The man who never went to the races

John Kelly, Jr. (1923 - 1965)

History of science is full of strange incidents, some of them bordering on the weird--like Kekule's dream about the benzene ring.

Horse racing too has a story that could compete with the weirdest stories from science. That story is about a man named John Kelly who had never been to the races*, but who, by pure co-incidence, made a gigantic contribution to the science of optimum money management for horse race gamblers.

An engineer by profession, John Kelly worked for Bell Laboratory (the telephone company) as telecommunications engineer in the 1950's. 

As luck would have it, Kelly was once asked by his employer, Bell, to work on a project that was designed to measure, in scientific terms, the "efficiency" of the telephone network installed by his company in a particular location. The idea was to record a fair estimate of the traffic on the telephone lines, and take into account lag or delay in connections due to jammed lines. 

As part of the same project, user perception of "efficacy" of the network was to be decided in the context of an "artificial tolerance level" beyond which the user would begin complaining.

Interestingly, to decide all this fancy scientific stuff John Kelly designed a thought experiment that was to radically change how a gambler looks at his betting capital.
 
Kelly reasoned there was an accepted level of disruption (noise) in communications network that a customer is used to expect, beyond which, his tolerance would snap and he would demand to know what was wrong. To exactly determine this level in scientific terms, he undertook the following thought experiment.
 
He imagined, as his company's customer, an illegal bookmaker (it is heartening to note that we match the Americans in this area) who accepts bets (on horses) on telephone lines. This bookie has a small office with telephone lines on which gamblers call up to place their bets. There is also a special telephone line that brings in the running commentary of the races live from the racetrack. Thanks to this access, the bookie instantly comes to know of the results, and effects swift payments after each race.

Kelly then imagined a dishonest technician, called lineman, from his company looking after the maintenance of the telephone lines installed at the bookie's office. This lineman cooks a crooked plan. The modus operandi runs like this.
 
The technician gets a tape recorder on which he can record the minute-long live commentary. Now he can put his plan into action. First, he cuts off the live commentary line going into the bookie's office. Then he records the live commentary with the help of the recorder, in the process getting wise to the fact which horse has won the race. Then he cottons on to that information by calling up the bookie on his other betting phone lines and placing a bet on the horse which he already knows to be the winner of the race. Shortly after he places the bet, he connects the live commentary line but relays the recorded commentary and the result. Unaware of his machinations, the bookie makes payments to all who had backed the winner.
 
Needless to add, our dishonest technician makes a handsome profit in the process.
 
The questions that Kelly asked were: How often the technician can play this scurvy trick on the bookie? And how much money he should be betting each time?
 
Since the only commentary line that goes into the bookie's office is under the sole control of the technician, the answer to the first question is simple----the crook can do it infinite number of times. 

He can do it in every race if he likes.

And how much money should he bet? Since he is 100% sure of his bet(?) being successful, the obvious answer is he should put all the money he has at his disposal on such sure winners.
 
In other words, he should bet all the cash in his pocket plus all the credit that he can be allowed to command--because he is going to make profit on every penny, every time.
 
Kelly then just added a tag to the same questions (and for which all serious gamblers must remain grateful to him forever). 

The questions now read: How many times the technician can play this scurvy trick on the bookie, and how much money he should be betting each time IF HE DOES NOT WANT TO AROUSE THE BOOKIE'S SUSPICION?
 
The simple answers will not do now as both these questions are related to the bookie's tolerance level regarding the efficacy of the telephone lines (he is obviously not going to like the line to go dead just when the commentary is about to start), the problem that John Kelly basically set out to investigate.
 
It now becomes clear that our dishonest technician will have to take into account the bookie's perception about how many "failures" he can expect on a normal day. It would be foolish for him to cross that line, just as it would be suicidal for him to win every race. 

So the crook now has a problem on hand. Besides such sure winning bets, now he has to also place some bets that he would risk to lose so that the bookie does not get suspicious about his exceptional luck. 

How much should he put on such "risky" bets? And how much should he put on the "sure things"?

In one sentence, how should he now manage his betting capital so that he can make maximum profits?

Kelly reasoned that he should put ALL his capital when he knew the result of the race (probability = 100% or 1). 

But how much should he bet when he was just taking a chance so that his motive--that of growing his capital at the maximum possible rate--is satisfied, without the bookie getting suspicious of foul play?

Kelly solved this problem by using Information theory, proposed by none other than his friend and colleague at the Bell Lab office, C E Shannon, whose pioneering work in this field is responsible not only for computers and telecommunications, but also the Internet.

Using impeccable logic, Kelly argued that a gambler must bet in proportion with his edge (the difference between fair odds based on his winning probability, and the market odds) if he has to maximize the growth of his capital. His complete logic and mathematical proof is given here.

(*The title of this article--The Man Who Never Went To The Races--is the result of the writer's lincece I have taken. This opinion is a mere guess, and must confess, is added to give just the dramatic touch to the headline, but may even be true, as nowhere in the material available on the internet, about John Kelly and his famous paper, it is mentioned that he actually ever attended the races anytime in his life.~ PG)