What about mirror go?

Bill Spight · #1

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.

Bill Spight · #2

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]

breaks the mirror. Still, White does not seem to lose anything by mirroring that far.

Joaz Banbeck · #3

Bill Spight wrote:

...

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]

gowan · #4

Wouldn't the absence of mirroring by AI bots just by itself indicate that mirroring is not a good strategy?

Joaz Banbeck · #5

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.

Uberdude · #6

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

jlt · #7

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.

Attachment:

winrate-graph.PNG [ 59.86 KiB | Viewed 10873 times ]

Bill Spight · #8

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.

Bill Spight · #9

Many thanks, jlt.

Verrrrrry interesting.

jann · **#10**

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.

ez4u · **#11**

Bill, what does ELF say? Isn't that your bot of choice at the moment?

Tryss · **#12**

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

And the graph :

Attachment:

Katago Mirror.png [ 96.28 KiB | Viewed 10831 times ]

Bill Spight · **#13**

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.

Bill Spight · **#14**

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.

Bki · **#15**

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.

Attachment:

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?

jlt · **#16**

Bki wrote:

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.

I agree that if White has a weaker fuseki and stronger middle game than Black, than playing mirror go at the beginning of the game can be a good strategy. But in the absence of information, if Black always tries to play the best move (and not some anti-mirror strategy), then the best choice for White is to try to play the best move, and not the mirror image of the previous one, which is generally suboptimal.

Uberdude · **#17**

Mirror go as white with komi, if played skillfully rather than just blindly mirroring, is an interesting strategy and not so easy to refute. The basic premise that white is seeking to exploit is that if mirroring continues in such a way that each get the same territory away from the centre and tengen becomes dame (or rather less valuable than komi) then white will win. So the onus on black is to steer the game in a direction that tengen becomes more valuable than komi. There are several ways to do this:
- use it to make some centre territory
- use it in a tactical sequence so they run out of liberties before you. This can be done centre fighting sequence or opposite ladders.
- make some fight so that it's useful. It doesn't actually have to be exactly tengen, sometimes nearby points work too in that sente is super valuable if White keeps mirriring, overlaps with tactic above
- make it tedomari
So if White sees Black's play leading to this he has to stop mirroring. Black has to be wary of playing tengen too early just to frustrate White's mirroring plan as it may be a bad move, and White then can't mirror but just plays a more valuable move than tengen and takes the lead. Also with a clock I think it's quite an effective strategy as black needs to put a lot of time and effort into a plan to make tengen valuable but White can generally play fast and think in black's time.

Fujisawa Hosai/Kuranosuke famously played mirror go as white even before Komi (but slowly). There are some excellent articles in GoGoD about how some pro, Yamabe iirc, finally convinced him it was refutable with some pretty deep two moyos colliding with tactical sequences collapsing the mirror ideas. This was after Fujisawa had been playing mirror go for decades. But such an idea is harder to construct than double ladders.

Here's a mirror game I played on OGS some years ago against one of the top players there after studying the GoGoD mirror articles and some of Fujisawa's games, in fact for I think for quite some moves we were playing the same as a game of his.

https://online-go.com/game/372110

jlt · **#18**

In the game you posted, you stopped mirroring at move 18, but things went better for Black only at move 34. Hard to conclude anything.

Attachment:

Capture.PNG [ 73.8 KiB | Viewed 10674 times ]

jann · **#19**

jlt wrote:

if Black always tries to play the best move (and not some anti-mirror strategy), then the best choice for White is to try to play the best move, and not the mirror image of the previous one, which is generally suboptimal.

This claim could use some proof though.

If B plays perfectly (and no anti-mirror), then by mirroring W may maintain a lead of 7.5 points - up to the point where stopping mirror is advisable for center-related reasons. This is more than could be reasonably expected: slowly eroding those 7.5 to compensate for B's advantage throughout the game (arriving at +.5 by yose).

OC B's center potential may grow quietly and unnoticedly, so in practice the 7.5 is not really maintained by mirroring either.

jlt · **#20**

As I said, of course if Black plays a perfect opening, or at least a much better opening than White, then White should play mirror go for a while. But if White is at least as good as Black, then White shouldn't mirror (*). For instance, if White is also a perfect player, then (by definition) the mirror image of Black's last play cannot be better than the perfect response.

(*) Possible exception: if time is limited, White may want to save thinking time for the middle game.

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