Friday, December 08, 2017

[ymvlbayj] Larger Dodgem with superko

The game of Dodgem with board sizes 4x4 and larger is loopy: optimal play from the initial position results in the game going into a loop.  Who wins (and how) if the game is played with a super-ko rule (as in go 囲碁), forbidding recreating a prior position?

There are several possible variations of a super-ko possible: if you have no choice but to recreate a prior position, do you lose or win?  Staying consistent with the stalemate rule of Dodgem, if you have no legal moves then you should win.  The rule could also be radically different: if you are in a position identical to a prior one (no prohibition on the previous player in recreating one) then you must play a different move than you previously played.

Dodgem has a feature similar to chess where pawns can't move backward.  Once a piece moves forward, previous state may be safely forgotten.

Might also be interesting to analyze the simple (not super-) ko rule: no recreating the position two moves ago.  The game can still go in a loop, but will it?

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