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The Hole-In-One Gang

An excellent example of how this concept applies to betting was demonstrated by two sharp punters - Paul Simmons and John Carter - the self-styled Hole-In-One-Gang. In the summer of 1991, after studying the form, they calculated the chances of any given golfer in a tournament hitting a hole-in-one at around 50%. So they toured the UK placing maximum bets on the chances of a hole-in-one 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 100-1 not uncommon.

That year, there were hole-in-one'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 hole-in-one, 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 hole-in-one, 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 hole-in-one stats since the 1950's and Scheid put the odds of a Tour player scoring a hole-in-one at 3,000-1. 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 hole-in-one gang were getting exceptional value on their bets playing at odds of 100/1 when in reality the chance of a hole-in-one 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. 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.