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

Beating the Dealer 
•
87
prove incredibly difficult. It involved calculating the probabilities of all 
of the possible hands, under all sorts of different circumstances. Mil-
lions of calculations.
this was just what a group of army researchers set out to do, begin-
ning in 1953. over the course of three years, using “computers” (which 
in the early 1950s meant people, perhaps with electronic adding ma-
chines), the army team worked out (almost) all of the possible hands, 
figured out their probabilities, and then devised what they claimed 
was the “optimal” blackjack strategy. It was this strategy that they pub-
lished in the Journal of the American Statistical Association, and that 
thorp decided to try on his trip to vegas. It wasn’t a winning strategy. 
According to the army’s calculations, the house had an advantage even 
if you played with their optimal strategy, because of the essential role 
of uncertainty about the dealer’s hand in the player’s decision making. 
But the advantage was tiny. If you made a thousand one-dollar bets at 
successive hands of blackjack using their strategy, the army predicted, 
you should expect to have (on average) about $994 left at the end of the 
day. compare this to slots, where you could expect to have about $800 
left, and the optimal blackjack strategy looked pretty good. Unfortu-
nately, the strategy wasn’t simple, so thorp had to make a cheat sheet; 
he wrote out all of the possibilities on a little card, which he consulted 
as he played.
He lost. Quickly. Starting with a pile of $10, thorp was down to 
$1.50 within the hour. But the other people at the table lost even more 
quickly, and by the time thorp left the table, he was convinced that the 
army’s researchers were on to something. He was also convinced that 
he could do better.
the problem with the army strategy, as thorp saw it, was that it 
treated each round of blackjack as independent: it was as though each 
time around, a brand-new deck was being used. But in real life, espe-
cially in 1958 (casinos have since changed the rules slightly), this wasn’t 
the case. A dealer would shuffle a deck and then keep playing as long 
as there were enough cards to go around. this changes everything. 
consider that the probability of receiving, say, an ace from a new deck 
is 4/52, since there are 4 aces in a deck of 52 cards. But suppose you’re 
on your second hand, and on the first hand 10 cards came up, two of 

---

which were aces. now the odds of getting an ace are 2/42, which is 
much less than 4/52. the point is that if your strategy depends on the 
probabilities of getting different card combinations, and if you’re being 
careful, you need to take into account what cards have already been 
played. Adopting such a strategy, where you keep track of what cards 
have already been played and vary your strategy accordingly, is called 
card counting.
card counting, thorp believed, could make the odds in blackjack 
even better than what the army researchers found. Using MIt’s IBM 
704, one of the first mass-produced electronic computers, thorp man-
aged to prove that the player would have an advantage if he combined 
a modified version of the army’s strategy with a simple card-counting 
technique. this was thorp’s in with Shannon. He wrote a paper de-
scribing what he had found, with the hope that Shannon would help 
him publish it.
When the day of the meeting arrived, thorp knew the pressure was 
on. He had his thirty-second elevator pitch ready: what he wanted; 
why Shannon should care.
As it turned out, thorp had little to worry about. Shannon imme-
diately saw what was interesting about thorp’s results. And after a few 
piercing questions, Shannon was convinced that thorp was the real 
deal. He made some editorial suggestions and suggested that thorp 
tone down the title (from “A Winning Strategy for Blackjack” to “A fa-
vorable Strategy for twenty-one”) and then offered to submit thorp’s 
paper to the Proceedings of the National Academy of Sciences, the most 
prestigious academic journal that would consider publishing such 
work (only members of the Academy could submit papers). then, as 
thorp prepared to leave, Shannon casually asked if thorp had any 
other gambling-related projects. this kind of math, with clear and fun 
applications, was right up Shannon’s alley. After a pause, thorp leaned 
forward. “there is one other thing,” he began. “It’s about roulette . . .”
It was dusk on a snowy winter’s evening in cambridge, Massachusetts. 
A dark sedan circled the block once and then slowed to a stop in front 
of the thorps’ apartment building. the doors opened, and from each 
side of the car a beautiful young woman emerged. Both women had 
88 
•
t h e p h y s i c s o f wa l l s t r e e t

---

Beating the Dealer 
•
89
mink coats draped over their shoulders. they stepped back from the 
car to reveal its third passenger, a short man in his early sixties. His 
name was Manny Kimmel. He was the owner of a growing parking 
lot and funeral home concern known as the Kinney Parking com-
pany. the Kinney Parking company was in the process of going pub-
lic. over the next decade, under the joint leadership of Kimmel’s son 
caesar and legendary ceo Steve ross, Kinney would rapidly expand: 
first to commercial cleaning and facilities management, and then to 
media. In 1969, Kinney Parking company would acquire Warner 
Brothers Studios as the first step in a transformation that would ulti-
mately culminate in time Warner, which is today the world’s largest 
media conglomerate.
In 1961 all of this was in the future. But Kimmel was already a very 
wealthy man. His fortune had been made the old-fashioned way: gam-
bling and booze. Legend has it that Kimmel won his first parking lot, 
on Kinney Street in newark, new Jersey, in a high-stakes craps game. 
And the early success of the Kinney Parking company had as much to 
do with Kimmel’s side business of running limousines to illegal gam-
bling houses as it did with people parking their cars. during Prohi-
bition, he teamed up with his childhood friend, the Jewish mobster 
Longy Zwillman. Zwillman would import rye whiskey from canada 
and then use Kimmel’s new Jersey garages to store it.
It was gambling that brought Kimmel to thorp’s doorstep that cold 
Sunday in february. A few weeks before, thorp had given a public 
talk on his national Academy paper at the American Mathematical 
Society’s annual meeting, in Washington, dc. this time around, he 
permitted himself a provocative title: he called the talk “fortune’s for-
mula: A Winning Strategy for Blackjack.” Blackjack aside, thorp’s talk 
was a winning strategy for attracting media attention. He delivered 
the talk to a packed audience, and soon the AP and other news out-
lets came knocking. Within days, stories had begun to appear in the 
national media, including the Washington Post and Boston Globe. the 
dry annual AMS meeting rarely attracted much notice in the news, but 
something about an MIt mathematician taking vegas to the cleaners 
struck a chord.
At first, thorp reveled in the attention. His phone began ringing off 

---

the hook, with reporters looking for interviews and gambling fanat-
ics hoping to learn thorp’s tricks. He boasted to reporters that if he 
could get sufficient funding for a trip to vegas, he would prove that 
his system worked in practice. As a publicity stunt, the Sahara, one 
of the big vegas Strip casinos, offered him free room and board for as 
long as he liked — trusting that thorp’s system, like the hundreds that 
preceded it, was at best a fantasy. But the Sahara wouldn’t front thorp 
gambling money, and on his $7,000-a-year salary, thorp couldn’t raise 
sufficient funds himself. (Since casinos have minimum bets, an early 
losing streak can wipe you out if you don’t have a pile of cash on hand
— even if you’re very likely to win in the long run.)
this is where Kimmel came in. Some men like fine wines or expen-
sive cigars. others prefer cars, or sports, or perhaps art. As an inveter-
ate gambling man, Kimmel was a connoisseur of the favorable betting 
system. When Kimmel read about thorp’s blackjack system, he wrote 
to thorp and offered to fund his experiment to the tune of $100,000. 
But first he needed to see the system in action. So when thorp con-
tacted him and agreed to meet, Kimmel took a car up from new York. 
When Kimmel arrived — introducing the two young women as his 
nieces — thorp began by showing Kimmel his proofs and explaining 
his methodology. But Kimmel didn’t care about any of that. Instead, 
he took a deck of cards out of his pocket and began to deal. Kimmel 
would believe a system worked only after he’d watched someone win 
with it. they played all evening, and then again the next day. over the 
coming weeks, thorp would drive down to new York regularly to play 
against Kimmel and an associate, eddie Hand, who was putting up