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Hyperactive kos are those whose mast values (counts) depend upon who is komaster. I coined the term, active ko, for those kos whose mast values remain the same under different komaster conditions, but whose temperatures (miai values) depend upon who is komaster. Active kos are rare. Kos whose mast values and temperatures remain the same, regardless of who is komaster, are call placid.RobertJasiek wrote:What is an example of an active (not hyperactive) ko?
This is a complicated position. I assume that if surrounded stones are cut off, they are dead. And, per convention, that the outer stones are alive.RobertJasiek wrote:How to calculate counts and move values of this hyperactive ko locally with komaster case analysis?
and win it. (Probably not right away, OC, but we can skip the ko fight.) The result is a local score of -15 (15 pts. for White).
actually makes a larger ko by giving up an extra stone when White wins the ko, for a swing of 32 pts. in 4 moves, or an average gain of 8 pts. per move. (Edited for correctness after Robert pointed out that I miscounted the net number of moves.) sente, so White will take and win the resulting larger ko.
@ 
White can take the ko back, make a larger ko and win it for a score of -16 pts. in one net play, instead of getting a score -15 pts. in two net plays. It isn't just that loses one point, it loses one play, as well. is a mistake. @ at is sente. (Edited for correctness, as above.) at is sente. @ 
, leaving a small ko. Let's analyze it, with White komaster. @ at is Black's threat, and is sente. The result is a local score of 1 pt., after 1 net play. 
is 0, with a local temperature of 1 pt. By comparison Black's threat to take and connect the ko with sente reaches a local score of 2 pts., and is the better threat. This result may seem counterintuitive. and wins the resulting ko in two net plays, for a local score of -15. @ Later edited again for correctness.This kind of comparison of, and decision-making between, two variations I was missing, many thanks!Bill Spight wrote: Assuming that this is Black's threat, there is a swing of 31 pts. in 5 moves, for an average gain of 6.2 pts. per move.
However, :b3: actually makes a larger ko by giving up an extra stone when White wins the ko, for a swing of 32 pts. in 5 moves, or an average gain of 6.4 pts. per move.
That makes :b3: sente, so White will take and win the resulting larger ko.
Let me try to understand how to calculate the tally and after what sequences' followers to calculate the swing:However, :b3: actually makes a larger ko by giving up an extra stone when White wins the ko, for a swing of 32 pts. in 5 moves
I understand this but...:w4: @ :wc:
If Black cuts with :b3: White can take the ko back, make a larger ko and win it for a score of -16 pts. in one net play, instead of getting a score -15 pts. in two net plays. It isn't just that :b3: loses one point, it loses one play, as well. :b3: is a mistake.
Other topic:In three moves Black can take the ko, make the larger ko, and win it. OC, White will prevent this from happening, but this is one threat. The resulting local score is 16 pts. (for Black).
Assuming that this is Black's threat, there is a swing of 31 pts. in 5 moves, for an average gain of 6.2 pts. per move.
However, :b3: actually makes a larger ko by giving up an extra stone when White wins the ko, for a swing of 32 pts. in 5 moves, or an average gain of 6.4 pts. per move.
That makes :b3: sente, so White will take and win the resulting larger ko.
Although White is the komaster, White 2 may not recapture due to the ko rule. White need not play 2 at 4 because he is the komaster and can force Black to first play at 3. Therefore, White's correct local move 2 is a pass.:b3: @ :wc:
You may consider "sente" to be informal here, but in the context of kos the term can acquire new technical meanings, if one bothers to define them. In this case, raising the temperature is part of the meaning. Because White is komaster, we already know that White's answer is correct play.RobertJasiek wrote:Why do you speak of "sente"? What is "sente" in a tree of a local ko endgame? Just an informal word to express that a player's local play is correctly answered by the opponent's next move being a local play?Bill Spight wrote: Assuming that this is Black's threat, there is a swing of 31 pts. in 5 moves, for an average gain of 6.2 pts. per move.
However,
That makes
You are asking a lot!RobertJasiek wrote:We can calculate the average gain of either variation because there is only one sequence started by White. In other initial positions, can it happen that there would be two or more sequences started by White to be considered? If yes, how to calculate each average gain, compare and decide between variations?
I speak of Black's threat because we do not expect Black, as koloser, to be able to carry it out. But we need to know it because we need to know when it is too small for White to prevent it. Assuming that we have found White's correct play and Black's correct threat, when the average gain of plays elsewhere (in the environment) is equal to the average gain of the ko plays, White will be indifferent between preventing Black's threat or not.RobertJasiek wrote:Why do you speak of "threat"? Is it not easier to speak of choice, strategy or tactical variation?
If you want to calculate the swing you have to let Black finish her threat.RobertJasiek wrote:Let me try to understand how to calculate the tally and after what sequences' followers to calculate the swing:However,
There is potential for confusion here. As koloser, Black should not be able to take the ko back.
Black did not take back withBlack continuation's excess plays = 2.
Black follower's count including the initial prisoner difference = 16 + 0 = 16.
. Good. Yes.White continuation's excess plays = 2.
White follower's count including the initial prisoner difference = -16 + 0 = -16.
Total excess plays = initial excess plays + Black continuation's excess plays + White continuation's excess plays = 1 + 2 + 2 = 5.
Swing = 16 + (-16) = 32.
Is this calculation right?
To discover Black's threat.If yes, why does White being the komaster allow Black 5 in Black's continuation?
, as komaster White should not allow Black to take the ko back.Because the comparison shows thatRobertJasiek wrote:I understand this but...
If Black cuts with
a) Black starts this sequence. Why may we compare it to the sequence started by White to assess that the former has the mistake Black 3?
is worse than a pass.We do not actually need it. However, since we are working top down and trying to find Black's best threat, we initially allowRobertJasiek wrote:b) If we use this reasoning in your text to identify the mistake Black 3, why do we need the following cited analysis?
In three moves Black can take the ko, make the larger ko, and win it. OC, White will prevent this from happening, but this is one threat. The resulting local score is 16 pts. (for Black).
Assuming that this is Black's threat, there is a swing of 31 pts. in 5 moves, for an average gain of 6.2 pts. per move.
However,
That makes
and 
. Having done so, this line of reasoning enables us to discover that is a mistake.I believe this comes from my analysis.RobertJasiek wrote:Other topic:
Although White is the komaster, White 2 may not recapture due to the ko rule. White need not play 2 at 4 because he is the komaster and can force Black to first play at 3. Therefore, White's correct local move 2 is a pass.
plays elsewhere because we want to discover Black's threat. Otherwise he would play his sufficiently large threat and take the ko back.IfRobertJasiek wrote:However, if White plays 2 at 4, Black's correct play in view of White being the komaster is to connect the ko. The resulting count is the same. IOW, the diagram shows a dominating White 2.
is at 4, the local temperature has dropped and Black should pass.If neither player is komaster, whoever wins the ko fight must ignore a ko threat to do so. That means that the properties of ko threats become significant. There is no single way to handle the no komaster case for non-placid kos.RobertJasiek wrote: ***
Now, we might also analyse the case "neither player is komaster".
***
That's because you have not learned thermography. The theory of non-placid kos depends upon thermographic ideas.RobertJasiek wrote:While I am approaching an understanding of analysis of this example, the general method remains a mystery for me.
Oh, it's not top secret, it's just not very important, and it is not so easy to explain. However, I should dig into my files and unearth an example or two.RobertJasiek wrote:On Sensei's and here, you define active ko. I understand that it is rare. Uh. So rare that you do not know any example, can you show some or is it top secret?
Maybe I put up an example on rec.games.go many years ago.Now, this citation has the problem of the ko recapture Black 5.Initial prisoner difference = 0.
Initial excess plays = 1.
Black continuation's excess plays = 2.
Black follower's count including the initial prisoner difference = 16 + 0 = 16.
White continuation's excess plays = 2.
White follower's count including the initial prisoner difference = -16 + 0 = -16.
Total excess plays = initial excess plays + Black continuation's excess plays + White continuation's excess plays = 1 + 2 + 2 = 5.
Swing = 16 + (-16) = 32.
You are right. The net play difference is only 4, not 5. Therefore the average gain per play is 32/4 = 8 pts., not 6.4 pts., as I said. SoRobertJasiek wrote:I need to study thermography some time in the future, when I have time.
3 excess plays
1 excess play.
Both sequences amount to the tally 4.
Therefore, I could not combine these two sequences to get the tally 5 proclaimed by you.
is sente for sure! 
silly question: what do you mean by komaster?The komaster concept was invented/discovered by Prof. Elwyn Berlekamp around 30 years ago. Basically, the komaster of a ko is able to win a ko fight for that ko without having to ignore the opponent's ko threat, but he can gain no further advantage from doing so. One way to think about it is that he has just enough ko threats that must be answered to win the ko. If he does not go ahead and win it when he has run out of those ko threats, the opponent can win the ko, so the komaster has to go ahead and win it at that point.Ian Butler wrote: