Equipment:
A number of counters (or coins or matches or any small objects)
Number of players:
2
The Set-up:
The counters are arranged into several 'heaps'.
Here is a typical three-heap game:
A Move:
At your turn you remove as many counters as you wish from one heap. You must remove a minimum of one counter from the heap and may remove the whole heap if you wish.
You win:
If your opponent has no valid move.
Comments:
In the game above it would be fatal for the opening player to remove one counter from Heap 2 thereby equalising Heap 2 and Heap 3. The best response to such an opening move would be for the second player to completely remove Heap1 leaving the following set-up:
Why does the player who first moves on a set-up with only two equal heaps always lose? (assuming the other player plays her best move all the time!)
Links:
Play the computer using a Java Applet created by Alexander Bogomolny.
Visit the Mathematical Analysis of Games Project Nim Page and also the United States Naval Academy Nim Page.
Variations:
Poker-Nim: At your turn you may opt for the alternative move of increasing the size of one heap using some (or all) of the counters that you gained in previous moves.
Lasker's Nim: At your turn you have an option to split one heap into two smaller non-empty heaps. If this option is taken then you remove no counters on your turn.
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