Lopsided Kos

  Difficulty: Expert   Keywords: Ko

Not all kos are worth the same to both sides; in the Ko fight Example, White had nothing to lose by playing the ko, so she need not have any qualms about starting it. However, some kos can cost more than they are worth. [100] Imagine a situation like the one here.

Big ko for both sides  

Here, if White starts the ko with a, but then loses the ko eventually, she will lose her lower right corner. If Black loses the ko, then he will lose his group on the lower edge.

Hence, the ko at a and b is important for White as well. In this situation White needs ko threats larger than her corner in order to win the ko. It would be of no use for her to play a ko threat of 10 points (say), as her corner is worth at least 15 points. Black would finish the ko by playing c and would have gained 5 points or more.

Comment: I have calculated the values of these positions (ignoring the ko threats on the left and assuming that the right side is Black territory). They are hyperactive, which means that their value depends on who can win the ko. Who can win the ko is called the komaster.

I have not included Black's territory on the right. If Black is komaster, White connects with sente. The local result is -1 (1 point for White, net). If White is komaster, the miai value of the position is 12 1/3. Either Black connects or White throws in. The local count is -2 1/3.

There is a new technique for evaluating kos, based on the idea that nobody is komaster, but one player can win the ko while the other gets an equitable exchange. That method gives a local count of -1, but Black connects with sente.


Alternative evaluation approach?:
[100] The expression "some kos cost more than they are worth" can can be explained simply for the given example:

  • the one who starts this ko is in a disadvantageous position after the opponent has immediately retaken the ko:
    the ko initiator? has to search for the first threat!
  • The opponent gets 2 moves in a row for simply "losing"/exchanging the ko.
  • The initial target as seen by white is 9 black stones + 6 points of territory to be gained in 2 moves (a+b).
    Firstly this is (would be) only an average of 12 points per move and
    - of course -
  • there is much more at stake:
    white could lose her 7 white stones by only one black move c! (Which would gain Black (1 point a + 1 captured white stone a, 7 white stones + 3 points of territory = 19 points)
    • [101] if White recklessly starts the ko, then Black can account 43 points (24+19) with one move c! White should have bigger ko threats instead of dreaming in the exchange.
    • [102] if Black recklessly starts the ko, then White can earn 24 points with one connection move.

Conclusion: This ko is so disadvantageous for the one who starts it, because __you create a direct ko for your opponent,
with the burden of looking for the 1st threat yourself (while it was undecided before).
Therewith it has similarities to a seki. --tderz

Bill: Once the ko is made, it is direct for both players. It is like a kind of 10000 year ko (which is like seki).
tderz A TwoStageKo transforms within one move into a direct ko, pl. cf. with 2-Stage-Ko.
Bill is simply correct that there is no TwoStageKo in [101]. (White could connect with one move c)

Bill: A ko that transforms in one move into a direct ko is an approach ko. In a two stage ko if we are at a point where one player with the move can win the ko, the other player must take the ko twice to reach a point where she can win the ko on the next play. A similar term, two step ko, has been used in English for both kinds of ko, which has led to confusion.

Lopsided ko for White  

This diagram is different. Here White has the marked stone in place and thus losing the ko for her means only losing the single stone at the edge. Black on the other hand may lose his group worth over 20 points. If White plays a ko threat worth 10 points in this situation, Black will finish the ko as well (again playing c), but this time White will be better off. She would gain 4 points compared to connecting at b instead.

Jasonred : In this example, is it correct to say that, for white, losing the ko means losing the chance to take that group which is over 20 points?

Comment: The ko, once set up, has a miai value of 10 1/3, and that is the size of equitable threats for it at that ambient temperature. (The ambient temperature is the size of the largest plays elsewhere.)

If Black is komaster, White starts the ko, losing it in exchange for plays elsewhere, when the ambient temperature is between 5 and 10 1/3, as a rule. Below that temperature White connects with sente. The local count is -6 1/3.

If White is komaster, either Black fills at a or White throws in. The miai value of a play at a is 9. The local count is -9.

By the no komaster method, the local count lies in between, at -7 2/3.

-- BillSpight

The importance of this difference is the following: If a ko is 'lopsided' in your advantage, you should have no qualms about starting it. You might well lose the ko, but you will get an unanswered ko threat to follow up in compensation. Thus, in the second diagram on this page, White should (if the ko is large enough) almost alway play at a if it is her move, and be happy whether she wins or loses the ko. In the first diagram on the other hand, she will have to count both players' ko threats first. If Black has more (sufficiently large) ko threats, it is best to play b. If White has more, a is better.

On the other hand, if it is Black's move, he should never (well, almost never) play the ko in the second diagram, but connect at a instead. In the first diagram, his choice too hangs on the balance of ko threats.

Jasonred : I don't understand why calculations come into this, or why a ko is lopsided in the first place. Isn't Go a zero sum game of sorts? Causing a disaster for your opponent should be worth the same as avoiding a disaster for yourself, also equal to winning points for yourself, and stopping your opponent from winning points.

Bill: Jason, I think that your attitude is correct. :-) But history plays a role. White's last play might have threatened this ko, for instance. Then the fact that it is lopsided would matter.

Is there such a thing as a ko draw?

In other words, I am saying that all ko's should be calculated based on how much they're worth in total, by taking the value of black winning, minus black losing, and remember sente.

Tas: I agree with your view on go beeing a zero sum game, and have been very near to writing something like that on many other pages. But in this particular case i can see the point. It is not so much about winning or losing the ko, as about wheter to start it at all. And the ko-starting move in the second diagram is much bigger when done by white than by black. The "ko-draw" you speak about, would here be repressentet by the peacefull event that each player connects on his side (Wa and Bb); a posibillity, of course, for the player holding sente to chose.


See also:

This page needs wiki master editing.

Lopsided Kos last edited by Unkx80 on March 11, 2014 - 16:01
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