Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Wythoff Game is where there are n-piles of stones and two players. Players take turn removing m stones from one pile, or m stones from more than one pile. The player who picks up the last stone wins.

In the game of Nim, a player can only pick from one pile at a turn. The nimnumber is the binary sum of the size of the piles. If the nimnumber is equal to zero, the current configuration is said to be a cold-position, the next player will lose if the other player plays optimally.

My question is there an equivalent use of the nimnumber for Wythoff's game?

share|improve this question
    
Are you asking about the Grundy values (sizes of equivalent Nim heaps) of Wythoff Game positions? Or a strategy for Wythoff's game? etc. –  Mark S. Jan 11 '13 at 1:06
    
The title is about a three-pile game, but this is never mentioned in the body. Is your question about the three-pile game or the general $n$-pile game? –  joriki Feb 3 '13 at 8:09
    
Do you lose if you pick the last stone from any one of the piles (so that one pile is now empty), or pick the last stone remaining in any of the piles (so all the piles are now all empty)? If you write a program for this, make sure to debug it extra carefully. If losing means taking stones so that no pile has one left, an easy stalemate strategy in a poor implementation is to always just take your stones from one particular pile, even after it has already run out, so that you are able to take 0 stones each time once it is exhausted. –  AJMansfield Jul 29 '13 at 18:25
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.