Origination of the article, here.
What is a bookie? Many
people ask this question and it was indeed one of the first
"puzzles" I solved when looking at betting exchanges. Curiously I
found no explanations anywhere on the internet or in bookshops. So
here is an explanation....
The art of making a book is
to 'balance' it so that a profit is made no matter what the
outcome. Bookmakers make money by offering odds that are different
to the real probabilities in the underlying event.
bookmakers offer prices that are overround. By overround we mean
that they offer prices for punters to back which exceed the total
probability in an event.
If we were offering
prices for the toss of a coin we know the probability of a head or
tail is 50%. Excluding complex variations we know the probability of
a head or tail being tossed is 100%. There are no other outcomes to
If we are a bookmaker
and want to make money on this event we simply offer up 100%
probability at a price higher than 100%. If we offered up a book of
105% we would simply lay heads or tails at 52.5%. This is the
equivilant of laying heads and tails at 1.90 (Digital odds).
Therefore the punter would back either event at 1.90 and we would
guarantee a profit as long as both side of out bet was matched. If
both sides of the bet was not matched we would end up paying out a
liability on one side and not cover the bet on the other. However as
long as our overround is big enough the good and bad days will
average each other out over time and in the long term we would make
Our bookmaker decides to
accept betting on an event where there are only two outcomes. He
decides to choose the the Oxford and Cambridge boat race.
The bookmaker might open his
book by offering odds of 2-1 on Cambridge and 6-4 against Oxford.
By a simple calculation (Two divided by three, the sum of the odds
(2+1=3)) we can see that 2-1 on represents a probability of 66.67%
and 6-4 against represents 40% (Four over ten).
The probabilities add up to
106.67% The excess of 6.67 over 100 percent is known as the
over-round. In short he has sold odds of 106.67% but the outcome can
only ever be 100%. There is a 100% chance that one horse or the
other will win. (We are talking simplistically here). The bookmaker,
if he can take bets in the proportion of the probabilities, say
?66.67 on Cambridge and ?40 on Oxford, will pay out ?100 whichever
wins on ?106.67 taken, a percentage profit to him of 6.25%.
In practice, of course, the
bookmaker will need to adjust his odds in accordance with supply and
demand. More money for Oxford than the estimated probability
indicates will cause him to shorten the odds against Oxford and
lengthen those for Cambridge. The same principle works on the stock
market when market makers buy and sell shares on their books at
different bid and offer prices.
His final book might look
like this :-
|$50 @ 2-1 on
||$40 @ 6-4
|$42 @ 4-6 on
||$32 @ 5-4
|$50 @ 4-5 on
||$30 @ Evens
In this example, he began by
seriously under-estimating the fancy for Oxford, and has been forced
to reduce his odds from 6-4 to evens, at the same time offering
better odds for Cambridge. Before adjusting his odds he stood
to pay out ?100 on Oxford, having taken only ?90 in stakes. The odds
offered on a horse race with many runners are calculated and
adjusted in the same way. The over-round usually increases
with the size of the field.
I have found a useful
Java applet that will "frame" a market for you. If you enter the
odds and the amount you wish to be over or under round this applet
will work out the market prices for you. You can find this applet
Bookmakers can not win against Betting exchanges
A bookmaker's over
round is only a theoretical over round as most of the money they
receive is placed on favourites. If a heavy odds on (Less than 2.00
digital odds) favourite loses the bookmakers can rub there hands.
However, if a favourite wins then the bookmakers are likely to be
out of pocket. Over time we know the odds are created fairly
accurately. Therefore if you are a bookmaker you will have periods
where lots of favourites win and you will be out of pocket and other
times when none win and you start planning the cruise to the
Bahamas. Overtime though you will win.
However because of the
lack of a balanced book and the likely hood of good and bad runs
against your bank balance bookmakers need a wider over round. By
doing this they ensure that if there is a bad run they will not go
out of business. Because a lot of large bookmakers are listed
companies with shareholders they are expected to report a steady
earnings stream. If bookmakers changed there odds and reduced the
over round to the sort of prices available on Betfair their profit
margins would be killed. Also because they can not ensure a balanced
book they could have a very bad run against them which could cost
them a lot of money at best and at worst, if they didn't limit there
exposure, there business. A lot of smaller bookmakers have gone this
There has been a lot of
publicity about betting exchanges, a lot of it negative, the big
bookmakers and people with seeking to protect the current status quo
and there interests have been waging a war against the betting
exchanges. Here is a typical example: -
Board chairman Peter Savill agrees that globally racing faces a
mounting crisis with the spread of on-line exchanges. 'Betting
exchanges have suddenly enfranchised 30 million plus people in
Britain to make money out of horses losing a race. When you add to
that figure every other person in the world with the desire to make
money out of horses in Britain losing races - including, possibly,
illegal Far East bookmakers and even organised crime - you have to
wonder whether the decision [to allow franchises] was reached after
appropriate research.' "
This is simply a stupid
and crazy statement, so obvioulsy a red herring to support the
failing case of people who oppose exchanges. If you wanted to lose
money on horses you have been able to do this for decades. You could
approach somebody to the lay the horse. If no one will you lay the
horse you simply back all other horses other than the one you want
to win in direct proportion to the odds available. If your horse
loses you will win on any of the others. Not strictly laying but a
modfied form and exactly the same result is ensure as laying. Indeed
people have done this for decades so this accusation that exchanges
increase the level of corruption in the sport is a null argument. In
fact exchanges probably help as they provide a clear audit trail. If
you have a wedge of cash on the course that is not possible to trace
but placed through an exchange you have a near perfect audit trail.
Pari-mutuel or totalisator system
Look up the definition in
and the following description appears roughly along these lines - "A
system of betting on races whereby the winners divide the total
amount bet, after deducting management expenses, in proportion to
the sums they have wagered individually."
This system cannot
lose, since it operates on the same principle as a lottery,
returning to winners a proportion of the total stakes. It is
the system used to bet on a lot of horse races in most parts of the
world. It was invented in Paris in 1865 by Pierre Oller.
In France it is called the pari-mutuel, in English-speaking
countries usually the tote, short for totalisator, the equipment
used to register and indicate the bets and dividends. The football
pools operates on this system.
The only hope for
winning any sum of this money on this system is to guess that the
betting has been very badly performed by the pool which leaves you
margin to gain, even after the pool has subtracted its commission.
The operation of this
works as such. Fundamentally all bettors submit their stakes to a
pool. When the results are in the company that is running the pool
takes a percentage from the pool for running expenses, profit and
A British football pool
works on a similar basis to the above, but there is a large
government tax on the total pool and the pools company takes a
further commission to cover expenses and profits of around 30-35%.
The share-out for winners is only probably about 30% of the total
pool. The odds on the football pools are not great. For a worse
example of share out you can look at the national lottery.
See my section on
winning the lottery for hints as how to improve your chances.
It is not difficult to work
out exact probabilities on soccer matches as you are able to make
first hand judgment on the outcome of a variety of games, all
judgments though are somewhat complex and still require an element
of subjectivity. Using such information people have now and again
been able to use to turn fantastic odds against in their favour by
correctly reading distortions in the underlying market.