# How to construct a position with area miai value of 1/2?

I’ve seen Bill Spight mention in passing that it’s possible to construct a position with similar properties to a button (see for instance here, search for “construction”), but I can’t figure out how to do this myself.

I believe that what we are looking for is a position with an area swing value of 1, and where both players end in gote after making their move (or possibly sequence of moves).

A single dame doesn’t qualify because it’s too big (swing value of 2).

The position below has swing value 1:

However, it doesn’t function as a button. For instance, suppose it is black to play, and there is only a single dame left elsewhere on the board. Correct play should be to fill the dame first, letting white “take the button”. But here black could “take the button” in sente by playing in the top left (forcing white to respond in the top right), and then also get the last dame.

Does anyone know of a position with the desired properties, or have ideas for how to construct such a position?

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One thought: the position has to involve a seki with an odd number of common liberties, otherwise a swing of 1 is not possible in Chinese rules.

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This swings between:

Draw

and:

White + 1

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Well obviously I messed the order of moves, taking the 3 White stones is bigger than making the seki.

So the correct sequences are:

• Black plays first. Black takes the three White stones, White avoids seki in the top-left, Black takes the dame. Black + 3.
• White plays first. White saves the three White stones, Black makes seki, White takes the last dame. Draw.
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Assuming we could modify this construction to get it back down to a swing value of 1 (right now it’s swing 3 right?), this would still have a similar problem as my first attempt: either player could play the biggest move in sente (forcing the other player to take the next biggest move) before completing the final endgame.

The desired behavior of the button is that if there is a single dame left elsewhere, you should be forced to choose between getting the button and filling the dame (and then filling the dame will be the right choice).

So if the position involves a series of moves, it would have to be such that you cannot make a partial gain by just playing out part of the sequence.

But that basically means that the position must not have a move with a swing value higher than 2?

Or alternatively, all moves must really be part of the whole sequence, where once you start playing it you can’t stop (maybe because of a semeai).

Yes, I’m guessing it will all have to be part of a local situation that has to be either left as-is or played out in full (if you tenuki partway through you suffer a loss). I think this could happen for a variety of tactical reasons (including but not limited to a semeai), but I really don’t have any idea coming close to a solution, hence this thread asking for help

What would be even more desirable* is if we can find a position where the “sequence” for both players is just a single move. For instance, this corner in isolation has a swing of 7, miai value of 3.5, requiring only a single move from either player to make their gain:

*More desirable as a substitution for playing with the button rule, since it would be less likely to interfere with the game in other ways, such as providing ko threats. Although ko threats can maybe be worked around by making the chains involved big enough that sacrificing any of them can never be worth it for a gain in the main game.

Somehow such a single-move button seems even less likely than one involving a sequence of moves, at least on the regular board… but what if we allow other graphs?

On a 5*1 board we can at least get down to a swing value of 5, miai value of 2.5, with this position:

But I don’t see how to push this lower - seems like this is a pretty minimal space to setup a seki with odd number of dame (you need one eye in the seki, one spot where black will play to create the seki, and one dame).

So currently it seems more likely that it’s possible to find a longer sequence of moves with miai value of 0.5. (I’m assuming it is possible since Bill Spight wrote that he had done it!)

Edit: This position that I constructed some time back features a move with a 3-point swing value, by getting around the need for a black eye. However, it’s a super delicate setup and relies on the superko rule and the global board state. (it would lose its special properties if considered together with another board where white could make a group with 3 eyes). And even ignoring all that the 3-point swing is still too big!

Maybe one can find a position in a complex seki where there is a dame such that:

• If white goes first, they can fill it and the local situation is now done, no more dame can be filled.
• If black goes first, they can fill it, but now there is a different one-sided dame elsewhere in the seki, that white can eventually fill at their leisure to recover 1 point, making a the first play a total eventual swing of 1 with no urgency by either player to respond to the other.

It would seem that the two different sekis need a different parity of number of dame in the final position, which might be tricky, but maybe it is possible.

Or perhaps, in order to get the correct parity difference, we can have an entirely different construction. How about a complex seki with a dame where:

• If white goes first, they can fill it and the local situation is now done, no more dame can be filled, and this seki has an odd number of dame in this final state.
• If black goes first, they can fill it, but because of that now white can profitably collapse the seki by sacrificing one of their own groups in it so as to capture a black group (possibly the one black just added a stone to? Or possibly a different one, in that black’s added stone changes an eyeshape or a liberty count or something that critically delays black from a line that would refute white’s collapse attempt), and white can start the collapse at their leisure at any time while black has no profitable followup. Collapsing the seki is a way to allow for the parity change of dame back to even. It needs to be the case that after collapsing the seki, white is precisely one point better than leaving it as seki (therefore precisely 1 point worse than if white had occupied the dame first, to produce the miai-value of 1/2), and that white cannot profitably collapse the seki if white was the one to fill that dame instead.
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I remember reading that at least the known construction
relies on there being no not-shown ko threats.
Given that there are no not-shown ko threats,
if I’ve calculated the values correctly then

`````` +---------------+
| - B B - W B - |
| - W B W W B B |
| W W W W B B - |    The four *s are each occupied,
| B B B B B B B |    but their colors do not matter.
| W W W * * * * |
| b B W W W W W |     One of the three  b s  is black, and
| - b b - W W - |    the other two of those three are empty.
+---------------+
``````

works.
(I believe the example I saw used either a rotation of the
upper-left or some other mannen-ko, but I have no recollection
of how that example managed a ko threat that’s 9 points in a
Lasker-Maas encore, so I had to figure that part out on my own.)

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Thank you, that is a very nice construction!

Starting from this position:

Black first achieves W+2:

(ending in gote - only playing part of the sequence seems like a bad idea for black)

White first achieves W+3:

(ending in gote, because black does not have to play 2 immediately)

So this does have all the desired properties - only drawback being that it relies on the global ko threat situation. But perhaps this is what Bill Spight had as well, in which case this might be as close as we can come to a “real” button.

If either of the two ideas from @hexahedron could be realized, I think those would be less sensitive to kos and ko threats. But they both seem quite difficult!

On the sensei’s page for one-sided dame there is only one example given:

What other variations are possible? I’m pretty sure I’ve seen at least one different one before, but I can’t remember it off the top of my head.

Pretty sure I found a tsumego in Cho Chikun’s “Intermediate” series that ended in a seki with a one-sided dame, I’ll post it here when I stumble upon it again. But it’s not going to be very different from the one from senseis.

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I don’t know any one-sided dame positions where the sidedness is toggleable by other things in the seki so that one would be hard.

I suspect the seki collapse one might be easier to do. If you can find any odd-dame collapsible seki that where there is a 2 point difference in the collapse variation’s final score depending on whether you change the color of one of the dame-filling stones, then it seems like there’s a some decent chance you can make it work by adjusting the values of the groups by adding or removing extra stones. Adding or removing stones from the groups can should be able to shift the collapse variation’s value by two-point increments relative to the leave-it-seki variation, and if you can shift it all the way so that the 2-point difference in the two collapses with the stone color change straddles the value of the leave-it-seki variation, then you should have a working example.

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There’s some button go related threads on l19

https://lifein19x19.com/viewtopic.php?f=45&t=12121&start=60

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Aha, the link at the end of that thread contains a position (Seemingly constructed by Bill Spight? The german thread is a bit confusing to me, probably something getting lost in the auto translation) that is very similar to the one @hoctaph reconstructed:

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