Plainim Misère

Plainim Misère is played on a checkered board by removing or adding chips. There are just a few rules.

  1. On a single move, one may only add/remove chips in a single row.
  2. At most one chip is allowed per square.
  3. One may only add chips to the right of a chip being removed on the same move.
  4. The one to remove the last chip loses.

To perform a move click on squares (in a single row) where you want chips placed or removed (see that you confirm to Rules 1-3). Then press the button "Make Move".


This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


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For Plainim Misère, a winning strategy is almost the same as for the Plainim itself. The strategy is to play as in normal Plainim until all non-empty heaps with one exception, contain a single counter. Then make a move so as to leave an odd number of single counter heaps. (By analogy with the normal games, which are equivalent to Nim heaps, one may expect this strategy to work for other impartial games. Suprisingly, this is not the case. The above strategy does not work even with the game of Scoring.)

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