Perfect komi on 7x7 Go, Japanese rules
Posted: Tue Apr 21, 2020 10:22 pm
The only komi value I've ever heard anyone seriously claim as the fair komi for 7x7 is 9. Including in Japanese rules, at least according to this page: https://senseis.xmp.net/?7x7ArticleByJDavies
Today I loaded up a recent KataGo 30 block net on 7x7, a board size which it actually plays a tiny percent of games on in the current run. It's pretty quick to hit tens of thousands of playouts on such a small board from the opening position, and doesn't take all that long to hit hundreds of thousands, on the cloud GPU I used. Searching from the opening position, ~200k playouts, 32 threads:
Tromp-Taylor-like rules: KataGo clearly agrees with 9 komi.
8.5 komi: 95% winrate for Black
9.5 komi, 5% winrate for Black
Chinese-like rules: KataGo clearly agrees with 9 komi.
8.5 komi: 95% winrate for Black
9.5 komi, 5% winrate for Black
Japanese-like rules: KataGo thinks the correct komi is 8.
7.5 komi, 94% winrate for Black
8.5 komi: 11% winrate for Black
Woah. What is the magic sequence that White uses to gain an extra point? Let's explore at 8.5 komi to see how White supposedly wins!
The Sensei's library article suggests white to continue at "a" or "b". KataGo dislikes "a" very rapidly and agrees it's losing for white (again, 8.5 komi). For "b" the first 200k or so playouts have the winrate fluctuate wildly all over the place, but eventually seems to converge on the move being also losing, 93% winrate for Black at 1 million playouts.
Instead, KataGo thinks that "c" for White wins.
Black can try "a" or "b" but KataGo thinks neither works (white answers either of them by playing the other). The variations after Black "a" White "b" are numerous and I don't understand them. But I found a neat gem in how KataGo thinks White refutes Black "b". I'm guessing this might be what human players have all missed so far? Of course there's always a chance KataGo missing something here too.
Now, what does White do next? Some simple things don't work.
If White blocks on the top, then Black hanes on the bottom: Next if White protects against "c", then Black will take "a" and win easily by a comfortable margin, having gotten both big endgame moves. But if White tries to take the top first with "b", Black will ignore and play "c". If you work out the endgame, Black will win again by a comfortable margin. (It's not that hard of an endgame to work out).
And if White instead of blocking on the top at all plays on the bottom, then the monkey jump easily destroys too much territory and Black is comfortably winning. You can pretty much already count, more or less: So, trusting KataGo is right and isn't missing something (always a chance for a blind spot), maybe we can try this as a nested puzzle if people enjoy trying to work it out.
White to play and win, 8.5 komi, Japanese rules.
Initial spoiler/hint and two followup questions:
Partial spoiler + hints for question 1:
Partial spoiler + hints for question 2:
Today I loaded up a recent KataGo 30 block net on 7x7, a board size which it actually plays a tiny percent of games on in the current run. It's pretty quick to hit tens of thousands of playouts on such a small board from the opening position, and doesn't take all that long to hit hundreds of thousands, on the cloud GPU I used. Searching from the opening position, ~200k playouts, 32 threads:
Tromp-Taylor-like rules: KataGo clearly agrees with 9 komi.
8.5 komi: 95% winrate for Black
9.5 komi, 5% winrate for Black
Chinese-like rules: KataGo clearly agrees with 9 komi.
8.5 komi: 95% winrate for Black
9.5 komi, 5% winrate for Black
Japanese-like rules: KataGo thinks the correct komi is 8.
7.5 komi, 94% winrate for Black
8.5 komi: 11% winrate for Black
Woah. What is the magic sequence that White uses to gain an extra point? Let's explore at 8.5 komi to see how White supposedly wins!
The Sensei's library article suggests white to continue at "a" or "b". KataGo dislikes "a" very rapidly and agrees it's losing for white (again, 8.5 komi). For "b" the first 200k or so playouts have the winrate fluctuate wildly all over the place, but eventually seems to converge on the move being also losing, 93% winrate for Black at 1 million playouts.
Instead, KataGo thinks that "c" for White wins.
Black can try "a" or "b" but KataGo thinks neither works (white answers either of them by playing the other). The variations after Black "a" White "b" are numerous and I don't understand them. But I found a neat gem in how KataGo thinks White refutes Black "b". I'm guessing this might be what human players have all missed so far? Of course there's always a chance KataGo missing something here too.
Now, what does White do next? Some simple things don't work.
If White blocks on the top, then Black hanes on the bottom: Next if White protects against "c", then Black will take "a" and win easily by a comfortable margin, having gotten both big endgame moves. But if White tries to take the top first with "b", Black will ignore and play "c". If you work out the endgame, Black will win again by a comfortable margin. (It's not that hard of an endgame to work out).
And if White instead of blocking on the top at all plays on the bottom, then the monkey jump easily destroys too much territory and Black is comfortably winning. You can pretty much already count, more or less: So, trusting KataGo is right and isn't missing something (always a chance for a blind spot), maybe we can try this as a nested puzzle if people enjoy trying to work it out.
White to play and win, 8.5 komi, Japanese rules.
Initial spoiler/hint and two followup questions:
at "a" next. What has White gained by doing all this, and how does White finish this game?
refutes white's probe and still Black wins the game. Black has to refute both 
as shown and 
I agree, a link to that would be cool too. 
didn't have a big enough followup. Black can get 
, and 
is gote, black can ignore it to play 
and white loses more in the lower left than can be gained in the upper right. But that was before white cut and made the exchanges inside black's territory.
is the key move for black), figuring out why