Maths of Laying
From
the basics to making your own book. Plus Lay strategies for Betfair and other betting exchanges.
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.
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.
A list of all my spreadsheets
lives here : betandlay.co.uk/strategies
Strategies for horse racing and football trading
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%
Overround or underround
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 overround 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% overround.
Overround or underround 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 overround, if less than
100%, the book is underround.
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%
overround.
If we only had evens, 3/1, and 4/1, our book would be 95%, so would be 5%
underround.
Be a bookie.
A racecourse bookie will price
up all the runners, with an overround 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% overround).
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, nomatter 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
Nomatter which horse wins, his profit would be in direct proportion to
his overround 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 oddsagainst.
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
overround 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 builtin overround profit.
Video 1 demonstrates inputs and how
the spreadsheet works.
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.
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.
Trade across more than one market.
Lay the Draw in
football markets with insurance
against a Nil  Nil result.
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 oncourse or
in the betting shop, and
betting on a betting exchange, to trade to a sure profit , nomatter 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 nomatter 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,
22, 23, 32, 33, plus any other score, targeting 33 and any other
score.
If the game finishes 00, 10 01, etc. you clean up with no payout.
If the match ends 22, 23, 32, you win.
If the match ends 33, or a bigger score, you have reduced liabilities
on your unsuccessful lay.
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
.Lay
several runners in a horse race, adjusting the stakes to balance
your trade
.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 32.
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.