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

Primordial Seeds 
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curring, essentially by counting. So, for instance, there are six possible 
outcomes of rolling a standard die; there is precisely one way in which 
to yield the number 5. So the mathematical odds of yielding a 5 are 1 
in 6 (corresponding to betting odds of 5 to 1). But what about yielding 
a sum of 10 if you roll two dice? there are 6 × 6 = 36 possible out-
comes, of which 3 correspond to a sum of 10. So the odds of yielding 
a sum of 10 are 3 in 36 (corresponding to betting odds of 33 to 3). the 
calculations seem elementary now, and even in the sixteenth century 
the results would have been unsurprising — anyone who spent enough 
time gambling developed an intuitive sense for the odds in dice games
— but cardano was the first person to give a mathematical account of 
why the odds were what everyone already knew them to be.
cardano never published his book — after all, why give your best 
gambling tips away? — but the manuscript was found among his pa-
pers when he died and ultimately was published over a century after 
it was written, in 1663. By that time, others had made independent 
advances toward a full-fledged theory of probability. the most notable 
of these came at the behest of another gambler, a french writer who 
went by the name chevalier de Méré (an affectation, as he was not 
a nobleman). de Méré was interested in a number of questions, the 
most pressing of which concerned his strategy in a dice game he liked 
to play. the game involved throwing dice several times in a row. the 
player would bet on how the rolls would come out. for instance, you 
might bet that if you rolled a single die four times, you would get a 6 
at least one of those times. the received wisdom had it that this was 
an even bet, that the game came down to pure luck. But de Méré had 
an instinct that if you bet that a 6 would get rolled, and you made this 
bet every time you played the game, over time you would tend to win 
slightly more often than you lost. this was the basis for de Méré’s gam-
bling strategy, and it had made him a considerable amount of money. 
However, de Méré also had a second strategy that he thought should 
be just as good, but for some reason had only given him grief. this 
second strategy was to always bet that a double 6 would get rolled at 
least once, if you rolled two dice twenty-four times. But this strategy 
didn’t seem to work, and de Méré wanted to know why.
As a writer, de Méré was a regular at the Paris salons, fashionable 

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meetings of the french intelligentsia that fell somewhere between 
cocktail parties and academic conferences. the salons drew educated 
Parisians of all stripes, including mathematicians. And so, de Méré 
began to ask the mathematicians he met socially about his problem. 
no one had an answer, or much interest in looking for one, until de 
Méré tried his problem out on Blaise Pascal. Pascal had been a child 
prodigy, working out most of classical geometry on his own by draw-
ing pictures as a child. By his late teens he was a regular at the most 
important salon, run by a Jesuit priest named Marin Mersenne, and it 
was here that de Méré and Pascal met. Pascal didn’t know the answer, 
but he was intrigued. In particular, he agreed with de Méré’s appraisal 
that the problem should have a mathematical solution.
Pascal began to work on de Méré’s problem. He enlisted the help of 
another mathematician, Pierre de fermat. fermat was a lawyer and 
polymath, fluent in a half-dozen languages and one of the most capa-
ble mathematicians of his day. fermat lived about four hundred miles 
south of Paris, in toulouse, and so Pascal didn’t know him directly, 
but he had heard of him through his connections at Mersenne’s salon. 
over the course of the year 1654, in a long series of letters, Pascal and 
fermat worked out a solution to de Méré’s problem. Along the way, 
they established the foundations of the modern theory of probability.
one of the things that Pascal and fermat’s correspondence pro-
duced was a way of precisely calculating the odds of winning dice bets 
of the sort that gave de Méré trouble. (cardano’s system also accounted 
for this kind of dice game, but no one knew about it when de Méré 
became interested in these questions.) they were able to show that de 
Méré’s first strategy was good because the chance that you would roll 
a 6 if you rolled a die four times was slightly better than 50% — more 
like 51.7747%. de Méré’s second strategy, though, wasn’t so great be-
cause the chance that you would roll a pair of 6s if you rolled two dice 
twenty-four times was only about 49.14%, less than 50%. this meant 
that the second strategy was slightly less likely to win than to lose, 
whereas de Méré’s first strategy was slightly more likely to win. de 
Méré was thrilled to incorporate the insights of the two great math-
ematicians, and from then on he stuck with his first strategy.
the interpretation of Pascal and fermat’s argument was obvious, 
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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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