Formulas and Math's of Dutching

Bet or Lay any number of selections to show an equal profit
no-matter what the outcome of the event
(providing you hit the winner).

Dutching is a method of staking several selections in the same race.
Stakes are calculated so that providing you hit the winner, each selection returns the same profit.

Dutching can be a very effective way of betting on a number of selections in order to show a profit, but whilst increasing the number of selections obviously increases your chance of hitting the winner, every additional selection also reduces your overall odds, and reduces your profit.

If Laying, the opposite applies.
Whilst increasing the number of selections obviously increases your chance of hitting the winner, every additional selection also reduces your overall odds, but increases your profit it you miss the winner, since all your Lays will be successful.
Bookies, or Betfair traders who Lay bets, are in effect Dutching the market.

The number of bets placed is only limited by the odds of your selections.
Once the combined percentage of all the odds of your selections exceeds 100%, the calculation for Dutching cannot work, and returns a loss on every selection.
You cannot Dutch an over-round book to profit by Betting.
Your Betting book must be under-round.
You cannot Dutch an under-round book to profit by Laying.
Your Laying book must be over-round.
Click on the Lay Tab above for an explanation of an over-round, under-round book.

Odds as a percentage.
To calculate the percentage of your odds, divide the decimal "Betfair" odds into 100.
For example, we know that even money is a 50 - 50 chance, so evens should equal 50%.
Decimal "Betfair" odds for even money is 2.0.
100 divided by 2 = 50%

1/1 is 2.0 in decimal odds, so 100 / 2 = 50%
3/1 is 4.0 in decimal odds, so 100 / 4 = 25%
4/1 is 5.0 in decimal odds, so 100 / 5 = 20%
9/1 is 10.0 decimal odds, so 100 / 10 = 10%

Those percentages added together = 105%.  The book is 5% over-round.
Odds of 1/1, 3/1 and 4/1 would = 95%.  That book would be 5% under-round. 

Simple Dutching.
This is the most commonly used method of Dutching.
I would guess that most Layers use this method to Lay selections to a profitable book, but the same calculation can be used to Dutch Bet a market.
The advantages of this method are that

• The math's involved are very simple

• Each stake remains the same regardless of the odds of other runners.

If used to Bet, there is no control of Total Stakes.
As we Bet more runners, our liabilities increase.
If used to Lay,  the increase of total Bet  £ accepted becomes an asset, as the liabilities on a winner are offset by successful Lays on other runners.
As we Lay more runners, our liabilities decrease.
We stand to lose a smaller amount on any winner due to successful Lays on additional losers.

Dutching Example Betting.
As an example, we can Dutch selections priced at 4.0, 5.0 and 10.0, (total 55%).
Stakes would be :-

An equal profit will be shown providing the percentage of the combined odds of your runners doesn't exceed 100%.
Above 100% will show an equal loss on all selections.
A big problem if Betting with Simple Dutching is that , our total stakes increase as we add more selections, so our liabilities increase on any winner.  (We stand to lose a greater amount).
If we add further selections with odds of 10.0, our total stake increases by £10,  (100/10).
With 2 selections priced 4.0, 5.0, our total stake stands at £45.
With 3 selections priced 4.0, 5.0, 10.0, our total stake increases to £55.
With 4 selections priced 4.0, 5.0, 10.0, 10.0, our total stake increases to £65.
With 5 selections priced 4.0, 5.0, 10.0, 10.0, 10.0, our total stake increases to £75.

The size of the increase is in proportion to the size of the odds.
Short odds add large increases, and longer odds add smaller increases.
For instance odds of 2.0 adds £50, whilst 20.0 adds £5.

If Laying using Simple Dutching, the increase of total Bet  £ accepted becomes an asset, as the liabilities on a winner are offset by successful Lays on other runners.  (We stand to lose a smaller amount on any winner due to successful Lays on losers).
If we don't hit the winner, our net profit is the total of the stakes we have accepted.

Now if we Lay further selections with odds of 10.0, our total payout decreases by £10, since we would have additional successful Lays.
With 2 selections priced 4.0, 5.0, our total bets accepted stand at £45.
With 3 selections priced 4.0, 5.0, 10.0, our total bets accepted increases to £55.
With 4 selections priced 4.0, 5.0, 10.0, 10.0, our total bets accepted increases to £65.
With 5 selections priced 4.0, 5.0, 10.0, 10.0, 10.0, our total bets accepted increases to £75.

In each case, as more bets are accepted, we have more funds available to pay out on a winner.
If we are able to Dutch a Lay market of more than 100%, we make a guaranteed profit.
Click on the Lay Tab above for an explanation of Laying and making your own book.

Set Amount (Stakes Limit) Dutching.
Set Amount Dutching uses a different formula to control our total stake to stop it spiralling as we add more selections.
In the simple Dutching example above, each stake remains the same regardless of the odds of other runners.
With this Dutching formula, the stake on each runner decreases as more runners are added.
In this way, the Total Stake remains constant.

The Set Amount Dutching formula can also be applied to any number of selections, providing the book percentage doesn't exceed 100%.
This example uses a total stake of £100.

A winner at odds of 4.0 wins 3 x 45.45 = £136.35 less losers of £36.36 and £18.18 = a net profit of  £81.81.

Before placing these bets, we could see that we would be betting odds-on, since the percentage of the odds combined exceeds 50%  (evens).
Another indication is that our profit of £81.81 is less than our total stake of £100.
If our percentage was less than 50%, our profit would be more than £100 and we would be betting odds against.

Setting a stakes limit on your Dutching is a very effective way of betting on more than one selection, especially if you follow a staking plan.

Dutching to a Profit Target.

• Simple Dutching, each stake remains the same regardless of the odds of other runners.
• Set Amount Dutching, the stake on each runner decreases as more runners are added.
  The total stake remains constant.
• Profit Target Dutching, the stake on each runner increases as more runners are added.
  The total stake increases as more runners are added.
  Desired profit remains constant.

The Profit Target Dutching formula can also be applied to any number of selections, providing the book percentage doesn't exceed 100%.

If horse A wins, we have £2.50 x 9 = 22.50, less a losing bet of £2.50 on Horse B = £20 profit.
If horse B wins, we have £2.50 x 9 = 22.50, less a losing bet of £2.50 on Horse A = £20 profit.

If we add another runner, our stakes increase, but net profit remains virtually the same :-

The Dutch to a Profit Target formula can be expanded for any number of runners and any profit target £ amount, and will work for any odds, provided your book doesn't exceed 100%.

Problems.
A problem with Dutching several runners is that placing a series of Bets or Lays takes time.
During that time, the odds of your selections often change.
You need to decide which Dutching method suits you best, a Set Amount for your Total Stakes, or uncontrolled Totals Stakes.

If you are using the Simple Dutching method, time makes no difference since your stakes remain the same regardless of the odds of other runners, but you will have no control over increasing Total Stakes.
Simple Dutching is best suited to Laying in my opinion.

Dutching to a Profit Target could be used as part of a staking plan.
This method is best suited to bigger priced selections, since short prices can cause dramatic increases in stakes.

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