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Tedomari
Path: CGTPath · Prev: WinningWays · Next: DifferenceGame Path: Endgame · Prev: SenteSente · Next: Miai Path: GoodPlay · Prev: SqueezeTesuji · Next: Tesuji
Keywords: EndGame, Strategy, Go term
Tedomari means the last play. It is used not only for the last play of the game, but for the last play at different stages, and for the last play before the size of plays (temperature) makes a significant drop. As a general rule you want to try to get tedomari. There is a saying about the last gainful play of the game, Tedomari is worth double. Getting tedomari is related to go infinitesimals and how to play them. See Tedomari Discussion. Tedomari problemsHere is a simple tedomari problem I (Bill Spight) composed.
How large are the plays, a, b, and c? (The optimal order of play obtains the best result for each player.)
A very nice example of tedomari that you can work out yourself are the
problems --dnerra
Robert Pauli: Here's a cute little tedomari example (DGoZ 5/03):
Locally best play isn't globally best play, as everyone will find out sooner or later.
I like these miai values (even if I'm still struggling with them), however, would they help White in any way ?? Bill: Gee, maybe I am missing something, but the best local play seems like the best global play to me. (OIC. It depends on what you mean by best play. I think you mean optimal play. I had orthodox play in mind. The normally best local play differs from the best global play at or below temperature 1. They are the same above that.)
Robert Pauli:
Locally best for the lower part, but missing the win.
Are you using some kind of mathematical never-ever-draw rules, Bill, or what am now I missing? ;-) So, how do miai values direct White to choose the "inferior" move? Bill: Here is what I mean:
After
( [1]
Bill: A fine point:
If White makes a mistake and plays
Robert Pauli:
Bill: This may help. It's from my talk at the Computers and Games 2002 conference. The slides are Suppose that we have the following game tree, with / indicating a play by Left (Black) and \ indicating a play by Right (White): G / \ / \ H -7 / \ / \ -2 -4 Suppose that Left (Black) plays first. We get the following backed-up minimax values. -4 / \ / \ -4 -7 / \ / \ -2 -4 For calculating the miai value of G, we add the parameter, t. G / \ / \ H -7+t / \ / \ -2-2t -4 Then we get these backed up thermographic values: max(min(-4,-3-t),-5) / \ / \ min(-4,-3-t) -7+t / \ / \ -2-2t -4 The top value represents the left wall of the thermograph of G. Solving for t in min(-4,-3-t) = -7+t we get t = 2 So the miai value of G is 2. That's kind of sketchy, but I hope you get the idea. (BTW, we are going to have to move some of this discussion. :-))
Robert Pauli: = -5 - / \ | = 2 / \ | = -3 -7 - / \ / \ -2 -4 Just an incident that it turns out to be the same ? Do I need to swallow thermography to get miai values ? (Move it whereever you want, Bill, I'm lost anyway. :-) Bill: Sorry, Robert. I was way too sketchy. You do not need to know thermography to figure out miai values. People, including myself, have been doing that for many, many years. :-) However, the thermograph (TG) gives more information than just the count and miai value. One thing it can indicate is which plays (each line in the TG is associated with at least one line of play) to choose under which circumstances. That is one question in the DGZ problem. To answer this kind of question you have to look at the walls of the TG. You brought up the question of minimax. The walls of the TG can be expressed in minimax terms, and that is what I showed.
Going back to the problem. The line of play to use when White plays first to figure out the count and miai value for the bottom right corner is The right wall of the TG for the corner tells us that, as a rule, the time to switch between those plays is at temperature 1. We could work that out without the TG by considering that playing on the 2-3 allows Black to make a 3 point reverse sente, while playing on the 3-4 is only 2 points worse, on average, than playing on the 2-3. We can gain one point by playing on the 3-4, at the cost of one move. Now, since the remaining play on the board has a miai value of one point, thermography does not give us a clue which play is right. However, as it happens, the play that is correct under most circumstances is still correct for the problem. The thing is, when you are looking for the best play in an area of the board, you do not as a rule look for the best play at temperature 0. That is not realistic in a real game. Usually you want the play that defines the miai value. That's why my eye immediately went to the 2-3 point. As for figuring miai values by taking averages, you realize that that does not work in the following example. = -3.5 - / \ | = 3.5 / \ | = 0 -7 - / \ / \ +4 -4 Path: CGTPath · Prev: WinningWays · Next: DifferenceGame Path: Endgame · Prev: SenteSente · Next: Miai Path: GoodPlay · Prev: SqueezeTesuji · Next: Tesuji This is a copy of the living page "Tedomari" at Sensei's Library. ![]() |