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PracticalEndgameTest5/Difference Games
Sub-page of PracticalEndgameTest5
The first miaiAt the first move in this problem White must choose between two plays of the same size (miai). One dominates, and, in fact, textbook commentary in a similar position says that you can even consider it to be worth more, despite the miai. Let's see what light difference games can shed on that question.
Here we have set up a difference game to compare the White plays
If White plays first she gets tedomari and wins by 1 point.
If Black goes first the result is jigo. (If
This difference game favors White, so White should play What about original play for Black?
Here we have set up a difference game to compare the Black plays
Black to play gets tedomari to win by 1 point.
If White goes first the result is jigo.
This difference game favors Black, so Black should also favor the play on the left in the original position, subject to the caveat about ko threats. That play dominates the other because of the possibility that White will be able to play the "reverse sente" (not really reverse sente because the play is ambiguous). This difference is not enough to alter the miai value of the play, but it does make an infinitesimal difference in the chilled game. This was not understood in 1980. Still, the textbook said that it was a better play. The second miaiIt did not matter in this problem, but let's compare plays in the second miai.
Here we set up a difference game to compare White plays
When White goes first the play is like the first difference game. White gets tedomari to win by 1 point.
And, as in the first difference game, Black can only get jigo.
White to play should take the simple gote and save her two stones. Now let's compare plays for Black.
Should Black play
First, White takes her sente with
Here again, White interpolates the sente exchange, Since the difference game favors White, Black should choose the miai that gives him sente, unlike the first choice of miai. The key difference is the size of the sente threat. Verrrry interesting! :-) -- Bill Spight This is a copy of the living page "PracticalEndgameTest5/Difference Games" at Sensei's Library. ![]() |