Games@Dal 2016 talk: "3-player Nim with podium rule" - Carlos Santos w/Richard J. Nowakowski and Alexandre M. Silva
Carlos's talk entered the somewhat-forbidden world of three-player games. He spoke of different ways of considering these games, but continued using Lee's Podium Rule from 1978: If you can't come in first, you should instead try to come in second. (Try to get as high up the podium as you can.)
In impartial games, this leads to a third outcome class: O ("Other") which has no P options, but at least one N option. Playing on Nim heaps, to find P positions, we now have to perform the nim sum, but mod 3 instead of mod 2. Thus, *7 + *17 + *22 + *23 is a P position. Zeroness in the sum only actually tells us about P positions; non-zero values might be O or N, so we need further criteria.
Carlos described these further criteria, then continued by describing how to define canonical forms for Nim.
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