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

part of the money for the casino trip.
It took about a month, but at last Kimmel was convinced that 
thorp’s system worked — and that thorp had what it took to use the 
system in a real casino. thorp decided that $100,000 was too much 
and insisted on working with a smaller sum — $10,000 — because he 
thought gambling with too much money would attract unwanted at-
tention. Kimmel, meanwhile, thought that Las vegas was too high 
profile, and besides, too many people knew him there. So over MIt’s 
spring break, thorp and Kimmel, who was once again accompanied 
by a pair of young women, descended on reno to test thorp’s system. 
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Beating the Dealer 
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It was a resounding success. they played, moving from casino to ca-
sino, until they developed a reputation that moved faster than they 
could. In just over thirty man-hours of playing, thorp, Kimmel, and 
Hand collectively turned their $10,000 into $21,000 — and it would 
have been $32,000 if Kimmel hadn’t insisted on continuing to play one 
evening after thorp announced he was too tired to keep counting. 
thorp would later tell the story — with Kimmel’s name changed to Mr. 
X and Hand’s to Mr. Y — in a book, Beat the Dealer, that taught readers 
how to use his system to take vegas to the cleaners themselves.
thorp developed several methods for keeping track of how the odds 
in blackjack change as cards are played and removed from the deck. 
Using these systems, thorp was able to reliably determine when the 
deck was in his favor, and when it was in the house’s favor. But suppose 
you are playing a game of blackjack, and suddenly you learn that the 
odds are slightly in your favor. What should you do?
It turns out that blackjack is extremely complicated. to make the 
problem tractable, it’s better to start with a simpler scenario. real coins 
come up heads and tails equally often. But it’s possible to at least imag-
ine (if not manufacture) a coin that is more likely to come up one way 
or the other — for now, suppose it’s more likely to come up heads than 
tails. now imagine you’re making bets on coin flips with this weighted 
coin, against someone who is willing to pay even money on each flip, 
for as many flips as you want to play (or until you run out of money). 
In other words, if you bet a dollar and win the bet, your opponent gives 
you one dollar, and if your opponent wins, you lose one dollar. Since 
the coin is more likely to come up heads than tails, you would expect 
that over the long run money will tend to flow in one direction (yours, 
if you consistently bet heads) because you’re going to win more than 
half the time. finally, imagine that your opponent is willing to take 
arbitrarily large or small bets: you could bet $1, or $100, or $100,000. 
You have some amount of money in your pocket, and if it runs out, 
you’re sunk. How much of it should you bet on each coin flip?
one strategy would be to try to make bets in a way that maximizes 
the amount of money you could stand to make. the best way to do this 
would be to bet everything in your pocket each time. then, if you win, 

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you double your money on each flip. But this strategy has a big prob-
lem: the coin being weighted means that you will usually win, not that 
you’ll always win. And if you bet everything on each flip, you’ll lose 
everything the first time it comes up tails. So even though you were 
trying to make as much money as possible, the chances that you’ll end 
up broke are quite high (in fact, you’re essentially guaranteed to go 
broke in the long run), with no chance to make your money back. this 
scenario — where your available funds run out, and you’re forced to 
accept your losses — is known as “gambler’s ruin.”
there’s another possibility — one that minimizes the chances of 
going broke. this is also a straightforward strategy: don’t bet in the 
first place. But this option is (almost) as bad as the last one, because 
now you guarantee that you won’t make any money, even though the 
coin is weighted in your favor.
the answer, then, has to be somewhere in the middle. Whenever 
you find yourself in a gambling situation where you have an advan-
tage, you want to figure out a way to keep the chances of going broke 
to a minimum, while still capitalizing on the fact that in the long run, 
you’re going to win most of the bets. You need to manage your money 
in a way that keeps you in the game long enough for the long-term 
benefits to kick in. But actually doing this is tricky.
or so it seemed to thorp when he was first trying to turn his analy-
sis of card-counting odds into a winning strategy for the game. fortu-
nately for thorp, Shannon had an answer. When thorp mentioned the 
money management problem to Shannon, Shannon directed thorp to 
a paper written by one of Shannon’s colleagues at Bell Labs named 
John Kelly Jr. Kelly’s work provided the essential connection between 
information theory and gambling — and ultimately the insights that 
made thorp’s investment strategies so successful.
Kelly was a pistol-loving, chain-smoking, party-going wild man 
from texas. He had a Phd in physics that he originally intended to 
use in oil exploration, but he quickly decided that the energy industry 
had little appreciation of his skills, and so he moved to Bell Labs. once 
he was in new Jersey, Kelly’s colorful personality attracted plenty of 
attention in his staid suburban neighborhood. He was fond of firing 
plastic-filled bullets into the wall of his living room to entertain house-
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