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Maths of Laying 
From the basics to making your own book.
Plus Lay strategies for Betfair and other betting exchanges.

List of all available spreadsheets.

The strategies available to Layers differ from those open to Bettors.

The most obvious difference is that :- 

  • As a Bettor makes more bets on a single event, his liabilities increase, since his payout is reduced by the unsuccessful bets on losing selections.
  • For a Layer, the opposite applies.
    As a Layer makes more Lays on a single event, his liabilities decrease, since his payout is reduced by the successful Lays on losing selections.

The math's of Laying are mostly based around getting your percentages right.

 

Other web sites with spreadsheets

betandlay.co.uk
Football trading

betandlay.co.uk/strategies
Strategies for trading Horses and Football

New web site  laybets.net
Lay your losers with a bit of imaginative staking.
Strategies with live trade videos


Over-round or under-round

Making a book.

Be a bookie 
Lay up to 25 selections to an equal liability or profit whatever the result.

New
Be A Bookie Place Market
Lay up to 25 selections to an equal liability or profit whatever the result
in Betfair Horse racing
Place markets.

Hedging

Coupled odds

Target 1 Lay  selection
Lay several runners, with liabilities on only one.
All the others are winners for you.

Target  2 Lay selections
Lay several runners, with liabilities on only 2.
All the others are winners for you.

New
Dutching to a Set Liability
Lay to your comfort level.
Choose how much to lose if you hit a winner with your lays.
Lay 1 to 25 runners, but your liability will remain the same.

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%

To calculate the percentage of fractional odds, add 1 to your odds and divide into 100.
For example, 3/1 + 1 = 4.
100 divided by 4 = 25%

Over-round or under-round of a book.
Now that Betting Exchanges such as Betfair allow us Lay bets as well as betting like an ordinary punter, we can be the bookie.
The big difference is that the over-round enjoyed by conventional bookies, is not available to us since betting exchange books usually have near 100% books.
A bookie's book will be more than 100% over-round.

Over-round or under-round is calculated by expressing all the odds of a horse race or other event as a percentage, and adding them together.
If the total is more than 100%, the book is over-round, if less than 100%, the book is under-round.

Making a book.
For example, a 4 horse race with the runners priced at evens, 3/1, 4/1, and 9/1,
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%
Adding all those percentages together gives 105%.  Our book is 5% over-round.
If we only had evens, 3/1, and 4/1, our book would be 95%, so would be 5% under-round.

Be a bookie.
A racecourse bookie will price up all the runners, with an over-round of (for example) 120%.
In an ideal situation, he would take bets on all runners, and have equal liabilities on each.

If it was a 4 horse race and he priced the runners up at evens, 3/1, 3/1, and 4/1, his book percentage would be 50% + 25% + 25% + 20% = 120% (20% over-round).
If he was able to take bets on each runner giving him a liability of 100 on each, these would be the bets taken :- evens 50,  3/1 25,  3/1 25,  4/1 20.
Total bets taken = 120.
Now, no-matter which horse wins, his payout is 100, but the bets he has taken total 120, leaving him with a profit of 20 after paying out on any winner.

Example 1.  The favourite wins at evens.
Payout = 100 (50 returned stake + 50 winnings).
Total bets taken = 120.
120 - 100 = 20 profit.

Example 2.  A 4/1 winner.
Payout = 100  (20 returned stake + 80 winnings).
Total bets taken = 120.
120 - 100 = 20 profit.

This table shows the math's for each winner.

Odds Stake Payout Total of other successful lays   Profit
1/1 (Evens) 50 - 50 + 70 20
3/1 25 - 75 + 95 20
3/1 25 - 75 + 95 20
4/1 20 - 80 + 100 20

No-matter which horse wins, his profit would be in direct proportion to his over-round and the size of the bets he accepts.
In this example, if his liability on each horse was 100, his profit would be 20 on any winner.
If he accepted more bets so that his liability on each horse was 1000, his profit would be 200 on any winner.

If he increased his book percentage to 125% by shortening the odds, his profit on any runner would be 25 on every 100 of liability of the bets he accepted.

An unbalanced book.
Most punters may concentrate their bets on just a few well fancied runners, giving him an unbalanced book, so that in reality, he may not be able to balance his liabilities by Laying sufficient amounts on each horse.

A very common strategy is to Lay only some of the runners.
If a horse that he has layed wins, he may make a small loss, but if a runner he has not layed wins, he has no liabilities, and he keeps all the bet amounts that he has layed.
A winner that he has not layed is refered to as a "Skinner".

If he is able to lay just 2 or 3 horses at short odds and no others, but in a large field of runners, he has only those 2 or 3 horses running against him, but all the others are running for him.

As an example let's look at the 6 furlong Golden Jubilee Stakes at Royal Ascot, June 24th 2006.
The first 5 in the betting were priced 7/2 fav, 6/1, 13/2, 7/1, 7/1.
There were 18 runners.
If we laid those 5 horses to lose 100 each, the total bets accepted for each of the 5 runners would be 22.22, 14.29, 13.33, 12.5, 12.5.  Total 74.84.
If the 7/2 favourite won, our payout would be, 22.2 x 3.5 = 77.7, (plus the returned stake of 22.2), but, we have taken 52.62 in bets on the other losing horses, so our payout is a loss of 77.7 less 52.62 = a net loss of only 25.08.

Now, we can see that even though we have not layed the whole field, our liability on the favourite is only 25.08, not 77.7.
We layed only 5 of the runners, so if any of the other 13 horses won, we would clean up to the tune of 77.7.
The 2006 Golden Jubilee winner was Les Arcs, priced 33/1.
Not many bookies would have lost on that race.

By taking a chance and laying 5 horses against the field, we could have 13 horses running for us and only 5 against us, but those 5 horses in the Royal Ascot example above, were the most fancied runners.
The financial risk we take if the favourite wins is a 25.08 loss against a gain of 77.7.
That is approximately a 1 to 3 chance for the bookie.
In our Golden Jubilee example, the first 5 in the betting would have to be successful 3 times in every 4 runnings of our 18 runner race, before we would make a very small loss.
The bookie is therefore betting odds-against.

As a Layer, if the favourite won, our bet was at odds of just over 3 to 1.
We stood to either win 77.7 or lose 25.08.
A punter betting on those 5 horses, and the favourite winning, would be betting almost 1 to 3, since he could either win 25.08 or lose 74.84.

The total % bet is 74.84%.
The return on any winner is approximately 25.16.

As a bookie lays a higher percentage book, his liabilities reduce.
If an additional horse had been layed to 100 liability at say, 9/1, we would have an additional 10 successful Lay (100 / 10.0 ).
That extra loser decreases our total liability to 15.16 against a gain of 84.84, approximately a 1 in 5 chance in favour of the bookie.
Our payout on the 7/2 favourite would be 22.2 x 3.5 = 77.7, (plus the returned stake of 22.2), but we have now taken 62.61 in bets on the other losing horses, so our payout is a loss of 77.7 less 62.61 = a net loss of 15.09.
The bigger the percentage of our lays, the less liability we have.
The downside is that we now have 6 horses running against us and only 12 running for us in that 18 runner race.

Once a bookie is able to Lay a 100% book, his liabilities are zero.
Lay more than a 100% book, and every winner shows a profit, providing the bets accepted are balanced across all runners.

You may hear on television that a well fancied horse has "taken the bookies to the cleaners".
Maybe their liabilities were not quite as bad as the television presenters suggest.
It is very naive to believe that a 5/1 winner has cost a bookie a huge payout at 5/1.
Even if it has been a market mover and the odds have tumbled from 10/1, he will probably have taken bets on other runners to cover the majority of his liabilities, and will of course live to fight another day.

We punters can now use a similar strategy on Betting Exchanges, but due to the near 100% books, the odds are not quite so favourable for us as they are for conventional bookmakers.
Bookies stick together and run an odds cartel.
Betfair users aren't unified in the same way, so prices are continually undercut, leaving us with near 100% books.
This means that we cannot blindly Lay all runners for a guaranteed over-round book and a guaranteed profit.

That is what makes it very difficult to make a profit from either Laying or Betting - 
the odds of near 100% books.

We can still copy what bookies do by laying just a few horses against the field, but remember that due to the near 100% books on Betfair and other exchanges, there is no built-in over-round profit.

Copyright notice.  In the 5 videos below, Betfair content shown is for demonstration purposes only, and is presented with the kind permission of The Sporting Exchange Limited.  The Sporting Exchange Limited.

  1. Video 1 demonstrates inputs and how the spreadsheet works.
  2. Lay several runners in a horse race, adjusting the stakes for almost an even money situation, even though we don't expect to hit the winner with the horses that we have layed.
    Link to my old startingstalls web site.
  3. Use the Adjust feature to favour one outcome over all the others.
    Dutch Match Odds in a football match to Lay the Draw and then Lay the 2 teams after a goal is scored.
  4. Trade across more than one market.  Lay the Draw in football markets with insurance against a Nil - Nil result.
  5. How to Lay or Bet below the 2 minimum.
    For a bigger view of the videos below, click the icon with
    4 small arrows near the bottom right hand corner, just below the " T " in the word "Tube".

 

Excel spreadsheets are a quick and reliable way of doing calculations.
You can build a spreadsheet using the percentage formulas above, or purchase an excellent spreadsheet here for only a fiver.
Be A Bookie spreadsheet.
You will need Excel 2000 or a later version to view this spreadsheet.

This Be A Bookie spreadsheet calculates instantly the lay stakes required to Lay up to 25 selections to an equal liability.
You could of course use this spreadsheet for any event other than horse racing.

Input the amount of your Total Payout, and as you input the odds of your selections, the spreadsheet shows :-

  • Total payout on any winner remaining constant at your original input.

  • The Lay stake required for each runner.

  • Equal liabilities against each runner.

  • Liability on each runner reducing as more runners are Layed.

  • Percentage of your book at all stages.

  • Total of Lay stakes at all stages - - - the "Skinner" amount.

The more runners you Lay, the less your liabilities become.
The more runners you Lay, the bigger the payout on a "Skinner" - a horse you haven't layed.

Note that this spreadsheet is also available on the Dutching web page.

After payment via PayPal, select the "Return to merchant" option on the PayPal screen.
PayPal should then route you to a download web page where you can obtain the Excel spreadsheet file.

Be A Bookie spreadsheet price = 5.
Payment is by PayPal, but you don't need a PayPal account to use the payment button below.

Hedging - An additional option is available to bookmakers :-
Bookmakers take a great deal of notice of betting exchange odds and usually make sure that bookie odds are nearly always slightly shorter than "Betfair" odds - that is why Betfair can claim that their odds are on average, 20% bigger than SP.
This slight difference allows a bookie the option of laying on-course or in the betting shop, and betting on a betting exchange, to trade to a sure profit , no-matter what the outcome of a race.
Betting high and Laying low in this way is called a Hedge.

If he has taken hefty bets on a runner at 5/1 and has an unbalanced book, the odds for that runner on Betfair may stand at 6/1, or even longer.
He has layed at 5/1, but has the option of betting at 6/1.
If he has layed 100 at 5/1, he can bet 85.71 at 6/1 for a certain profit of 14.30 no-matter what the outcome.
Here are the maths :-
Horse loses.
Lay bets taken = 100 successful Lays, less losing bet of 85.71 = +14.29 profit.
Horse wins.
Bet 85.71 at 6/1 = 85.71 x 6 = 514.32 less Lay liabilities of 500 (100 at 5/1) = + 14.26 profit.
There may be lots of bookies who don't trade, but there will be plenty who use betting exchanges to offset liabilities in this way.
Follow the Hedge Tab link for a description of Hedging. 

Coupled odds.
You may hear television presenters refer to coupled odds.
"Coupled odds" refers to the prices of 2 or more runners added together.
The resultant price is the "odds coupled".
One way to calculate coupled odds, is to add the percentages together.
Then to convert the total percentage back to decimal Betfair odds - - - - divide 100 by the total  percentage of the coupled odds.

Here are the math's :-
An easy starting point is 3/1 and 3/1, which coupled, equals even money.
3/1 and 3/1 gives percentages of 25% + 25% = 50%
Divide 100 by 50 = 2.0 which is even money.

In this way, we can see that 9/4 (3.25) and 5/1 (6.0) coupled would make approx odds of 11/10.
3.25 (30.77%) + 6.0 (16.67%) = 47.44%.

To convert a percentage to decimal "Betfair" odds, divide 100 by the percentage.
100 / 47.44 = 2.1,  which equals 11/10 (one and one tenth).

Laying one selection to lose.
Bookies may lay a few runners against the field, but another strategy is to lay several runners but make only one targeted runner a loser.
We do not Lay the whole field, but just a few of the runners.

Using this strategy, we win on all runners except one, and if that horse wins, our liabilities are reduced by our lays on other runners.
In this way, we have only one runner against us, but with reduced liabilities.
All the others are running for us.
This is not the same as Laying a single runner.
We are reducing our liabilities on one targeted runner by laying lesser amounts on other runners.

Here are the math's :-
Supposing there were 20 runners.
We could lay 4 horses (for example), but only the one will  make a loss for us.

We Lay horse 1.
Then we lay horses 2, 3, and 4 but with lesser amounts.
The size of these stakes is dependant on the size of our larger stake on horse 1.
In this way, we reduce our liabilities on horse 1 by laying 3 other horses.
We could carry on laying more horses if we wish.
If the winner does NOT come from the 4 horses that we have layed, we have 4 successful lays, and clean up, with no payout.
Once we have layed 4 horses, if the winner comes from horses 2, 3 or 4, we still make a profit.
If horse number 1 wins, we make a loss, but our liabilities have been reduced by the successful lays on horses 2, 3 and 4.

Lay 2 selections to lose
This strategy can be used to lay 2 (or more) horses to lose.
Once again, we do not Lay the whole field, but just a few of the runners.
The math's is exactly the same, but this time, 2 horses are targeted to lose.
All the additional lays are staked to reduce the liabilities on those 2 target horses.

Liabilities on horses 1 and 2 will be reduced by the additional lays on horses 3 upwards.
This strategy of targeting 2 horses works better than targeting a single horse to lose since a large slice of liability is reduced on horse 1 by the stake on horse 2, and a large slice of liability is reduced on horse 2 by the stake on horse 1.
This strategy is particularly effective if horses 1 and 2 are at short odds.
The downside is that we have 2 horses running against us instead of 1.

If the winner does NOT come from the horses that we have layed, all our lays are successful and we clean up, with no payout.
Once we have layed 4 or more horses, if the winner comes from horses 3, 4, 5, 6, etc., we still make a profit.
If one of the first 2 horses win, we make a loss, but our liabilities have been reduced by the successful lays on the other horses, particularly horse 1 or horse 2.

This is not the same as just Laying 2 runners.
We are reducing our liabilities on 2 targeted runners by laying lesser amounts on additional runners.

You could use this strategy in the Correct Score market of a football match.
You may decide that the 2 teams are closely matched, and that there will be very few goals scored.
You could lay several score lines with plenty of goals, for example, 2-2, 2-3, 3-2, 3-3, plus any other score, targeting 3-3 and any other score.
If the game finishes 0-0, 1-0 0-1, etc. you clean up with no payout.
If the match ends 2-2, 2-3, 3-2, you win.
If the match ends 3-3, or a bigger score, you have reduced liabilities on your unsuccessful lay. 

1 or 2 Losers spreadsheet.
Copyright notice.  In the videos below, Betfair content shown is for demonstration purposes only, and is presented with the kind permission of The Sporting Exchange Limited.  The Sporting Exchange Limited.

  1. Video 1 demonstrates inputs and how the spreadsheet works.
    We can Lay lots of runners but only show liabilities against 1 or 2 runners, with a profit shown against all our other lays

  2. .Lay several runners in a horse race, adjusting the stakes to balance your trade

  3. .Target 2, 3, or 4 runners to drastically reduce your liabilities on targeted runners.
    The football match described near the end of this 3rd video ended with a score of 3-2.

  4. How to Lay or Bet below the 2 minimum.
    For a bigger view of the videos below, click the icon with 4 small arrows near the bottom right hand corner, just below the " T " in the word "Tube".

 

Excel spreadsheets are a quick and reliable way of doing calculations.
You can build a spreadsheet using the examples above, or purchase an excellent spreadsheet here for only a tenner.
1 or 2 Losers spreadsheets.
You will need Excel 2000 or a later version to view these spreadsheets.

These 1 or 2 Losers spreadsheets calculate instantly the lay stakes required to Lay up to 20 selections to reduce the liability on either 1 or 2 target horses.
You could of course use this spreadsheet for any event other than horse racing.
This Excel file contains 2 separate spreadsheets for your tenner.

1 loser spreadsheet
Only the first horse will have a negative liability.
Once you lay more than 2 horses, a profit will be made on horses 2 to 20.

2 losers spreadsheet
Only the first 2 horses will have negative liabilities.
Once you lay more than 3 horses, a profit will be made on horses 3 to 20.

If none of the Layed horses win, we clean up with the total of all the lay amounts staked - we have a "Skinner".

The more runners you Lay :-

  • The less your liabilities become on your target horses

  • The more profit you show on other laid horses

  • The bigger the payout on a "Skinner" - a horse you haven't layed.

After payment via PayPal, select the "Return to merchant" option on the PayPal screen.
PayPal should then route you to a download web page where you can obtain the Excel spreadsheet file.

1 or 2 Losers spreadsheets price = 10.
Payment is by PayPal, but you don't need a PayPal account to use the payment button below.

Dutching (Laying) to a Liability Target
This Dutching method offers total control of your liabilities whilst you lay up to 25 runners.
Use this spreadsheet to lay up to 25 runners for a liability of your choice if you hit a winner.

  • Dutching to a Liability target.

  • The stake on each runner increases as more runners are Layed.
    The total stake (your "Skinner" amount if you don't hit the winner) increases as more runners are added.

  • Desired liability remains constant.

This Lay staking method may be suitable for use with a staking plan.

  • Lay big odds for small liabilities if you choose.

  • Limit the amount you lose if you Lay the winner - in any sport.

  • As you lay more runners, your liability remains at the level of your choice.

  • As you lay more runners, your Total Stakes increase.
    If you don't hit the winner with your lays, all your lays are successful and you clean up with profit equal to the total of all your lay stakes.

A problem with this method of Lay Dutching is that the odds of all your selections need to be put into the spreadsheet before you start to place your lays.
If you alter any of the odds or you add another runner, ALL the stakes will change in order to maintain your liabilities at your chosen level.

How to Lay several ruinners at once on Betfair.

  • Click the Lay odds on Betfair and input your stake as usual, but don't hit "Submit".

  • Do the same for all your selections until you have all your lays with stakes on show.

  • Once you are satisfied with your staking, hit "Submit," and "Confirm" your Lays.

  • All your lays will be submitted together in one go.

Excel spreadsheets are a quick and reliable way of doing calculations.
Purchase an excellent spreadsheet here for only a fiver.
Dutch to a Lay Liability Target spreadsheet.
You will need Excel 2000 or a later version to view this spreadsheet.

This Dutch to a Lay Liability Target spreadsheet calculates the stakes required to Lay up to 25 selections for an equal liability if you hit the winner with your Lays.
The only inputs required are the names of your selections, the amount of the Liability that suits your comfort level, and the Lay odds of your selections.
The spreadsheet shows the stakes required for each selection and maintains the liability on all selections at the level that you set.
As you input more runners, the stakes adjust and your liability always remains the same.

The spreadsheet shows your Liability, total stakes, and for interest, the percentage odds of your selections, plus total percentage of your book..

This spreadsheet also has an Adjust feature which allows you to increase or decrease the size of your Liability on any individual runners whilst maintaining your chosen Liability target on all other runners.
You can therefore bias your liability on any runners that you think may be more likely to lose.

After payment via PayPal, select the "Return to merchant" option on the PayPal screen.
PayPal should then route you to a download web page where you can obtain the Excel spreadsheet file.

Dutch to a Lay Liability Target spreadsheet price = 5.
Payment is by PayPal, but you don't need a PayPal account to use the payment button below.

Contact me
Copyright H. Hutchinson 2009 All rights reserved
Copying text or any other kind of content from a web site is a criminal offence.

 

My spreadsheet websites.

betformulas.co.uk
Formulas and maths of trading

betandlay.co.uk
Football trading

A list of all my spreadsheets lives here :-
betandlay.co.uk/strategies
Strategies for horse racing and football trading

Laying web site
Different ways of laying using a bit of imaginative staking.
Also, videos showing live trades.