Nim is now used as a simple illustration of the SpragueGrundy theory of games.
A version of this game is played in Alain Resnais' movie L'année dernière à Marienbad.
A typical normal game starts with heaps of 3, 4 and 5:
A B C (Heaps A, B, and C) 3 4 5 I take 2 from A 1 4 5 You take 3 from C 1 4 2 I take 1 from B 1 3 2 You take 1 from B 1 2 2 I take entire C heap 2 2 0 You take 1 from A 1 2 0 I take 1 from B (In the misere game I would take the entire 2 heap) 1 1 0 You take 1 from B 1 0 0 I take the last 1 and win.
Nim has been mathematically solved; that is, there is a defined and guaranteed way to win. In a typical misere game that starts with heaps of 3, 4, and 5, player 1 should always win.
011 Heap A in binary 100 Heap B in binary 101 Heap C in binary  010 The digital sum[?] of heaps A, B, and C
To win, you must end every turn with a digital sum[?] of 0, unless you are playing the misere game. In the misere game play normally until only heaps of size 1 will remain and move to ensure an odd number of heaps. Let's play a misere game:
A B C Sum (Heaps A, B, and C) 3 4 5 010 I take 2 from A, leaving a sum of 000, so I will win. 1 4 5 000 You take 3 from C 1 4 2 111 I take 1 from B 1 3 2 000 You take 1 from C 1 3 1 011 I take 2 from B leaving 3 heaps of size 1 1 1 1 You take 1 from C 1 1 0 I take 1 from B leaving 1 heap of size 1 1 0 0 You take the last 1 and lose.
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