Recognizing Value
by Pinnacle Sportsbook
Risk is part of everyday life, more so than most people probably
realize. From crossing the road to the more obvious financial
decisions such as buying a house, or starting a business, all
involve varying amounts of uncertainty which must be considered.
Gambling is the purest expression of risk, yet even when
presented with a seemingly simple choice of potential outcomes
for an unknown event, such as a football match, many bettors
display a worrying ignorance of the concept of value and the
fundamental mathematical principals involved. In simple terms,
if a bettor cannot recognize 'value' they will never be a long
term winner.
The Monty Hall Problem
Take a look at this seemingly simple mathematical puzzle, known
as the Monty Hall paradox (named after the host of "Let's Make a
Deal", a popular US show in the 60's & 70's which formed the
basis of the poser).
An unbiased gameshow host has placed a car behind one of three
doors. There is a goat behind each of the other doors. You have
no prior knowledge that allows you to distinguish among the
doors. "First you point toward a door," he says. "Then I'll open
one of the other doors to reveal a goat. After I've shown you
the goat, you make your final choice whether to stick with your
initial choice of doors, or to switch to the remaining door. You
win whatever is behind the door." You begin by pointing to door
number 1. The host shows you that door number 3 has a goat.
Do you gain value and see your chances of winning the car
increase by switching to Door 2 or do you stay with Door 1 as it
has an equal chance with only two doors left to choose from?
When this question was posed in Parade magazine, 10,000 readers
complained that the published answer was wrong  including
several maths professors.
The assumption of "equal probability", while being intuitively
seductive, is wrong. The simple answer is to always switch
doors. The car is behind one of the two closed doors, but you
have no way of knowing which. Most contestants intuitively see
no advantage in switching and assume that now there are only two
doors, each must have an equal probability of revealing a car.
In fact, your chances of winning the car actually double by
switching to the door the host offers. If you switch, you gain
value as theoretically you now have a 2/3 chance of winning the
car. If you stayed with your original selection you have just a
1/3 chance of winning.
The principle is underlined by increasing the number of doors to
100. If 99 doors have a goat behind them and only one has a
prize, if the player picks a door and then the host opens 98 of
the other doors that were all shown to contain goats and then
gives the player the opportunity to switch, the intelligent
player would switch. The reason being that on average, in 99 out
of 100 times the other door will contain the prize, as 99 out of
100 times the player first picked a door with a goat.
The HoleInOne Gang
An excellent example of how this concept applies to betting was
demonstrated by two sharp punters  Paul Simmons and John Carter
 the selfstyled HoleInOneGang. In the summer of 1991, after
studying the form, they calculated the chances of any given
golfer in a tournament hitting a holeinone at around 50%. So
they toured the UK placing maximum bets on the chances of a
holeinone being scored by any player at a major that year.
Lazy bookmakers who didn't take the time to study the
statistical likelihood put a finger in the air, and quoted
amazing odds with 1001 not uncommon.
That year, there were holeinone's scored at 3 of the 4 majors
and the pair's winnings were reputed to be around £1million.
Although it is difficult to put exact odds on a holeinone, it
is clear that it is nowhere near 100/1. Due to the tradition of
buying everyone in the clubhouse a drink after a successful
holeinone, you can now buy insurance against it happening.
Most insurers would probably refer to Francis Scheid's (retired
chairman of Boston University Maths Dept) 2000 study for Golf
Digest. The magazine has kept holeinone stats since the 1950's
and Scheid put the odds of a Tour player scoring a holeinone
at 3,0001.
You can make a rough calculation for an average event like this
week's Johnnie Walker Championship at Gleneagles.
4 (short holes)*156 (players before cut)*2(rounds) PLUS 4*70
(players after the cut) * 2 = (1,248+560) 1,808 attempts against
an average frequency of 1 in 3,000.
Probability Yes:
1,808/3,000=0.6026 or a 60% chance of occurring with true odds
of 1.66
Probability No:
1,192/3,000=0.3973 or a 39% chance of occurring with true odds
of 2.52
The holeinone gang were getting exceptional value on their
bets playing at odds of 100/1 when in reality the chance of a
holeinone occurring using Scheid's figures was no more than a
2/3 (1.666) shot at true odds.
Such notions are all too common mistakes in gambling when
bettors and bookmakers frequently act against their best
interests. It doesn't matter if it's a game show, playing the
lottery or sports betting, understanding and finding value is
the key to profit. Like the Monty Hall question, successful
betting requires the skill to understand whether the odds
offered on an event represent the statistical probability of
that event occurring  if it doesn't then you will have an edge
and gain value.
