Sente, gote and endgame plays

[RobertJasiek]

We learn that it can be correct to calculate traversal values but this does not necessarily imply traversal play, although it is optional if ko threats need not be preserved. Or it can be correct not to calculate traversal values but traversal play can be possible. Calculation and play are two different things. Reversal is a third animal. There are relations but they depend on additional value conditions. Maya script!

[RobertJasiek]

Maybe I should overcome my prejudice and perceive the example as an ordinary reverse sente with Black's 1-move gote sequence followed by White's sente follow-up. Initial values are the same.

[Bill Spight]

Maybe I should overcome my prejudice and perceive the example as an ordinary reverse sente with Black's 1-move gote sequence followed by White's sente follow-up. Initial values are the same.

I think that the 1 is a typo for 7.

[Bill Spight]

We learn that it can be correct to calculate traversal values but this does not necessarily imply traversal play, although it is optional if ko threats need not be preserved. Or it can be correct not to calculate traversal values but traversal play can be possible. Calculation and play are two different things. Reversal is a third animal. There are relations but they depend on additional value conditions. Maya script!

To a first approximation, average counts and miai values are a good guide. For more accuracy, further thermographic information may be useful. Often ko considerations apply. And sometimes difference games can cut through uncertainties and ambiguities.

[RobertJasiek]

I think that the 1 is a typo for 7. :)

Without smiley, I might suggest to override move values by profit values of the currently next moving player during the alternating sequence. Then the 1 is overridden by the 7. Not that I would have worked out a complete theory for such, shall we say, incentives. Traversal is a matter of interpretation, isn't it?

[RobertJasiek]

Code: Select all

......A...........
...../.\..........
..../...\.........
.0.X.....B.-15|7..
......../.\.......
......./...\......
.-7|8.C.....Z.-22.
...../.\..........
..../...\.........
.1.Y.....D.-15....

C is a simple gote. B is Black's simple sente.

We have t(B) = 7 and t(C) = 8.

We test the tentative gote traversal move value aka local temperature t'(A) = (x - d) / 2 = 7.5. Bill, this contradicts the conditions you suggest: t'(A) <= t(B), t(C) <=> 7.5 <= 7, 8 are partially violated. Therefore, according to your conditions, A is not White's long gote but can only be a simple gote or simple sente.

Next, we test the tentative gote move value t'_gote(A) = (x - b) / 2 = 7.5 and tentative sente move value t'_sente(A) = x - c = 7. The condition t'_gote(A) > t'_sente(A) <=> 7.5 > 7 identifies White's simple sente and excludes 'ambiguous'. This contradicts t'_sente(A) = t(B) <=> 7 = 7 identifying 'ambiguous'. Due to the contradiction, we do not have a simple sente, either.

The condition t'_gote(A) > t(B) <=> 7.5 > 7 identifies a simple gote. This contradicts t'_gote(A) > t'_sente(A) <=> 7.5 > 7 identifying White's simple sente. Due to the contradiction, we do not have a simple gote, either.

Using your suggested conditions, t'(A) <= t(B), t(C), the local endgame does not have any type. Since this contradicts that each local endgame has a type, your conditions are wrong! The example is a counter-example for them.

***

Code: Select all

......A.-7.5|7.5..
...../.\..........
..../...\.........
.0.X.....B.-15|7..
......../.\.......
......./...\......
.-7|8.C.....Z.-22.
...../.\..........
..../...\.........
.1.Y.....D.-15....

Make the hypothesis of White's long gote with m'(A) = (x + d) / 2 = -7.5 and t'(A) = (x - d) / 2 = 7.5.

Let us study the profits of the moves of White's alternating sequence: P1 = 7.5, P2 = 8, P3 = 8.

Let me again suggest the conditions t'(A) <= P1, P2, P3 as the requirement for calculating traversal values of a long gote.

Applying them, we find the conditions t'(A) <= P1, P2, P3 <=> 7.5 <= 7.5, 8, 8 fulfilled.

I suppose, we have analogue conditions for longer long gotes. How about long sentes? Can we keep move values aka local temperatures for them or do we also need profits?

[Bill Spight]

Code: Select all

......A...........
...../.\..........
..../...\.........
.0.X.....B.-15|7..
......../.\.......
......./...\......
.-7|8.C.....Z.-22.
...../.\..........
..../...\.........
.1.Y.....D.-15....

There is no question that A = {0 | -15}, i.e., that White's move to B reverses through C to D. m(A) = -7½, and t(A) = 7½.

However, as you point out, the temperature of B is 7, which is less than 7½. Therefore, there will be times that Black will want to save B as a ko threat and not immediately continue to C. But since 7 is close to 7½, there will also be times that Black should continue to C to prevent White from getting the reverse sente from B to D. Because of the half point difference, this is a close call.

Edit: In either case, A is gote.

[RobertJasiek]

Bill, I know too little about history of research in using counts and move values for evaluating gote and sente after Sakauchi Jun Ei and until 2016. CGT (and Mathematical Go Endgames) studies a lot but, AFAIK, not in terms of count and move value, as go players use them: unchilled, without infinitesimals. Has everything in between been your invention? I wonder because everything I read had been written by you: comparing counts or move values, gains, distinguishing types, conditions for move order in environments etc. What of that has been your invention and what has been invented by others (whom)?

[Bill Spight]

Bill, I know too little about history of research in using counts and move values for evaluating gote and sente after Sakauchi Jun Ei and until 2016. CGT (and Mathematical Go Endgames) studies a lot but, AFAIK, not in terms of count and move value, as go players use them: unchilled, without infinitesimals. Has everything in between been your invention? I wonder because everything I read had been written by you: comparing counts or move values, gains, distinguishing types, conditions for move order in environments etc. What of that has been your invention and what has been invented by others (whom)?

Among the first go books I bought were Sakata's Killer of Go series and Takagawa's Go Reader series. One of the Sakata books deals with tsumego and yose, one of the Takagawa books is about the yose. Both mention miai counting, but Sakata regards it as useful only in special cases. Takagawa is clearer, and simply mentions both deiri and miai counting. Both authors, however, start with finding the count. Neither mention the problems with double sente.

My own efforts were mainly based upon my understanding of Takagawa. Most go books start out with assuming that a play is a double gote (sic!), a one-way sente (sic!), or a double sente (sick! ), and make the calculations accordingly. On my own I discovered that if you start out assuming that all plays were simple gote, you could derive a contradiction when the value of the opponent's reply was larger than the assumed value of the supposed gote. Then you got a sequence of plays that was sente or gote depending upon when the size of the plays dropped below that of the original play. With this method I was able to get all the temperatures and mean values of non-ko thermography, a few years before thermography was invented. I don't know whether I improved on Takagawa or not, since I had donated the Go Reader set to the Yale library before I concentrated on yose calculation. It took me a few years before I abandoned the idea of local double sente. I had never actually calculated one, only assuming that plays that had humungous follow-ups for both players were double sente. But I managed to prove, to my satisfaction, that they did not exist. (Before 1976.) I even sent an article to the Go World saying that they did not exist, but Bozulich did not bite.

I developed my own theory of ko evaluation, but it is not very practical. You have to know too much to apply it, as a rule. I touch on it at the start of This 'n' That. It is at the root of the CGT idea of komonster, and my classification of types of ko threats, and the idea of the ko ensemble. After studying CGT I came up with the idea of ambiguous plays. I also discovered how to evaluate multiple kos and superkos, in 1998. And a few years later I discovered the relation between simple approach kos and Fibonacci numbers (Edit: in a neutral threat environment). (Edit: Earlier I had regarded approach kos as a kind of sente. In an environment with sparse ko threats, that might be more accurate. For instance, the proverb says that a three move approach ko is no ko at all. In an NTE, it is worth 1/13 of the swing, which is often worth fighting. As a sente, it is worth 1/24 of the swing, which is closer to 0.)

Talking about how much a play gains, on average, is just another way of talking about miai values. Less scary and unfamiliar, I think. Colored thermographs add a bit of clarity. They make it easy to describe privilege, for instance.

I owe a lot to Takagawa's clarity. I doubt if I would have gotten very far on my own without that. Like most players, I probably would have remained mired in deiri values, deciding between sente and gote by the seat of my pants.

[RobertJasiek]

Very interesting history!

Application I: From move 2 on, increasing or constant move values every second move identify a long gote sequence. Treat it like one move. Then, for the first move, verify the simple sente condition.

Application II: From move 1 on, for each 2-move sente sequence part, verify its simple sente condition. And verify increasing or constant move values every second move to link the parts.

Which application is correct?

Neither is correct. Currently, I am successfully testing my idea of increasing or constant gains.

Luckily and probably, this also means that we do not need my conjecture "Proposition 2" in forum/viewtopic.php?p=229609#p229609

[dfan]

Bill, I would like to continue to encourage you to produce that endgame book you occasionally threaten to write! I get bits and pieces of the theory here and on Sensei's Library (and Robert has been very helpful in this thread by forcing you to clarify things ) but I would really love to be able to work through it in a logical fashion, from fundamentals on up. I'm sure it would sell dozens of copies

[RobertJasiek]

dfan, please see viewtopic.php?p=230911#p230911

[RobertJasiek]

Assume a local endgame without complex kos, not doubly ambiguous, with Black's alternating sequence creating followers with the counts B1, B2, B3,... and White's alternating sequence creating followers with the counts W1, W2, W3,... Calculate the gains of the moves. Testing longer before shorter sequences worth playing successively, determine the count C and move value M of the local endgame so that M is at most each gain.

The method has a theoretical problem: we must show that there is only one solution. We must prove that two solutions (one for a longest black sequence, one for a longest white sequence) cannot exist. Maybe prove by contradiction. (A proof can rely on the already proven non-existence of local double sente.)

Have CGT or thermography already proven this unequivocality?

Bill, you often say that any assumption can be made for the type and values of the local endgame because contradictions occur until we find the correct values. Is there a proof why necessarily at least one contradiction occurs?

[Bill Spight]

Assume a local endgame without complex kos, not doubly ambiguous, with Black's alternating sequence creating followers with the counts B1, B2, B3,... and White's alternating sequence creating followers with the counts W1, W2, W3,... Calculate the gains of the moves. Testing longer before shorter sequences worth playing successively, determine the count C and move value M of the local endgame so that M is at most each gain.

The method has a theoretical problem: we must show that there is only one solution. We must prove that two solutions (one for a longest black sequence, one for a longest white sequence) cannot exist.

It is quite possible that the solution involves the longest sequence for each player. With thermography, without double ambiguity you can show that the solution for move values is unique. The solution for territory values is unique, anyway. That is easy to show, because the right wall cannot decrease as the temperature increases and the left wall cannot increase as the temperature increases. So when the scaffolds meet, we have the territorial count and the minimum temperature, and when they cross we have the maximum temperature. (That is not the case with ko thermographs, OC. )

Testing longest sequences first can be efficient, and you won't miss any reverses.

Bill, you often say that any assumption can be made for the type and values of the local endgame because contradictions occur until we find the correct values. Is there a proof why necessarily at least one contradiction occurs?

If the assumptions are correct, no contradiction occurs. If you will notice, my pre-thermography methods always start with counts. Move values are derived, not assumed.

[RobertJasiek]

This is very good news, thank you! For now, I have to believe you because I have not studied thermography enough to do the proof or imply it from an algorithm of drawing a thermograph. However, I find the underlying constructive reasoning ("the right wall cannot decrease as the temperature increases and the left wall cannot increase as the temperature increases") convincing.