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 Post subject: Re: What about mirror go?
Post #21 Posted: Sun Nov 10, 2019 10:09 am 
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OC W cannot be better than by perfect play on his own - but why should he be necessarily worse off? In particular, why should mirroring perfect play necessarily lose at least 1 pt by move 20-30 or so?

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 Post subject: Re: What about mirror go?
Post #22 Posted: Sun Nov 10, 2019 10:27 am 
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There are many ways to counter mirror go early in the game by for example creating ladders or making tengen a big move. It is harder to achieve this later in the game because the board is more crowded and because the middle game is less forgiving then the opening. Some special plan involving ladders or what not might be OK in the opening because the value of many moves is similar but in the middle game the best move starts to stand out and there are less good options.

If there is a limited window in the early game to counter mirror go strategies with a special strategy then one strategy by black could be to play into a wild middle game situation making it hard to impossible to break mirror go but only at the last moment play tengen and play mirror go himself from that point to the end :evil:

If every other move in the game cancels out and even a weirdly timed tengen move is at least 7 points then black wins, right? :lol:

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 Post subject: Re: What about mirror go?
Post #23 Posted: Sun Nov 10, 2019 10:28 am 
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I have a slightly different, though similar perspective on what would be the point of mirror go: Typically, you get a slight advantage from having the initiative in a local sequence, i.e. if both sides play the same number of moves alternately in the same region of the board, locally, the player who comes first should get the slightly bigger piece of the cake. Of course this is only small difference, but small differences can add up.

To Illustrate this, have a look at the following joseki:

Click Here To Show Diagram Code
[go]$$B
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . 4 . . . |
$$ . 6 . . 2 . . 5 . . |
$$ , . . . . . 1 . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . 3 . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]


Modern AI would play differently for white, but humans considered this even for a long time even though both players played the same number of stones(3) and black secured just a little bit more points than white with them. To me, this is explained by the fact that black deserves a little bit more just for being there first. It also goes in line with the common wisdom to first take empty corners, than approach others. If you play a game having black take the first, white approaching, then this joseki finishing in black sente, then black taking the next corner, white approaching and so on, unsurprisingly Elf gives 88% for black after the joseki is played in all for corners.

what does this have to do with mirror go? Now white gets komi, because black plays first. What does black get? He doesnt get more corners, in which he can have the first move, bacause 4 is even, which mans the 4 coners are miai, both get to start in 2 of them. The advantage of playing first comes now: black gets to approach/invade(in newfound AI 3-3 style), which is generally something considered to be "moderately sente", i.e. something you want to react to. Then a joseki of some kind will be played. You might say, what is the big deal, now white approaches one of blacks corners and they a similar joseki there with colors reversed.

This is true if white gets sente from the first joseki, but also black might get sente and use his next move maybe to protect his corner, so white doeosnt get to approach it in a state, where there is one black stone , but there already are two. And there it is the microscopic gain of playing first in a corner. In the same way, It is also a slight bit better for to have b-b-w-b-w-b-...-w ending in white (so locally one stone more for black) than b-w-b-w...-b ending in a black play (also locally one more move for black), i.e. being the "first" to play the second move in a local situation.
Which means white might give up just a little bit in order to take sente in the first corner black approached, so as to be able to approach one himself and so on..

Now another idea for white would be to say: I dont think your approach is sente. Yes, locally you threaten to do something, but I`ll just approach another corner and threaten something of similar size. That way, I preempted your attempt to be first in both places. But, if white does that he needs to make sure his threat really is as big as the other one, so that mutual damage would be okay for him.
Mirror go does just that: answering blacks initiative move with another initiative move of the same size: its mirror image. Of course this works only as long as the battles are local. Once they spread out to the center, white needs to be careful, because the "you do something here, I do the same thing to you there" concept doesnt work, once black gets to do things first, that help in BOTH fights.

I personally have problems against mirror Go with black in the 9x9 games I sometimes play on Go quest. I would be less scared on 19x19, cause I have much more time, to plan out, how I can drag the battle in the center, while on 9x9 it happened to me multiple times, that I took the left side and white got the right one, and the center is dame - I lose.


Last edited by Schachus on Sun Nov 10, 2019 10:30 am, edited 2 times in total.

This post by Schachus was liked by: Bill Spight
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 Post subject: Re: What about mirror go?
Post #24 Posted: Sun Nov 10, 2019 10:28 am 
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jann wrote:
why should mirroring perfect play necessarily lose at least 1 pt by move 20-30 or so?


I didn't say that... In fact nobody knows if mirroring perfect play loses nothing, or 1 point, or more. Nevertheless, if you have two procedures A and B, and if procedure A produces an equal or better result than B, then you should use procedure A.

Here, procedure A is: choose the best move you can think of. Procedure B is mirroring.

I would even say that mirroring is psychologically risky for White because White might be tempted to copy the move without much thinking, when a better move would be available. On the other hand, mirroring also has psychological effects on Black, since Black might be angry at being mirrored, or might be tempted to use a suboptimal anti-mirror strategy.

Of course, these psychological aspects don't exist when one of the players is a bot.

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 Post subject: Re: What about mirror go?
Post #25 Posted: Sun Nov 10, 2019 10:55 am 
Honinbo

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Mirror go by the second player on the 3x3


Difference game setup

Click Here To Show Diagram Code
[go]$$ White mirrors, Black does not
$$ ---------------
$$ | . . . | . . . |
$$ | W , B | . B W |
$$ | . . . | . . . |
$$ ---------------[/go]



Best play by Black, who did not mirror

Click Here To Show Diagram Code
[go]$$B Black plays first
$$ ---------------
$$ | . . . | . 3 . |
$$ | W 1 B | 2 B W |
$$ | . . . | . 4 . |
$$ ---------------[/go]


Black wins.

Best play by White, who did mirror

Click Here To Show Diagram Code
[go]$$W White plays first
$$ ---------------
$$ | . . . | . . . |
$$ | W 1 B | 2 B W |
$$ | . . . | . . . |
$$ ---------------[/go]


Jigo. White does not win.

Therefore, mirroring the first move on the side is not good.

(As though we didn't know. ;))

But note that komi is irrelevant, because komi on the second board is the negative of komi on the first board. Komi - komi = 0. ;)

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