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Fibonacci nim
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<p>Fibonacci nim is a mathematical <a href="/facts/Subtraction_game/LmUhrYwL">subtraction game</a>, a variant of the game of <a href="/facts/Nim/JfDdzxyc">nim</a>. Players alternate removing coins from a pile, on each move taking at most twice as many coins as the previous move, and winning by taking the last coin. The <a href="/facts/Fibonacci_number/mqxpAUQD">Fibonacci numbers</a> feature heavily in its analysis; in particular, the first player can win if and only if the starting number of coins is not a Fibonacci number. A complete strategy is known for best play in games with a single pile of counters, but not for variants of the game with multiple piles. </p>