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Street Science

How To Design A Franc-Carreau or Fair-square Game

The origins of geometric probability!

How To Design A Franc-carreau or Fair-square Game — An illustration showing a 6x6 square grid with a circular pink coin inside one of the grids without touching any grid lines, and a circular green coin that touches four grid lines. Pink coin → Win; Green coin → Loss
A Franc-Carreau Game (illustration created by the author)

The Franc-Carreau or fair-square is a game of chance from a time when the mathematical notion of probability was just seeping into the world of gambling. Back in the 18th Century, Georges-Louis LeClerc, Comte de Buffon of Burgundy, France, was aiming to make it into the Royal Academy of Sciences in Paris as a…

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