This post is long and takes a while to get to the point, but I hope some readers find the journey interesting!
The convention in combinatorial game theory is that a game ends when one player has no legal moves (and that player loses). Thus when formulating the rules of go in this setting, passing can obviously not be allowed. No Pass Go is quite similar to regular go, but has some peculiarities (in particular a much longer endgame). This is “fixed” by introducing Prisoner Return, which yields regular go with Group Tax.
Now, suppose we are making a ruleset with prisoner return, legal suicide and positional superko. We could use the CGT convention and end the game when one player has no legal moves (for this case, that would typically be when every move is a one-stone-suicide, violating PSK).
But suppose we don’t care about combinatorial game theory, we just want to make the rules as “simple” as possible. Rather than say
- Repeating a board position is illegal
- The first player without a legal move loses
we could simply say “The first player that repeats a board position loses”. This works especially nicely here since ko is the only type of forbidden move, but the same idea works if we also want to “forbid” suicide, just make suiciding a losing move.
Obviously this distinction between making a move illegal or losing doesn’t affect the game at all, except at a very superficial level. I think it’s aesthetically pleasing to allow every intersection on the board to be played as a legal move, but for a good user experience on a go server it also makes sense to just not let a player make a ko move. So I’m not here to argue that this formulation is “better”, but I think it is an interesting different perspective on the rules: The players take turns making moves until one of them violates superko.
While pondering these things last night as I went to sleep (as you do), I wondered what would happen if we made this one small change: what if the first player to “violate” the ko rule won instead of lost? This means that you can never take a simple ko-shape, because the opponent takes back and wins. Also, some fun stuff happens with Sending two, returning one:
Black just played 1. If white captures at A1, black will recapture at A2, repeating the position before 1 and winning the game (note that the distinction between positional and situational superko matters here). If white had had a ko threat elsewhere on the board, white could play that first and then capture at A1, but in this case there is no ko threat. So white will have to pass/return a prisoner/play a random move inside black’s territory, depending on the specifics of the rule set. Next black captures two stones, white recaptures one stone, and black plays atari:
Is white dead? No! Black can never ever capture at B4 (white would recapture and win). White is therefore alive with two eyes. In fact, even something like this would be alive:
So far I’ve glossed over the other details of this variant ruleset, because I’m not sure what they should be yet… if we allow suicide and use positional superko, then making a one-point eye is an automatic loss (the opponent suicides one stone, repeating the board position). Let’s save that crazyness for the future, and make a more familiar ruleset by disallowing suicide, and if you have no legal move you lose. Or, to incorporate the idea from earlier in this post:
- If you repeat a board position, you win.
- If you suicide, you lose.
This should lead to a pretty standard go endgame, where the player with more territory wins (especially if we add in prisoner return). To make it even more “practical” we can reintroduce passing and use regular old boring scoring. This variant can easily be played on OGS by using any ruleset with PSK (for instance Chinese): if you manage to get the “illegal ko move” or “illegal board repetition” error message you have automatically won. Else the game continues normally to scoring after both players pass. Would someone like to try a game?
For the more theoretically inclined, can you find a way to make this ruleset more “pure”? No disallowing suicide, no “player without a move loses”. Basically, I would like to always end the game with a repetition. Clearly if we continue playing long enough, eventually one player will manage to repeat. But I’m not sure such an endgame actually favors the player with more “territory”, so the game could become unrecognizable (and probably not very interesting). Is it possible to fix this with some tweaks to the rules?