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

Beating the Dealer 
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As the spring semester came to an end in new Mexico, thorp found 
himself with a few weeks to spare before his move to california. He 
began to riffle through the RHM documents. the writers at RHM 
apparently thought of warrants as a kind of lottery ticket. they were 
cheap to buy, usually worthless, but occasionally you could strike it 
rich if a stock started trading well above the warrant’s exercise price.
Where RHM, and most other investors, saw a lottery ticket, thorp 
saw a bet. A warrant is a bet on how a stock will perform over a fixed 
period. the price of the warrant, meanwhile, is a reflection of the mar-
ket’s determination of how likely the buyer is to win the bet. It also 
reflects the payout, since your net profit if the warrant does become 
valuable is determined by how much you had to pay for the warrant 
in the first place. But thorp had just spent an entire summer reading 
about how stock prices are random. He pulled out a piece of paper and 
began to calculate. His reasoning followed Bachelier’s thesis closely, 
except that he assumed prices were log-normally distributed, à la os-
borne. He quickly arrived at an equation that told him how much a 
warrant should really be worth.
this was valuable, if not trailblazing. But thorp had an ace up 
his sleeve, something Bachelier and osborne never imagined. With 
five years of gambling experience, thorp realized that calculating a 
“true” price for a warrant is a lot like calculating the “true” odds on 
a horserace. In other words, the theoretical relationship that thorp 
discovered between stock prices and warrant prices gave him a way 
to extract information from the market — information that gave him 
an edge, not in the stock market directly, but in the associated war-
rant market. this partial information was just what thorp needed to 
implement the Kelly system for maximizing long-term profits.
thorp was energized by this work on warrants. It seemed to him that 
he had finally found the perfect way to use his gambling experience to 
profit from the world’s biggest casino. But there was a problem. When 
he finished his calculations and plugged some numbers into a com-
puter (thorp wasn’t able to solve the equations he set up explicitly, but 
he was able to come up with a way to use a computer to do the final 
calculations for him), he discovered that there was no advantage to 

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buying warrants. In other words, you couldn’t go out and buy warrants 
and expect to make a profit — according to the Kelly betting system, 
you should invest nothing! the reason for this wasn’t that warrants 
were all trading at exactly what they were worth; rather, they were 
trading at much too high a price. the dirt-cheap lottery tickets that 
RHM Warrant Survey was advertising were actually much, much too 
expensive.
If you think of investing as a kind of gamble, buying a stock repre-
sents a bet that the stock price will go up. Selling a stock, meanwhile, 
is a bet that the stock will go down. thorp, like Bachelier before him, 
realized that the “true” price of a stock (or option) corresponds to the 
price at which the odds of the buyer winning are the same as the odds 
of the seller winning. But with traditional trades, there’s an asymme-
try. You can virtually always buy a stock; but you can sell a stock only if 
you already own it. So you can bet against a stock only if you’ve already 
chosen to bet for it. this is similar to a casino: it would be highly desir-
able, in roulette, say, to bet against a number. this, after all, is what the 
house does, and the house ultimately has the long-term advantage. But 
it isn’t possible. no casino will let you bet that your blackjack hand will 
lose.
In investing, however, there is that possibility. If you want to sell a 
stock you don’t already own, all you need to do is find someone who 
does own the stock but doesn’t want to sell it, and who is willing to let 
you borrow the shares for a while. then you sell the borrowed shares, 
with the expectation that at some later time you will buy the same 
number of shares back and return them to their original owner. this 
way, if the price goes down after you sell, you see a profit, since you 
can buy the shares back at the lower price. Whoever loaned you the 
shares, meanwhile, is no worse off than if he had simply held on to 
them. the origins of this investment practice, known as short selling, 
are obscure, but it is at least three hundred years old. We know this 
because it was banned in england in the seventeenth century.
today, short selling is perfectly standard. But in the 1960s — indeed, 
for much of the practice’s history — it was viewed as dangerous at best, 
and perhaps even depraved or unpatriotic. the short seller was per-
ceived as a blatant speculator, gambling on market moves rather than 
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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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