What about mirror go?

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Bill Spight
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What about mirror go?

Post by Bill Spight »

Several years ago I surmised that with komi, mirror go would favor White, by lowering the overall temperature and hence, the effective komi. OC, at some point you have to stop mirroring. ;)

Well, the bots don't mirror. But maybe that is the result of path dependency. So I wonder. . . .

What if you trained a top bot against a variant of itself that, as White, always mirrored through tengen, if possible, up through a certain number of moves, such as 100? Or 50? Or 30?

We might learn strategies to defeat mirror go, or we might learn that mirror go is an effective opening strategy. :)
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Bill Spight
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Re: What about mirror go?

Post by Bill Spight »

One mirror sequence. Thanks to AlphaGoTeach ( https://alphagoteach.deepmind.com ).
Click Here To Show Diagram Code
[go]$$B Mirror go 1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . a . . . . . . . . . . 0 7 . . . . |
$$ | . . . 4 . . . . . , . . . . 6 , 1 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 2 , 5 . . . . , . . . . . 3 . . . |
$$ | . . . . 8 9 . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
AlphaGoTeach prefers a for :b5:, which it does not mirror. :b5: is its second choice.
Click Here To Show Diagram Code
[go]$$Bcm11 Mirror go 1, continued
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O X 1 . . . |
$$ | . . . O . . . . . 6 . . . 4 O , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 5 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 7 . . . . . . . . . . . . . . . . |
$$ | . . O , X 3 . . . , . . . . . X . . . |
$$ | . . . 2 O X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
:w16: breaks the mirror. Still, White does not seem to lose anything by mirroring that far.
Last edited by Bill Spight on Mon Nov 25, 2019 1:48 am, edited 1 time in total.
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Joaz Banbeck
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Re: What about mirror go?

Post by Joaz Banbeck »

Bill Spight wrote:...
:w16: breaks the mirror. Still, White does not seem to lose anything by mirroring that far.
My gut says that 17 is a better move than 16. I'd rather have black here.
Do the computers say that 16 is as good as 17?


BTW, even though white has the ladder breaker, the cut at D5 does not work:
Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . 6 X 1 . . . . .
$$ | . 3 O 2 X X . . .
$$ | . . 4 O O X . . .
$$ | . . 5 . . . . . .
$$ | . . . . . . . . .
$$ ------------------[/go]
Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . 8 . 0 . . .
$$ | . X X O 9 . . . .
$$ | . O O X X X . . .
$$ | . 7 C O O X . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ ------------------[/go]
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Re: What about mirror go?

Post by gowan »

Wouldn't the absence of mirroring by AI bots just by itself indicate that mirroring is not a good strategy?
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Joaz Banbeck
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Re: What about mirror go?

Post by Joaz Banbeck »

gowan wrote:Wouldn't the absence of mirroring by AI bots just by itself indicate that mirroring is not a good strategy?
Were I a bot programmer, I would note the fact that there are published tactical refutations of mirroring too far. So I would give it a shortcut, telling it to not mirror. ( I would do this by incorporating a do-not-mirror weight in the algo for move choice. The weight would be zero for the first ten moves or so, then slowly get larger through move twenty )

In other words, the fact that bots don't mirror cannot be used to infer that they have calculated that it does not work. They may have been told that it does not work.
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Re: What about mirror go?

Post by Uberdude »

Wouldn't the absence capturing stones in a ladder which works by AI bots indicate that ladders are not a good strategy? ;-)
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Re: What about mirror go?

Post by jlt »

Mirror go cannot be a good strategy. There is no need for a bot to invent anti-mirror strategies. When Black plays, he tries to find the best move, but there is no reason why White's best move should be the mirror image of Black's last move.

Here is a game of myself against LeelaZero. I stopped when LeelaZero took tengen (and could capture a stone).



The winrate graph (for Black) is steadily increasing.
winrate-graph.PNG
winrate-graph.PNG (59.86 KiB) Viewed 11661 times
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Bill Spight
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Re: What about mirror go?

Post by Bill Spight »

gowan wrote:Wouldn't the absence of mirroring by AI bots just by itself indicate that mirroring is not a good strategy?
The problem is that there may be a shared blind spot between programs with a similar learning history (what I am calling path dependency). The bots may not discover when mirroring is good because they do not explore mirroring branches, and neither does their opponent.
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Bill Spight
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Re: What about mirror go?

Post by Bill Spight »

Many thanks, jlt. :D

Verrrrrry interesting. :)
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Re: What about mirror go?

Post by jann »

jlt wrote:The winrate graph (for Black) is steadily increasing.
For me only in the last dozen or so moves, where the tengen loss becomes more and more apparent. Otherwise W constant 53%-54% in opening and early game.
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Re: What about mirror go?

Post by ez4u »

Bill, what does ELF say? Isn't that your bot of choice at the moment?
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Re: What about mirror go?

Post by Tryss »

Here is a run of Katago against me, playing mirror until the Tengen is played :



And the graph :
Katago Mirror.png
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Bill Spight
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Re: What about mirror go?

Post by Bill Spight »

Thanks, guys! :)

The games and graphs are enough for me to do some speculation. First, the 7th line may be close enough to tengen that the first player can get an advantage in the center that overcomes komi. IOW, one strategy for White might be to mirror until the opponent makes a play on the 7th line or higher. Another thought is to mirror until move 50 or thereabouts. That might be short enough time that plays near tengen don't gain enough for Black, but long enough time to lower the effective komi.
Last edited by Bill Spight on Fri Nov 08, 2019 6:39 pm, edited 1 time in total.
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Bill Spight
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Re: What about mirror go?

Post by Bill Spight »

ez4u wrote:Bill, what does ELF say? Isn't that your bot of choice at the moment?
The Elf commentaries are, for me, a great resource. Not only is Elf quite strong, it makes a lot of playouts for the commentary. The playouts for a single choice are frequently over 100k, and I have even seen one with over 300k. And the commentaries give more information than AlphaGoTeach.

When mirror positions arise after move 4, Elf generally prefers Black. As with other bots, a mirror play by White is usually off its radar.
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Re: What about mirror go?

Post by Bki »

jlt wrote:Mirror go cannot be a good strategy. There is no need for a bot to invent anti-mirror strategies. When Black plays, he tries to find the best move, but there is no reason why White's best move should be the mirror image of Black's last move.

Here is a game of myself against LeelaZero. I stopped when LeelaZero took tengen (and could capture a stone).



The winrate graph (for Black) is steadily increasing.
winrate-graph.PNG
Your reasoning is kind of weak here. "Serious" mirroring isn't about playing mirror until your opponent play tengen or some other anti-mirror go strategy, but to do so until you can get an advantage by breaking the symmetry (or I guess, start the middle game with a roughly even position if you're not confident in your fuseki), or until black play a premature anti-mirror move that give you an advantage.

That said, I think Fujisawa Hosai played a lot of mirror go as white until he decided it was slightly unsound. But the komi (if any, he even played mirror go in no komi games) was smaller back then so who knows?
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