Miai Values List / 0.00 to 0.99

Sub-page of MiaiValuesList

See Miai Values List for conventions and explanation.

Table of contents Table of diagrams
[Neutral point]
Miai
Ko threat (teire)

Connect [ko]
Take [ko]
Hidden ko
Make ko
Take ko in sente
Make ko
Make ko (2)
Make ko (2a)

Copy 1
Copy 2
Copy 3
Take away potential point
Defend potential point
Take stone
Take away potential territory
Jump to take away potential point
Defend potential point
Take away potential point
Take away potential point
Defend potential point
Under the stones sacrifice
Prevent sacrifice
Real half point ko
[Real half-point ko], W [komaster]
Make [damezumari]
Make territory plus
[Real half-point ko], B [komaster]
Take away potential point, set up ko capture
Defend potential point, prevent ko capture
Defend potential point, set up ko capture
Take stone to set up ko
Make ko
Take two stones
Take away potential territory (i)
Take away potential territory (ii)
Take three stones
Take away potential point ([corridor])
Defend potential point, set up [0.67 position|#toc5]
Take away potential point
Sente
Reverse Sente
Protect, threaten [0.67 play|#toc5]
Take away potential point ([corridor])
[One more number]
Take away potential point
Take away potential point ([corridor])
Take away potential point ([corridor])
Hidden ko (2)
Index of sub-pages

0.00 (Exactly 0)

There are other types of neutral (dame) points including: protective moves (teire) against the cut when outside liberties are filled; capturing stones in seki, etc.



[Diagram]
Miai  

Either player can play first, with the same result.

[Diagram]
Ko threat (teire)  

B1 may be a ko threat. At the dame stage, an immediate W2 is a protective play.



0.17 (``sf0.1bar{:sf6:} = ``1/6)

[Diagram]
 

By the method of multiples. Original count: -0.83

If White is komaster Black will not play B1. If Black is komaster the miai value is 0.44 (4/9) and the original count is -0.55.

0.33 (``sf0.3bar{:sf3:} = ``1/3)

[Diagram]
Connect ko  

Initial count: -0.33

White has 1/3 point equity in the black+circle stone. We may think of it as 1/3 captured.

[Diagram]
Take ko  

HolIgor: This move together with the one above should give a point, shouldn't it?

Bill: Yes, but Black started with 1/3 point net equity white+circle, so each move gains 1/3 point, on average. :-)

See half-point ko.

[Diagram]
Hidden ko  

B3 fills.

Initial count: 0.67

1 and 2 are miai points.[3]



[Diagram]
Make ko  

Initial count: 8.67



[Diagram]
Take ko in sente  

Initial count: 5.67

[Diagram]
Make ko  



[Diagram]
Make ko (2)  

B1, preventing the ko, would also be worth 0.33.

[Diagram]
Make ko (2a)  



0.39 (``sf0.3bar{:sf8:} = ``7/18)

[Diagram]
 



Bill: When White is komaster the play is in the indicated ko, with a gain of 1/3. When Black is komaster the play is in the throw-in ko, with a gain of 1/2.

Matti: Let's first have thee copies.

[Diagram]
Copy 1  



B3 connects ko.

[Diagram]
Copy 2  



[Diagram]
Copy 3  



In copies 2 and 3 white has 2 5/6 points. Now, let's assume that we had 18 copies of the original position and have now 6 positions of copy one.

As shown above white has 5 points in six positions in the corner. In one position of the six he has one point at the edge and in five others two points at the edge, total of 16 points in six positions, thus 2 2/3 points. So black has gained 1 + 2 5/6 - 2 2/3 = 7/6 from total of three kos. One ko is thus worth 7/18 points.

Bill: I believe that the final position in copy one is significantly different from the position above with a miai value of 1/6. In 3 copies of that position White has 7 2/3 points on average (not counting the stone already captured in the ko), 23 points in 9 copies. Since White in one move can get 3 points per copy, we have a miai value of 4/9, which is the same as we get in a neutral threat environment. Since 4/9 > 7/18, we cannot stop in the "final" position in copy 1. Besides which, it is not clear when to play on the 2-1 point, or whether it is better than taking or filling the original ko.

0.50 (``= ``1/2)

[Diagram]
Take away potential point  

Initial count: -0.5

[Diagram]
Defend potential point  



[Diagram]
Take stone  

Initial count: 1.5

[Diagram]
Take away potential territory  

B3 at 1.

[Diagram]
Jump to take away potential point  

Initial count: -3.5

[Diagram]
Defend potential point  

Initial count: 2.5

[Diagram]
Take away potential point  



[Diagram]
Take away potential point  

Initial count: -0.5

[Diagram]
Defend potential point  



[Diagram]
Under the stones sacrifice  

Initial count: -2.5

After B3 the corner is worth -2. White has captured 3 Black stones, but Black can claim the W2 stone.

(Note: If White is komaster she can make ko to protect W2, but Black gets 3 moves elsewhere.)

[Diagram]
Prevent sacrifice  

After W1 White gets 2 Black stones plus 1 point of territory.

[Diagram]
Real half point ko  

Next Black can fill at white+circle in sente.





0.58 (``sf0.58bar{:sf3:} = ``7/12)

[Diagram]
Make damezumari  

Now there is a 0.33 point play at a.

[Diagram]
Make territory plus  

Now there is a 0.5 point play at a.

The swing is 1 point at circle plus 0.5 - 0.33 = 0.17 in the corner in gote. That yields a miai value of 0.58.

If B were komonster, it would be 0.75.



0.67 (``sf0.6bar{:sf6:} = ``2/3)

[Diagram]
Take away potential point, set up ko capture  
[Diagram]
Defend potential point, prevent ko capture  
[Diagram]
Defend potential point, set up ko capture  

Left Count: 1.33, Right Count 0; Initial Count 0,67

[Diagram]
Take stone to set up ko  

Ambiguous.

[Diagram]
Make ko  
[Diagram]
Take two stones  
[Diagram]
Take away potential territory (i)  
[Diagram]
Take away potential territory (ii)  
[Diagram]
Take three stones  



0.75 (``= ``3/4)

[Diagram]
Take away potential point (corridor)  



0.83 (``sf0.8bar{:sf3:} = ``5/6)

[Diagram]
Defend potential point, set up 0.67 position  

The initial position has a local count of 2 5/6. The result after B1 has a local count of 3 2/3. B1 gains 5/6 of a point.

[Diagram]
Take away potential point  

The local score after W1 - W3 is 2. The hane-and-connect gains 5/6 of a point.

[Diagram]
Sente  

Take stone in sente, leaving 0.67 point play.

[Diagram]
Reverse Sente  

Save stone, leaving 0.5 point play.

[Diagram]
Protect, threaten 0.67 play  



0.88 (``sf0.875 = ``7/8)

[Diagram]
Take away potential point (corridor)  
[Diagram]
Take away potential point  



0.94 (``sf0.9375 = ``15/16)

[Diagram]
Take away potential point (corridor)  



0.97 (``sf0.96875 = ``31/32)

[Diagram]
Take away potential point (corridor)  



For higher values see /1.00 to 1.99, /2.00 and more.

Footnotes

[3] Bill, now I'm confused - I think. Black's sente - I've switched the colours for B1, W2. OK, so using miai values means sequences don't need to be flagged as such (sente, or gote). Ah, I get it: White connecting on either side leaves

[Diagram]
Hidden ko (2)  



where Black has in effect 0.33.

Leaving this comment for others' benefit. Charles

Bill: This is an ambiguous position. Its miai value is 1/3, but Black can take one stone and threaten to connect with sente. Then, OC, the position still has a miai value of 1/3, and Black's sente has gained nothing locally. (It may have been a ko threat.) In thermographic terms, it has a blue mast up to temperature 1 2/3.


Miai Values List / 0.00 to 0.99 last edited by RobertPauli on February 2, 2019 - 12:53
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