> > (effectively) zero. Therefore epsilon should be pretty tiny. It must be > large enough that there is a chance of the frisbee being at least 50% over > the line (i.e. epsilon > 0), but small enough that the chance of it going > 70.7% over the line is vanishingly small (otherwise we would be allowing it > to be displaced onto the diagonally adjacent positions). >
I do not understand, I think that we do not need to ensure that the stone cannot land diagonally by small epsilon, since ingo defined it s.t. it cannot. Having small epsilon as you suggest makes any attempts at writing a specialized frisbee-go code not really fruitful, since the displacement is quite rare; so realistically, with small epsilon, no-one would probably bother to do anything different than to run current programs unchanged. I think that frisbee-go is much interesting for larger epsilons - e.g. 1/8, 1/6 - because it has nontrivial strategical/tactical implications. For instance, seki are no longer sekis in this setting, since the loosing party can always improve its expected outcome by trying to be lucky, and therefore the winning side can do the same (of course sometimes this is quite like starting the "10000 year ko"). Also when the game ends each dame is essentially assigned "randomly", so under chinese rules score can "change randomly". Moreover, larger epsilons change the game's dynamic s.t. it is easier to live and harder to kill (hypothesis). Another thing is that the MCTS might work much better with this setting (since random playouts are much more true). ingo: One note for rules (you should add) is that when players throw stone to a location where the probability of landing on a valid location is exactly zero (all 5 positions are stones or invalid) this counts as a pass (otw, the loosing party might play the "non-voluntary pass" moves and make the game infinite. (sorry if I overlooked someone mentioning this already) Regards, Josef
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