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About All About Ko by Bozulich and Van Zeijst

Well, of course, this book is not **all** about ko, but it covers the field well and explains a lot, with interesting real game kos and problems. It is a significant addition to the English go literature.

That being said, this book, like so many, falters on the question of evaluation. Except for the simplest kos, ko evaluation was a mystery until the 1990s, when Professor Berlekamp discovered the placid ko vs. hyperactive ko distinction and showed how to evaluate hyperactive kos using the komaster concept. Later yours truly showed how to evaluate multiple kos and superkos. None of this advancement is reflected in the book, but some of it is available here on SL.

Still, the book does better in this department than the usual fare. For instance, they start out by saying that the value of a ko is the difference between winning and losing it. But then they go on to point out that you need to be aware of how much each play in a ko gains, and that for a simple, direct ko that is 1/3 the difference between winning and losing.

Then they go on to explain the rule of thumb that the value of a ko threat (T) should be 2/3 the value of the ko (K). The easy explanation is that the difference between answering a simple threat and completing it is the (deiri) value of the threat, and so each play gains 1/2 that amount (T/2). Each play in the ko gains 1/3 the (deiri) value of the ko (K/3), so if answering the threat gains the same as winning the ko, T/2 = K/3, which means that T = (2/3) K. However, they try to explain it by an example, and go astray.

In their example each move in the ko gains 7 1/3 points and each move in the threat gains 8 points (close enough). There are also two gote, one where each play gains 4 points and one where each play gains 1 point. The ko threat and the larger gote have sufficient structure to complicate things a little, but their aim is to show that the ko is approximately equal to the threat plus the larger gote. Unfortunately, they do this by adding deiri values: the deiri value of the ko is 22 points, the deiri value of the threat is 16 points, and the deiri value of the larger gote is 8. 16 + 8 = 24, which is slightly larger than 22. About this they state:

"The ko threat plus the follow-up constitutes two moves, so, if there is a third move with a value of one third of the ko threat {sic. They mean ko, not ko threat.}, the ko threat plus the follow-up should be two thirds the value of the ko. This example shows that the theory does conform to practice."

But, as we know, you cannot just add and subtract deiri values. You should add and subtract gains and losses (miai values) instead. Let's do that with their example.

In this variation Black takes the larger gote, allowing White to take the ko. Then White ignores Black's threat and wins the ko.

White now plays a 1 pt. reverse sente with and then Black plays sente with - . The end result is a 1 pt. win for Black.

Now let's add up the gains and losses. The original position has a value of -3 1/3. In the first variation gains 7 1/3, for a value of 4, and then - gains 4 pts. for a value of 0. Next the players share the 1 pt. plays evenly, for a final result of jigo. In the second variation gains 4 for a value of 2/3. Then White takes the ko for a value of -6 2/3, Black plays his threat, for a value of 1 1/3, White wins the ko for a value of -6, and Black completes his threat for a value of 2. Next White gains 1 pt. in reverse sente and Black gains nothing for his sente, for a final result of 1 pt. for Black.

The key thing to note in this comparison is that in the first variation Black gains 3 1/3 points after two (alternating) plays, and in the second variation Black gains 5 1/3 points after five plays. Black has made an extra play. Each player gets the last play that gains 4 pts., and then the size of plays drops. Under normal conditions the 4 pt. play will not be worth trading for a 7 1/3 pt. ko play. To see that, let's assume a more normal situation where, in addition to the ko and threat we have gote that more gradually decrease is size, gaining 4 pts., 3 pts., 2 pts., and 1 pt. Then the two lines of play add up this way.

Win ko: -3 1/3 + 7 1/3 - 4 + 3 - 2 + 1 = +2 . Black wins by 2 pts.

Take gote: -3 1/3 + 4 - 7 1/3 + 8 - 7 1/3 + 8 - 3 + 2 - 1 = 0 . Jigo.

There is another problem with this example, however. In the last diagram White takes the wrong reverse sente.

(If at 3, at 2, for the same result.) gains 3 pts. instead of 1 pt., so that White wins by 1 pt. (!)

kb: Bill, you have enough knowledge and material about evaluation of the endgame and kos that you should write your own book!

RobertJasiek: Nah. Not one book. 10 books!

Bill: Thanks, guys! (I just noticed your comments.) Yes, a book on evaluation is in the works, and it will include a lot about ko evaluation. :)