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Miai Values List Discussion
Difficulty: Advanced
Keywords: EndGame
A page for questions and discussion about material on the Miai Values List pages. 1.92
KarlKnechtel: I did a bunch of math with pen and paper just now, and got a miai value of 1.98 for this situation (2 - 1/48) and 1.04 for the two-stone capture. But I don't think I have a perfect understanding of these calculations, and also it's 3:30 AM here. If it will help global understanding any, I could explain my calculation later on but I don't suppose that should go on this page :\ Andre Engels: My calculation gets to 1 11/12, which is indeed 1.92 rounded to 2 decimals. Here is the diagram: 1 11/12 / \ / \ 3 5/6 0 : X O O O O O, no prisoners / \ / \ 5 \ X . . X X O, 3pr. \ \ 2 2/3 / \ / \ 3 1/3 2 X . X O . O 2pr. X . O O . O, 2 pr. Note: the 1 11/12 is not the 1 11/12 in this diagram, but the difference between the 1 11/12 and the 3 5/6. Karl Knechtel: I have the 2 case in my figuring split up further, reflecting the fact that if black makes the next two plays from that position, he captures again. And we allow black to move twice to find the 5 case, so I don't see how it's different... Anyway, my values are 1/3 for a single stone (simple ko), 25/24 for two stones, 2 - 1/48 for three stones, and in general (n - (13/12) + 2^(-n-1)) for n>=3 stones. The above derivation is taking out the little exponential correcion for the n=3 case. Bill: Karl, what do you mean by the 2 case and the 5 case? Do you mean the scores? They are the local scores. That's it. There is no further move in the 5 case. In the 2 case Black has a ko threat, that's all. Another way to look at it is as a miai. White fills and Black plays the dame, or vice versa, except that if Black plays first it's a ko threat. Andre Engels: The difference is sente or gote. In general, we are looking at diagrams of this form: ??? / \ / \ (A+B)/2 C / \ / \ A B In general, the value of ??? will be 0.5C+0.25(A+B). But not always. If A is much larger than B, then the first player's move to (A+B)/2 will always be answered by a move to B. In that case, provided B is greater than C, the first player will move to (A+B)/2 at some time, and the second player will answer by moving to B, so the actual value of A and C does not matter, and the value of ??? is B. In general, it is the lowest of the two values. Tristan: Could somebody clear up one thing for me please? I note many calculations produce numbers with decimals (what's the mathematical term for such numbers?), e.g., 2.3 or 1.93. Now, given that the smallest unit in a go game is one point (discounting the half-point in komi), does it matter if one plays a move evaluated at, say, 1.52 instead of one evaluated at 1.94? (All other things, such as sente/gote considerations, being equal.) HolIgor: The unit is half point. So, as Bill claims it is enough to have values like 1.5+ and 2.0-. In the end of the game the decimal points are converted into the whole ones by getting the last move. I don't know if 1.98 has more chances to become a point in the end of the game than 1.92. Perhaps this can be proven, perhaps not. Bill: See Numbers for an example where a mistake of 1/32 point ends up costing a point. ;-) To expand upon Andre's point, say that we have this kind of situation: A / \ / \ / \ B C / \ / \ D E F G where D >= E >= F >= G. The idea is that E >= A >= F, because if Black plays first White can reply and hold Black to E, while if White plays first Black can reply and hold White to F. (This does not mean that the eventual local result won't be D or G. But in that case, with correct play there will be compensation elsewhere.) Ok. So we should evaluate A as max(F, min (E, (D+E+F+G)/4))? I.e. the normal value is given by the usual averaging, but must be at least F (black response to white's first play being sente) and at most E (white response limiting black sente). Did I get that right? -- Karl Knechtel Bill: Right, Karl. :-) (Subject to the restraints, OC.) Notation proposalWhen referring to "points", there seems to be some confusion between miai and deiri points. Since we agreed to go to 2 decimals, I propose to measure points from miai counting in "cents" and write it as e.g. "33 ¢" or "450 ¢". The first occurrence on a page could be written as "¢" -- Sebastian Deebster: Could we use a character everyone has on their keyboard? Sebastian: Actually, entering it is not a problem - on any keyboard, you can type "¢", and it will display nicely as "¢". But just because I love choices: Another alternative would be to spell it out - similar to what Europeans do if they don't have the Euro sign. Bill: What confusion? Both types of values measure differences between the counts of different positions, which are expressed in points. Differences between points are also points. This is a copy of the living page "Miai Values List Discussion" at Sensei's Library. ![]() |