# He couldn't calculate the odds, so he counted.

- Series: [The Better Guess](https://miu.fm/thebetterguess.md)
- Published: 2026-10-09
- Page: https://miu.fm/thebetterguess/he-couldn-t-calculate-the-odds-so-he-counted

## Story

He couldn't calculate the odds, so he counted.

In 1946 the mathematician Stanislaw Ulam, recovering from a serious illness, played solitaire and asked what the odds were of a game coming out. There are more ways to shuffle 52 cards than atoms in the Earth, and the mathematics got him nowhere. So he wondered: why not lay it out a hundred times and simply count?

That is the Monte Carlo method. A hundred games pin the odds to within about five points; ten thousand, to half a point. Four times the games, twice the precision. A person can't deal ten thousand games, but a machine could. John von Neumann wrote out in 1947 how a computer could follow neutrons the same way, a random number deciding each collision, and in April 1948 ENIAC ran the first computerised Monte Carlo simulation, with code largely written by Klara von Neumann. The name came from Nick Metropolis: Ulam had an uncle who borrowed money from relatives because he just had to go to Monte Carlo.

The game on screen is Clock solitaire, a stand-in with no choices and odds of exactly 1 in 13. We don't know which solitaire Ulam played.

What would you rather count than calculate?

Sources: Roger Eckhardt, "Stan Ulam, John von Neumann, and the Monte Carlo Method", Los Alamos Science 15, 1987; Nicholas Metropolis, "The Beginning of the Monte Carlo Method", Los Alamos Science 15, 1987; Metropolis and Ulam, "The Monte Carlo Method", Journal of the American Statistical Association 44(247), 1949; Haigh, Priestley and Rope, "Los Alamos Bets on ENIAC", IEEE Annals of the History of Computing 36(3), 2014.
Sounds: Freesound, CC0 (RealSquink, SomeoneCool15, magnus1906, tt_runscript); Apple iMovie sound effects.

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