Fibonacci nim
... that the first player can win a game of Fibonacci nim unless it starts with a Fibonacci number of coins?
... that the first player can win a game of <b id="mwA-Y"><a href="./Fibonacci_nim" id="mwA-c" rel="mw:WikiLink" title="Fibonacci nim">Fibonacci nim</a></b> unless it starts with a <a class="mw-redirect" href="./Fibonacci_number" id="mwA-g" rel="mw:WikiLink" title="Fibonacci number">Fibonacci number</a> of coins?