Dutching

Dutching betting system is a betting formula which consists of distributing an overall stake over several events.
This technique is very valuable because it ensures a fixed gain regardless of the winning prediction in the selection: only one is needed!
Furthermore, the winnings can also be combined and render high profits.
All the details, developments, calculations and mathematical proofs are developed in this page. By using the calculator on this page you can freely choose the number of events to dutch, the total bet as well as the odds of each event: the calculator simply gives the exact distribution of bets, the fixed gain obtained and the minimum probability of this gain.

Dutching Calculator

Choose the number of events to bet, the total bet, and enter odds: the calculator then automatically computes everything, the exact distribution of bets and the total payout obtained.





Net profit ensured
Minimum probability of winning
Max Profit

The "Net profit ensured" calculated corresponds to the net winnings for a single prediction won in the list of selected events and odds. Of course, if several predictions are won, the profit is even greater. The maximum profit calculated and displayed corresponds to the net profit if all predictions are won at the same time.
The "minimum probability of winning" is the probability of winning at least the "ensured net gain".

Mathematical analysis of dutching on 2 bets

We begin the mathematical analysis with two bets on two events: The total stake invested in dutching is thus M = m1 + m2
If my prediction is exact on event 1, I win the net gain G1 = m1c1 − M, and if it is exact on event 2, I earn the net gain G2 = m2c2 − M.
We wish to balance these two gains, which we note G, therefore: G = G1 = G2
We thus have,
G = m1c1 − M G = m2c2 − M
By dividing the 1st equation by c1 and the 2nd by c2, we obtain
G×1/c1 = m1 − M×1/c1 G×1/c2 = m2 − M×1/c2
We now add these last two equations, term by term, to obtain
G×1/c1 + G×1/c2 = m1 + m2 − M×1/c1 − M×1/c2
We now use the total stake M = m1 + m2, and we factor by further setting α = 1/c1 + 1/c2 to get
Gα = M − Mα = M(1−α)
which gives the formula which determines the constant guaranteed gain according to the total stake:
G = M 1/α − 1

When is dutching beneficial?

Dutching is then worth considering when the prévious gain is positive, that is therefore when
1/α − 1 > 0
that is
1/α > 1 ⇔ α < 1
As we had set α = 1/c1 + 1/c2 we have just found here the surebet condition, a condition also for a winning dutching
α = 1/c1 + 1/c2 < 1

Dutching on two events is therefore interesting by applying the same calculation rule as the surebet. The essential difference here is that the two events on which we bet are independent, whereas for surebet we seek to bet on different results of the same event.
In particular, dutching leaves the possibility of winning much more, if all pronotics are exact at the same time.



Calculation of the distribution of individual bets

Once this total payout has been calculated, we find the bets on each event:
G = m1c1 − M ⇔ m1 = G + M/c1
and the same for the 2nd bet
G = m2c2 − M ⇔ m2 = G + M/c2

Maximum expected net gain

In a dutching strategy, we bet on several events in such a way that as soon as a prediction is exact (it doesn't matter which one), we ensure a fixed gain. This is an undeniable advantage of this dutching strategy: securing risky bets.
But we remain a bettor with this strategy: it is still possible to win several bets, or even all! In such an event, if all bets are won, the profit is maximum, and is simply calculated by
Gmax = m1c1+m2c2 − M
This maximum net gain can also be calculated using the previous calculator.
In summary, we can say that we are trying a big shot, by aligning several bets on risky events, giving hope for a very important gain, but that at the same time we are securing our bet: it is enough that only one of the predictions is exact to still ensure a profit.
We can therefore repeat this strategy many times: we regularly win a little, and from time to time we win big .

Probabilities of winning and losing

Mathematical analysis clearly lacks interest if it is not supplemented by calculations of probabilities of gain and loss.
Indeed, for dutching strategy to be advantageous, it is necessary to select events with fairly high odds in order to satisfy the mathematical relation of surebet α<1.
The probability of the maximum gain is very low: you must win all the bets at once! Its probability is therefore
P = 1/c1 × 1/c2
If you only aim for the maximum gain, it is a very risky bet, in the same way as for combined bets.
On the other hand, the probability is much greater of winning at least one of the bets, it is
P = 1 − 1−1/c1 × 1−1/c2
As soon as a pronostic is correct, we have assured ourselves a gain.
The calculator on this page gives the results of these calculations automatically.

What is the difference between dutching 2 bets and a Double Chance bet?

These two mathematical betting strategies are very close: we distribute an overall bet over two outcomes, thus reducing the probability of loss.
For double chance, we actually bet on two different results of the same event (for example on the victory of a team or a draw). This gives you a greater chance of winning, but you cannot win both bets at the same time.
If you want to dutch on two bets, you can bet on two different events. Beyond this distinction, the principle is the same, to reduce the probability of loss since only one of the pronotics has to be correct to achieve a minimum gain. On the other hand, it is possible here to win all the predictions at once (or at least several of them for dutching on more than 2 events).


Generalization: Dutching of n bets

All the previous analysis generalizes quickly for dutch n events. We similarly set the coefficient
α = 1/c1 + 1/c2+…+1/cn
and we find for a total stake M the gain We then find the same formula for the gain
G = M 1/α − 1
which is positive, therefore advantageous as soon as α<1, that is to say
α = 1/c1 + 1/c2+…+1/cn < 1
The distribution of bets is then done as follows: on the i-th event we bet
G = mici − M ⇔ mi = G + M/ci
These mathematical formulas are those used directly in the calculator at the top of this page.


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