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

partial information you do receive.
Kelly worked out the solution to this problem, provided you want 
to maximize the long-term growth of the money you start with. As 
in the example above, where you could make out a t sound but noth-
ing else, partial information can be sufficient to give you an advantage 
over a bookie who is setting odds without any information about how 
the race turned out. the advantage can be calculated by multiplying 
the payout — the number b when someone gives you b-to-1 odds — by 
what you believe is the true probability of winning (based on your par-
tial information), and then subtracting the probability of losing (again, 
based on your partial information). to figure out how much of your 
starting money to bet, as a fraction of what you have, you divide your 
advantage by the payout. this gives the equation now called the Kelly 
criterion or Kelly bet size. the percentage of your money to bet on any 
given outcome is
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t h e p h y s i c s o f wa l l s t r e e t

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Beating the Dealer 
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95
advantage
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payout
If your advantage is zero (or negative!), Kelly says not to bet at all; 
otherwise, bet the fraction of your wealth given by the Kelly criterion. 
If you always follow this rule, you will be guaranteed to outperform 
anyone adopting another betting strategy (such as betting it all or 
betting nothing). one of the most surprising things in Kelly’s paper, 
something that feels almost mystical, is a proof of what will happen 
if you follow his rule in a scenario like the horse betting story, where 
you have a stream of (partial) information coming in: if you always use 
the Kelly criterion, under certain ideal circumstances your wealth will 
increase at exactly the rate that information comes in along the line. 
Information is money.
When Shannon showed Kelly’s paper to thorp, the last piece of the 
blackjack puzzle fell into place. card counting is a process by which 
you gain information about the deck of cards — you learn how the 
composition of the deck has changed with each hand. this is just what 
you need to calculate your advantage, as Kelly proposed. Information 
flows and your money grows.
As thorp and Kimmel made their preparations for reno, Shannon 
and thorp were collaborating on thorp’s roulette plan. When he 
heard thorp’s ideas, Shannon was mesmerized, in large part because 
thorp’s roulette idea combined game theory with Shannon’s real pas-
sion: machines. At the heart of the idea was a wearable computer that 
would perform the necessary calculations for the player.
they began testing ideas for how the actual gambling would work, 
assuming they could make sufficient progress on the prediction algo-
rithm. they agreed that it would take more than one person for it to go 
smoothly, because one person couldn’t focus sufficiently on the wheel 
to input the necessary data and still be prepared to bet before the ball 
slowed down and the croupier (roulette’s equivalent of a dealer) an-
nounced that betting was closed. So they decided on a two-person 
scheme. one person would stand near the roulette wheel and watch 

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carefully—ideally while doing something else, so as not to attract at-
tention. this person would be wearing the computer, which would 
be a small device, about the size of a cigarette pack. the input device 
would be a series of switches hidden in one of the wearer’s shoes. the 
idea was that the person watching the wheel would tap his foot when 
the wheel started spinning, and then again when the ball made one 
full rotation. this would initialize the device and synchronize it to the 
wheel.
Meanwhile, a second person would be sitting at the table, with an 
earpiece connected to the computer. once the computer had a chance 
to take the initial speeds of the ball and the rotor into account, it would 
send a signal to the person at the table indicating how to bet. It was 
too difficult to predict just what number the ball would fall into, as the 
calculations for that level of precision were far too complicated. But 
roulette wheels are separated into eight regions, called octants. each 
octant has four or five numbers in it, arranged in an order that would 
seem random to someone who didn’t have the roulette wheel memo-
rized. thorp and Shannon discovered that in many cases, they could 
accurately predict which octant the ball would fall into, narrowing the 
possible outcomes from thirty-eight to four or five. the computer was 
designed to indicate whether there was a higher-than-normal chance 
that the ball would fall into a particular octant. once the person at the 
table received the signal, he would quickly place bets on the appropri-
ate numbers — using a betting system based on the Kelly criterion to 
decide how much to bet on each.
By the summer of 1961, the machine was ready for action. thorp, 
Shannon, and their wives traveled to Las vegas. Aside from broken 
wires and the night the earpiece was discovered, the experiment was 
a (middling) success. Unfortunately, technical difficulties prevented 
thorp and Shannon from betting any substantial amounts of money, 
but it was clear that the device did what it was intended to do. With 
Shannon’s help, thorp had beaten roulette.
the trip as a whole, though, proved more stressful than it was 
worth. Gambling can be tense enough without the constant possibil-
ity that burly enforcers will descend on you. Meanwhile, thorp had 
already received the job offer in new Mexico when the two couples 
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t h e p h y s i c s o f wa l l s t r e e t

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