Hackenbush
Draw a 'ground' line, then sprout any number of connected line segments above it, like a stick-figure hedge. Two players alternate erasing one segment at a time; whenever a segment loses its last connection to the ground, it falls away too. Whoever can't move loses. It sounds like a children's doodling game — so why did mathematician John Conway use it to help build an entire number system?
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Conway showed that Hackenbush positions, played with color-coded rules (one player can only cut red edges, the other only blue, with green edges anyone can cut), correspond precisely to numbers — including fractions and even infinitesimally small ones, not just whole numbers. By analyzing which player wins a given position, Conway derived the surreal numbers, a number system vastly larger than the real numbers, encompassing infinities and infinitesimals within one unified framework. He published the game and the theory behind it in his 1976 book On Numbers and Games.
— John Horton Conway, On Numbers and Games — 1976
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