PracticalEndgameTest5/Difference Games

Difference game 1, setup  

Here we have set up a difference game to compare the White plays and ( in the mirror position). Does this position favor either player?

Difference game 1, White first  

If White plays first she gets tedomari and wins by 1 point.

Difference game 1, Black first  

If Black goes first the result is jigo. (If at , at makes jigo.)

This difference game favors White, so White should play in the original diagram, unless ko threat considerations predominate. This is so regardless of other plays on the board, except for kos.

What about original play for Black?

Difference game 2, setup  

(captured stones)

Here we have set up a difference game to compare the Black plays and ( in the mirror).

Difference game 2, Black first  

(captured stones)

Black to play gets tedomari to win by 1 point.

Difference game 2, White first  

(captured stones)

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 it is an ambiguous move). 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 miai

It did not matter in this problem, but let's compare plays in the second miai.

Difference game 3, setup  

(captured stones)

Here we set up a difference game to compare White plays and ( in the mirror).

Difference game 3, White first  

(captured stones)

When White goes first the play is like the first difference game. White gets tedomari to win by 1 point.

Difference game 3, Black first  

(captured stones)

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.

Difference game 4, setup  

Should Black play or ( in the mirror)?

Difference game 4, White first  

First, White takes her sente with - and then takes the right miai to get tedomari with and win by one point.

Difference game 4, Black first  

Here again, White interpolates the sente exchange, - , to get tedomari, for jigo.

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