The reversed ending
Choose one non-empty heap and remove any positive number from it. Play stops when no counters remain, but the player who made that final removal loses and the other player wins.
Misère Nim
Avoid taking the final counter while forcing the computer to make the last move.
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How to play
Avoid taking the final counter while forcing the computer to make the last move.
- Choose one non-empty heap on your turn.
- Remove one or more counters from that single heap.
- Keep playing until the player who removes the final counter loses.
Strategy tips
- Use ordinary Nim planning while several heaps contain more than one counter.
- When only single counters remain, aim to leave an odd number for the opponent.
- Reduce the last large heap to zero or one according to the number of singletons.
Complete guide
Rules, scoring, and strategy
Misère Nim keeps Nim's one-heap move rule but reverses the finish: taking the final counter loses. That one change makes the last collection of one-counter heaps strategically different.
Normal planning until the end
While at least two heaps contain more than one counter, ordinary nim-sum reasoning still guides most positions. The exception arrives when the game collapses to singletons or one remaining large heap.
Count the singleton parity
With only one-counter heaps left, an even number is winning for the player to move and an odd number is losing. When exactly one larger heap remains, reduce it to zero or one so the opponent receives the unfavorable singleton count.
The common final-counter mistake
A move that would win normal Nim may lose immediately here. Before clearing a heap, count how many counters and nonempty heaps will remain, then verify who is forced to make the final take.
Questions players ask
How does Misère Nim differ from Nim?
The legal moves are identical, but the player taking the final counter loses instead of winning.
Is zero nim-sum always the goal?
Not in the all-singleton ending. Misère play uses a parity rule once every remaining heap has size one.
Can I take an entire heap?
Yes, provided at least one counter is removed from only that heap; just remember that taking the final counter loses.