Komaster / Discussion

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Changeover to forums

Bill: I copied everything below to the new forum pages. As JuhoP pointed out, that was not the thing to do. I had not considered the editing problems involved. With the exception of an anonymous question and my immediate response, I have deleted everything else I copied. My apologies.

I have left titles of some forum topics intact, in case people wish to move their own material there.

Meanwhile, I am making titled sections of this page, which would have been a better idea to start with.

(Later): I have been reassured by the powers that be that such problems can be fixed, if need be. So, I will not touch Juho's material. He can start a thread if he wants to. Otherwise, if no one else objects by Oct. 15, I will copy material from here to the forums.


Is Komaster something internal or external?

I'm confused. Is the property of someone being Komaster internal to the ko, or is it a matter of external ko threats? It seems to me that in the first diagram Black does have to ignore White's ko threat with 7. Does this mean that Black is komaster because White has no ko threats (or none big enough)?

--jsha


Bill: From an analytical point of view, one beauty of the komaster concept is that you do not have to work out exactly what it takes for a player to become komaster. The komaster has just enough ko threats to win the ko without having to ignore an opposing threat. In practice, of course, there is often a trade-off between winning the ko and allowing the opponent to complete a threat. This is called the ko exchange.

In the first diagram, if Black is komaster White has no ko threat to play at move 7. If White plays a small ko threat that Black has to ignore, Black is not komaster.


Breakthrough to Komaster?

Jan: Hey Bill, when are you going to write Breakthrough to Komaster? I'm sure Ritchie Press will want to publish it?


How do I know who is Komaster?

It would be nice if someone could write down the answer to the question "How do I know who is komaster?". If I knew how to determine it I might understand it :). The above discusion really doesn't seem to clarify anything for me. It sounds an awful lot like the komaster is simply the person who has enough excess ko threats to win. There is also a lot of asigning points in the above, which seems difficult if not impossible without knowing the position on the rest of the board.

Bill: In the precise technical meaning of the term, for a player to have just exactly enough threats that are large enough so that she is komaster is against the odds. Usually one player or the other has more than enough large enough threats to win the ko without having to ignore an opposing threat, or neither player is komaster.

Simple examples can be given, however. The simplest is that of a simple one-step ko where neither player has a ko threat. The player to take the ko is komaster.

Charles It's a modelling term, anyway. The better question is 'how can I tell whether the results from the model apply to my game?'

Bill: The beauty of the komaster idea, IMO, is that for the first time it gave us a way to calculate the value of single kos in a manner similar to the way we calculate the value of other plays. For that, it's vagueness in terms of what conditions need to be met on the the go board for a player to be the komaster for any specific ko fight is a virtue, just as the vagueness for calculating the value of non-ko plays about other plays on the board is a virtue.

For non-ko plays we have a good idea of the conditions on other plays that have to be met so that we can have confidence in the theoretical results. I. e., that the largest play is the best play. Furthermore, we know that these conditions are typically met, so that playing the largest play is usually correct.

For placid kos, which have the same value regardless of who is komaster, we can be relatively confident. However, komaster calculations do not provide absolute limits, so we cannot be as confident about any ko as about non-kos.

For hyperactive positions, such as approach kos, mannen kos, and positions which threaten fights for large placid kos, the story is different. Being able to calculate their value gives some guidance, where before there was none, but little is known in general about conditions for komaster, so our level of confidence is much lower.

There are other ways, which I pioneered, of theorizing about such positions by analyzing kos and threats together in what I term a ko ensemble. However, that theory is so complex that it is not yet of any real practical use.


Is there an objective definition of ko threat?

But is there some objective definition of a 'ko threat'? Isn't 'ko threat' just a relative term? Doesn't almost every reasonable move threaten some follow-up? So how is it possible to connect a ko without ignoring a threat? And doesn't this make 'komaster' quite a vague term?

-- JuhoP

Bill: I do not believe that there is a comprehensive formal definition of a ko threat. There are definitions for specific types of ko threats. Like sente, ko threat is a fuzzy term.

Yes, most reasonable moves have follow-ups. But that does not mean that the follow-up is a threat.

E. g., suppose that we have the following plays, as well as a simple ko:

                    A          B
                   / \        / \
                  C   0      6   0
                 / \
               10   6

If Black plays from A to C as a ko threat, White will surely ignore it. Either she will win the ko or respond in B.

Komaster is not a vague term. It is precise. However, as Charles points out, it belongs to a model. That model may apply to the current situation to varying degrees, or not at all. Maybe nobody is komaster.

Let me add that the explanation I gave of komaster is not its formal definition. For that, see [ext] http://www.msri.org/publications/books/Book29/files/ber.pdf. I tried to explain the term for the average go player. :-)


I am not sure I understand Komaster.

RobertJasiek: I am not sure whether I understand "komaster". Is this, for a particular ko,

  • the player that has more ko threats than the opponent,
  • the player that has more ko threats that are bigger than the ko's temperature than the opponent, or
  • the player that, when dissolving the ko, leaves the opponent with threats of size at most 0 or being passes?

Bill: None of the above, although they may also be the case. The idea of komaster is an abstraction that allows us to evaluate certain types of ko positions. Any particular ko threat situation may well not fit the bill exactly.

Bill:Probably the simplest example of komaster is this. There is a simple, direct (one stage) ko. Neither player has a ko threat. In that case the player who can take the ko is its komaster.

Bill:Another example: There is the same ko, but if one player takes the ko the other has a single humungous ko threat that must be answered by correct play. That player is the komaster, not the one who takes the ko.

RobertJasiek: So komaster requires perfect play, then looks who wins the ko, and then calls this person the komaster? Virtual-force works vice versa: First enable one player to recapture in the ko without making a threat (unless that player's previous move was a ko-capture elsewhere), then watch the move-sequences, and then (if this was the "something" of the aim) we will have found out whether the player could win the ko.

What, in this respect, are "neutral threat environments"?

Bill: Komaster does not require perfect play. You can make either player komaster and do the analysis. But if you want to find out who, if anybody, is komaster, then you have to look at the ko threat situation and assume perfect play.

Application to Superkos

RobertJasiek: How, by definition, does komaster apply to superkos? Examples?

Comparison to Virtual-Force

RobertJasiek: What are the differences between komaster and virtual-force?

Bill: I looked at the virtual-force definition on that page, and I do not understand it.

RobertJasiek: What is it that you do not understand?

Bill: The English. Give it its own page and explain more.

RobertJasiek: Let me make a start:

  • Currently virtual-force is defined only for basic kos. This will change in future though when presumably its reference to basic ko and ko-capture will be replaced by reference to ko in general and cycle-play.
  • Komaster models virtual ko threats by actually executing them and their one-play answer. Virtual-force models virtual ko threats by simply allowing immediate recapture in a ko.

Bill: I suppose that I gave that impression, because I was talking to go players. By Berlekamp's original definition, however, the komaster is allowed to take the ko back immediately. The komaster must then make a second play in the ko.

  • I do not know yet how komaster applies in a sequence of ko-captures. Virtual-force does not give extra rights then.

Bill: If you are talking about an iterated ko, the komaster is not required to make a second ko capture (unless that is the only play in the ko), and if she does she is not required to make a third, or to make another play in the ko.

  • Komaster provides just enough threats. Virtual-force provides an arbitrary number of threats.

Bill: My statement that the komaster has just enough threats is an attempt to explain the concept to go players. It is not part of the mathematical definition. If virtual-force allows a player to gain by delaying the win of the ko, then that player is komonster.

  • Komaster requires virtual threats to be just large enough. Virtual-force does not care for sizes of threats.

Bill: Komaster says nothing about virtual threats. Don't confuse what I said to explain the concept to go players with the mathematical definition.

RobertJasiek: Are komaster and virtual-force just different models or can we say that the latter is the easier model? I think that also virtual-force is a tool to enable us assessing the value of a ko: We get the outcomes of a ko if either player moving first may virtual-force and we can count how often a player took advantage of virtual-force by recapturing immediately. This suffices for determining the ko's value (although so far only for basic kos).

Bill: I think that we can say that komaster is the simpler model. :)

RobertJasiek: What about writing the formal definition here? Maybe then I get a chance to understand it. Afterwards we can compare simplicity again :)

Bill: I did not give the formal definition here, but gave a link to Berlekamp's exposition, because this is a go site, not a math site. :)

RobertJasiek: Go is also about maths and go. So SL discussion should also be about that instead of self-censoring it (and other go-related things). - I had a look into Berlekamp's paper, do not care much for the details of thermography, and tried to understand ko master neverlessless. But his description of ko master is buried among too much informal text; I do not know what shall belong to a definition and what not. I am missing a paragraph starting with "Definition: A komaster is [...]".


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