Recognizing Value - the Key to Gaining a Gambling Edge

Risk is part of everyday life, more so than most people probably realize. From crossing theroad to the more obvious financial decisions such as buying a house, or startinga business, all involve varying amounts of uncertainty which must be considered.Gambling is the purest expression of risk, yet even when presented with a seeminglysimple choice of potential outcomes for an unknown event, such as a footballmatch, many bettors display a worrying ignorance of the concept of value andthe fundamental mathematical principals involved. In simple terms, ifa bettor cannot recognize ‘value’ they will never be a long term winner.

Take a look at this seemingly simple mathematical puzzle, known as the Monty Hall paradox (namedafter the host of ‘Let’s Make a Deal‘, a popular US show in the 60’s & 70’swhich formed the basis of the poser):

An unbiased game-show host has placed a car behind one of three doors. There is a goat behindeach of the other doors. You have no prior knowledge that allows you to distinguishamong the doors. ‘First you point toward a door,’ he says. ‘Then I’ll open oneof the other doors to reveal a goat. After I’ve shown you the goat, you makeyour final choice whether to stick with your initial choice of doors, or toswitch to the remaining door. You win whatever is behind the door.’ You beginby 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 doyou stay with Door 1 as it has an equal chance with only two doors left to choosefrom? When this question was posed in Parade magazine, 10,000 readers complainedthat 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 twoclosed doors, but you have no way of knowing which. Most contestants intuitivelysee 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 chancesof 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 ofwinning the car. If you stayed with your original selection you have just a1/3 chance of winning.

The principle is underlined by increasing the number of doors to 100. If 99 doors have a goatbehind them and only one has a prize, if the player picks a door and then thehost opens 98 of the other doors that were all shown to contain goats and thengives 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 willcontain the prize, as 99 out of 100 times the player first picked a door witha goat.

The Hole-In-One Gang
An excellent example of how this concept applies to betting was demonstratedby two sharp punters - Paul Simmons and John Carter - the self-styledHole-In-One-Gang. In the summer of 1991, after studying the form, they calculatedthe chances of any given golfer in a tournament hitting a hole-in-one at around50%. So they toured the UK placing maximum bets on the chances of a hole-in-onebeing scored by any player at a major that year. Lazy bookmakers who didn’ttake the time to study the statistical likelihood put a finger in the air, andquoted amazing odds with 100-1 not uncommon.

That year, therewere hole-in-one’s scored at 3 of the 4 majors and the pair’s winningswere reputed to be around £1million. Although it is difficult to put exactodds on a hole-in-one, it is clear that it is nowhere near 100/1. Due to thetradition of buying everyone in the clubhouse a drink after a successful hole-in-one,you can now buy insurance against it happening. Most insurers would probablyrefer to Francis Scheid’s (retired chairman of Boston University MathsDept) 2000 study for Golf Digest. The magazine has kept hole-in-one stats sincethe 1950’s and Scheid put the odds of a Tour player scoring a hole-in-oneat 3,000-1. You can make a rough calculation for an average event like thisweek’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 hole-in-one gang were getting exceptional value on their bets playing at odds of 100/1 whenin reality the chance of a hole-in-one occurring using Scheid’s figureswas 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 actagainst their best interests. It doesn’t matter if it’s a game show, playingthe lottery or sports betting, understanding and finding value is the key toprofit. Like the Monty Hall question, successful betting requires the skillto understand whether the odds offered on an event represent the statisticalprobability of that event occurring - if it doesn’t then you will have an edge and gain value.

Why is a Bookmaker telling me this?
PinnacleSports.com’s philosophy is that if we can improve the sophistication of players everywhere,more bettors will recognize the benefit of our unique pricing model, which offersup to 60% better odds. PinnacleSports.com benefits from educating its players,as it is sharp bettors who firm up our early prices on all markets offered,that allows us to provide the highest limits and most competitive odds around.