The Physics of Wall Street: a brief History of Predicting the Unpredictable

Beating the Dealer 
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guests. He was an ace pilot during World War II and later earned some 
local notoriety by flying a plane underneath the George Washington 
Bridge. But despite the theatrics, Kelly was one of the most accom-
plished scientists at At&t — and the most versatile. His work ran the 
gamut from highly theoretical questions in quantum physics, to en-
coding television signals, to building computers that could accurately 
synthesize human voices. the work he’s best known for now, and that 
was of greatest interest to thorp, was on applying Shannon’s informa-
tion theory to horseracing.
Imagine you’re in Las vegas, betting on the Belmont Stakes, a major 
horserace held in elmont, new York. the big board in the off-track-
betting room shows various odds: valentine at 5 to 9, Paul revere at 14 
to 3, epitaph at 7 to 1. these numbers mean that valentine is expected 
to have a roughly 64% chance of winning, Paul revere has an 18% 
chance of winning, and epitaph has a 13% chance of winning. (these 
percentages are calculated by dividing the odds of each horse winning 
by the sum of the odds of that horse winning and losing — so, for val-
entine, if your odds are 5 to 9, you divide 9 by 14.)
In the first half of the century, there was often a delay in commu-
nicating racing results between bookies. this meant that sometimes a 
race would be over, while people in other parts of the country contin-
ued betting on it. So if you had a particularly fast method of commu-
nication, you could in principle get the results before betting closed. 
By 1956, when Kelly wrote his paper, this had become quite difficult: 
telephones and television meant that bookies in Las vegas would 
know what had happened in new York almost as soon as the people 
in elmont. But suspend disbelief for a moment and imagine that you 
had someone in elmont who could send you messages about the Bel-
mont Stakes instantaneously — faster, even, than the bookies got their 
results.
If the messages you were receiving over your private wire service 
were perfectly reliable, you’d be wise to bet everything, since you’re 
guaranteed to win. But Kelly was more interested in a slightly different 
case. What happens if you have someone send you correct racing re-
sults, but there’s noise on the line? If the message that comes along is so 
garbled that you can’t make out much of anything, your default guess 

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is going to be that valentine is going to win, since that’s what the odds 
were to begin with and you haven’t received any new information. If it’s 
garbled but you’re pretty sure you heard a t sound, you’ve gotten some 
information — you have good reason to think Paul revere didn’t win, 
since there’s no t in his name. If pressed, you would probably guess 
that your contact said “valentine,” because that’s the more likely mes-
sage, but you can’t know for sure. You wouldn’t want to put all of your 
money on one horse, because you still have a chance of losing. But you 
can rule out one possibility, which gives you an advantage: you now 
know that the bookie thinks valentine’s and epitaph’s chances aren’t 
as good as they really are, because the bookie is assuming Paul revere 
has an 18% chance of winning. So if you make a combined bet on both 
valentine and epitaph in the right proportions, you’re guaranteed to 
win one of them for a net profit. Hence even the partial information is 
enough to help you decide what bets to place.
Shannon’s theory tells you how much credence to give a message 
when there’s a chance that the message is being distorted by noise, or 
when the level of noise makes it difficult to interpret the message in 
the first place. So if it’s difficult to decipher your racing tips, Shannon’s 
theory provides a way of deciding how to place your bets based on the