Maths of Laying 

From the basics to making your own book.

On this web page :-
Laying.  From the basics to making your own book.
Plus Lay strategies for Betfair and other betting exchanges.

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.

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.

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. 

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