Bus thoughts about solving Go

I’m on a bus, so let’s talk about solving Go, by which I mean komiless Go. The way I see it, there are six gradually more rigorous levels of solution.

  1. Partial ultra-weak. This excludes one or more outcomes. There is a partial ultra-weak solution to all symmetrical games, which is the strategy-stealing argument. This states that whatever strategy is used by the second player can be used by the first player first, and that therefore the second player can’t win.

  2. Complete ultra-weak. This proves the outcome of the game. Go on large boards, like 19x19, can be shown to be a win for Black. This is because Black moves first and the value of the optimal move decreases throughout the game.

  3. First weak solution. This is a complete game record in which Black wins and White cannot be proven to have made a critical mistake. Middlegame and opening mistakes can be very hard to actually prove, which is why we have the next level.

  4. Second weak solution. This is a level 3 solution in which no observer can identify a critical mistake by White (in their opinion).

  5. Third weak solution. This is the first grindy solution, in which it must actually be proven that no possible defence by White can alter the outcome. A huge amount of positions have to be explored and this is well beyond current computational capability.

  6. Strong solution. The strong solution provides an optimal path to the correct outcome from any possible Go position.

It’s totally solved since 2002, at least if you don’t care about large board sizes like 6x6 or larger. :wink:



Last thing I heard 6x6 was strongly solved and there was a weak solution for 7x7 and maybe even 8x8.