Like Cheating on an Exam
Recently I watched this talk by Yasser Seirawan on an endgame (
https://www.youtube.com/watch?v=YI5CQL_ ... 3&frags=wn ). At about 5 min. in he asks his audience how many people spend 10% of their time devoted to chess, both play and study, studying endgames? 25%? 50%? We don't see the audience, but Seirawan notes that a lot of them spend 25% of their time studying endgames. (OC, this was an endgame lecture, so that's probably high for the chess playing population as a whole.) He goes on to relate something that Michael J. Franett, Washington State Champion in the early 1970s, told him early in his career. "Yasser," he said, "studying endgames is like cheating on an exam. because you know you're going to be asked the questions down the road."
OC, the endgame at go is not as consequential as the endgame at chess, but there are many predictable situations in go, such as standard corner life and death positions, common endgames, and ladders. I have stated that I think that dan players should be able to play the late endgame almost perfectly. Not that unfamiliar positions don't arise, but they are usually easy to analyze in a matter of seconds. Even 5 kyus are A+ at filling dame, where the shortage of liberties can potentially lead to big swings. Playing the last 30 moves correctly is not too difficult, if you have put in a little study. But who does?
Recently I was surprised
to find that one of my endgame problems has an 8 dan rating on goproblems.com. Here it is.
- Click Here To Show Diagram Code
[go]$$Wc White to play and win. No komi.
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O , O . . . X , . |
$$ | . . O . O X X . X . . |
$$ | . . O . X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . . X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
Now, reading the solution out may take a little time, but an SDK who has studied chilled go infinitesimals should see the first few plays almost instantaneously. This really should not be an 8 dan problem.
Mathematical Go came out in 1994, and the SL material on go infinitesimals has been available for many years.
As for smaller plays, the prototypes for them are corridors. True, complicated positoins can arise, but usually they are easy to calculate. For instance,
- Click Here To Show Diagram Code
[go]$$Wc Corridors
$$ -----------------------
$$ | . . . . . . . . . . . |
$$ | . . . . . . . . . . . |
$$ | . . O O O X X X X . . |
$$ | . . O W O . . . X , . |
$$ | . . O . O X X B X . . |
$$ | . . O . X X . X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . . X X . X O X |
$$ | . . . O O O X X O , O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
I have add a Black stone and a White stone to the position, so that the plays in the center each gain less than 1 pt. of territory. Everybody knows that the 2 space White corridor is worth -½ pt. from Black's point of view. The 3 space Black corridor is worth 1¼ pt. for Black. To see that, Black to play closes the corridor for 2 pts. and White to play advances into the corridor for a position worth ½ pt. Both of these plays are gote, so we take their average to get the territorial value of 1¼. The White shape in the center is not a corridor, but it is not hard to calculate its value.
Hint:
----
Speaking of corridors, there is a kind of diagram that appears in nearly every endgame book, of corridors of increasing length, side by side. Like so.
As everybody learns, the correct play is in the longest corridor. And we learn that the territorial value of each corridor is the length of the corridor minus 2 plus a fraction. The value of a length 2 corridor is ½, the value of a length 3 corridor is 1¼, the value of a length 4 corridor is 2⅛, etc. What the textbooks don't teach, not the ones I have seen, anyway, is that after White enters the longest corridor, the result is a kind of miai. That is, the corridors taken together have a territorial score which is the same, no matter who plays first in the combination. This SGF file illustrates that fact.
This fact has been discovered independently, it seems, by Antti Tormanen, David Wolfe, myself, and, I am sure, many others.
I discovered that fact by considering the miai of the two longest corridors, which, when played, yield another miai in the two longest corridors, and so on. From David's Theorem 8 in
Mathematical Go, I suspect that David figured it out by noting that the fractions all add up to 1.
David went even further and noticed that if the fractions add up to more than 1, then there will be some number of corridors whose fractions add up to exactly 1, and form this kind of miai. Well done, sir!
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