The connection between solitaire and the Monte Carlo method is real, but it is often compressed into an overly simple origin story. Solitaire supplied Stanislaw Ulam with a useful example of estimation by repeated trials; the computational method was then developed collaboratively at Los Alamos by Ulam, John von Neumann, Nicholas Metropolis, Robert Richtmyer, and others.

The question Ulam asked

In his autobiography, Ulam described thinking about the probability of successfully completing a solitaire game while recovering from illness. An exact combinatorial calculation looked impractical. Playing many deals and recording the proportion of wins offered another route: estimate the answer experimentally rather than derive it in closed form.1

That is the essential Monte Carlo idea. When a system is too complicated to analyze directly, simulate many random trials and use the distribution of outcomes to estimate the quantity of interest. The estimate has uncertainty, but that uncertainty can itself be measured and reduced with more trials.

From cards to neutron transport

At Los Alamos in the 1940s, the important problem was not a card game. The researchers needed practical ways to model branching processes such as the paths and interactions of neutrons. The arrival of electronic computation made large numbers of sampled histories feasible. Los Alamos records credit Ulam, von Neumann, Metropolis, and colleagues with the early development of modern Monte Carlo particle-transport methods.23

Why the method is called “Monte Carlo”

The name refers to games of chance and the Monte Carlo casino. Historical accounts generally credit Nicholas Metropolis with choosing the label. The name was memorable because random sampling is central to the method, even though the scientific calculations themselves are carefully designed rather than casual gambling.3

Solitaire also appeared in the published explanation

Metropolis and Ulam's 1949 paper used estimating the probability of winning at solitaire as an accessible example alongside mathematical and particle- diffusion applications. The example demonstrates both the power and the limitation of simulation: observed outcomes estimate a probability only for the precise rules, deal process, and decision policy being simulated.4

What the story does—and does not—show

Solitaire did not single-handedly create modern simulation, nor did one game instantly produce a finished algorithm. It helped Ulam recognize a general pattern: repeated random experiments could make an otherwise difficult probability question tractable. Turning that insight into a computational method required collaborators, machines, random-number procedures, and application-specific models.

Sources and notes

  1. University of California Press: Stanislaw Ulam, Adventures of a Mathematician
  2. Los Alamos National Laboratory / OSTI: The History of Monte Carlo and MCNP at Los Alamos
  3. Los Alamos National Laboratory: Monte Carlo reference collection
  4. Nicholas Metropolis and Stanislaw Ulam, “The Monte Carlo Method” (1949)

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