Our paper "Combinatorics of Go" has some results on this, in a rule system allowing suicide. See http://tromp.github.io/go/gostate.pdf, in particular Section 7 on Hamiltonian games.
-John On Thu, Nov 19, 2015 at 10:13 AM, Marc Landgraf <mahrgel...@gmail.com> wrote: > Hi, > there is a question that lately crossed my mind. Considering an nxn Go > board, no suicide allowed and with a rule that does not allow repetition of > a position, unless caused by a single pass: > What is the maximum number of board positions that can be run through in a > single sequence starting from an empty board? > Different wording: What is the maximum game length if not counting passes? > > It can easily be proven that for n>=3 this number must be lower than the > number of legal positions. I didn't check for n=2, simple bruteforce would > probably solve that. > > What happens to the ratio between the number of legal positions and the > longest possible sequence with growing n? > > Is this already known? Or does anyone have a clue how to figure it out? > > ~Marc > > > > _______________________________________________ > Computer-go mailing list > Computer-go@computer-go.org > http://computer-go.org/mailman/listinfo/computer-go _______________________________________________ Computer-go mailing list Computer-go@computer-go.org http://computer-go.org/mailman/listinfo/computer-go
