.5) + (1 ÷ 3) -1), which is equivalent to (0.05 + 0.1 + 0.67 + 0.33 - 1) or 15%. Since the former (33.33%) is higher than the latter (15%), then it is possible to set up a portfolio of bets that result in hedged profits. This time, rather than splitting a stake, we consider that the bet on any horse should give out a pay-out of €30 just like the original bet. So bets of €1.50, €3.00 and €10 are placed at odds of 20.0, 10.0 and 3.0.
The calculation of this is simply the pay-out divided by the odds (so €30 divided by odds of 20.0 = €1.50). This approach would guarantee a pay-out of €30 following total bets of €10, €1.50, €3 and €10 to equal €24.50, so a hedged profit of €5.50.
What if the odds had changed to 10.0, 7.0, 1.5, and 2.25 (i.e. not that much of a change)? The market spread would be 35.39% which is higher than 33.33%, meaning that a dutching hedge is not possible. Indeed, using the same analogy of attempting to get a pay-out of €30 from any outcome would mean stakes of €3, €4.29 and €13.33 at odds of 10.0, 7.0 and 2.25. These together with the original stake of €10 means that any outcome would yield a loss of about 62 cents.
Insert odds of Dutching Portfolio:
up to 5 odds used in this example
Click the button to display the number of the number field. Odds should be greater than zero.
This article introduced dutching as a concept – it is not only useful to split up risk, but can also be used to bet against an event. Some simple examples were provided on how to create a dutching portfolio. The approach could be used to hedge bets should odds change favourably.
The more mathematically inclined reader would find it interesting to read our paper and Pinnacle is thanked for disseminating these thoughts.