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 Post subject: Endgame Study
Post #1 Posted: Sat Jun 01, 2019 11:17 am 
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Endgame Study

Importance

Professional players say that the greatest weaknesses of amateur players are tactical reading and endgame evaluation. This has also been my observation. According to a frequently heard wisdom, becoming strong at physical or mind sports requires effort and patience when studying and practising. It is no coincidence that tactical reading and endgame evaluation are our greatest obstacles because both aspects require effort and patience.

In scored games, the endgame phase covers half of the game. Endgame evaluation also affects many moves during the opening and middle game. Many decisions cannot be solved by tactical reading but require endgame evaluation. Quite a few other decisions require both aspects. More than half of all moves greatly profits from endgame evaluation.

Development

Despite its extraordinary importance, less than 5% of the go literature has studied endgame evaluation. Why? The reason cannot be the required effort and patience because there are many books on tactical reading. Since we play a scored game, we should not be afraid of numbers. What then is the reason and why have many books on traditional endgame evaluation had many calculation mistakes? The reason is that the theory of endgame evaluation has been very under-developed in comparison to its importance and go theory for other aspects of the game.

Traditional theory of endgame evaluation has been inconsistent and very insufficient. During the 20th century, mathematicians have developed combinatorial game theory, infinitesimals and thermography but application of these theories is often hard and impractical for go players. We need a consistent, powerful and applicable theory: modern endgame theory.

Modern endgame theory is consistent because its already calibrated values can be compared to each other naturally. The theory is powerful because it evaluates sequences, individual moves and positions, and relates their values to enable advanced decision-making. Modern endgame theory is well applicable with its basic arithmetic calculations and pairwise value comparisons.

The theory has been developed by a few amateur players. Sakauchi Jun'ei made some early contributions. Bill Spight has researched in modern endgame theory since the 1970s. Besides earlier contributions, Robert Jasiek has done full-time research and writing about the endgame since 2016. Because such research requires formulation and mathematical proving of theorems, professional players with different skills could hardly contribute to the development of modern endgame evaluation. However, once the theory is developed, its application is straightforward for amateur and professional players. Writing related books remains difficult for they require very much more proofreading than books on other topics.

Effort

When we use tactical reading to determine a status of connection or life+death of a group or its moves, we invest the effort of first assessing the statuses of the follow-up positions and moves. Similarly, when we use endgame evaluation to calculate a value of a position or its moves, we invest the effort of first calculating the values of the follow-up positions and moves. Tactical reading and endgame evaluation are combined to select the best move achieving a desired status. For example, a group shall live while optimising the endgame. However, as soon as several moves are available and different local positions must be considered together, exhaustive 'reading and counting' is too complex and we need endgame evaluation for our decisions.

Do I hear a complaint that evaluation requires the effort of calculation? We must always recall that becoming strong requires effort and patience. Instead of complaining, we should welcome the necessary effort for greatly improving our game. Now that we know the truth, we can appreciate the calculations further below.

They are easy enough so what is the real effort? Like we have to avoid accidental mistakes in tactical reading, we must also avoid accidental calculation mistakes in endgame evaluation. If we consider a local position with several follow-up positions in tactical reading, we must determine and recall several statuses while not confusing them. Similarly, if we consider them in endgame evaluation, we must calculate and recall several values while not confusing them. Furthermore, we must know what values to calculate and which to compare. With patience, we learn to assess more difficult positions with more follow-ups.

Calculations

We determine the value of a position (its 'count'), the value of first playing in a position (the 'move value') or the value of an individual move (its 'gain'). We need positive numbers favouring Black and negative numbers favouring White. For example, we express "White has 3 points" by the negative count -3. What is the count of a local gote endgame position if the starting black player achieves 11 points or the starting white player achieves -3 points? We calculate the average of the two numbers: the count is (11 + (-3)) / 2 = 8/2 = 4 points. Such calculations require brackets. We also need fractions because division by 2 can create them. Suppose Black achieves 1 point or White achieves 0 points. Let us calculate the average: (1 + 0) / 2 = 1/2. This is the expected count of the initial position.

Which move value, 7 or 1/2, indicates the more valuable move? We determine the answer by comparing the two numbers: 7 > 1/2. We choose the move with the larger move value 7. Quite like we identify different persons by their names, we identify different values by their variables. A position has its count C and move value M.

Suppose a position has the count C = 4 and move value M = 7. The starting Black achieves the resulting count C + M = 4 + 7 = 11. Instead, the starting White achieves the resulting count C - M = 4 - 7 = -3. This negative number favours White. All we need is such basic school mathematics.


Text as a webpage: http://home.snafu.de/jasiek/Endgame_Study.html

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 Post subject: Re: Endgame Study
Post #2 Posted: Sat Jun 01, 2019 1:40 pm 
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I am having trouble applying modern endgame theory to actual game positions.
See https://senseis.xmp.net/?DieterVerhofst ... calEndgame

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 Post subject: Re: Endgame Study
Post #3 Posted: Sat Jun 01, 2019 1:54 pm 
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I think I've read somewhere here on this forum that a lot of professionals don't actually calculate the points of endgame plays and instead just memorize a couple hundred situations with point values attached.

I wonder if this ends up being less work than all the calculation western players go through :scratch:

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 Post subject: Re: Endgame Study
Post #4 Posted: Sat Jun 01, 2019 2:29 pm 
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Application to actual game positions: some partial application becomes necessary. Approximative tools of modern endgame theory may be more useful than exact tools, e.g., consider an ensemble and model the remaining, smaller values by a temperature. Positional judgement might be more appropriate during the middle game than endgame evaluation. Interaction between different regions can make combined application of reading and evaluation necessary, and other strategic concepts, such as influence, might have to be considered, too. Knotwilg, hence your experience is not surprising. However, I think you create extra problems for yourself by fuzzy tools, whose use do not convince me. You might open your mind by replacing some of them by mine. Of course, I cannot eliminate all the complexity mentioned before.

paK0, of course one can: not use exact calculations and then boast about speed... Always approximating is definitely wrong. Approximation is good when many local situations are involved and strategic choices allow for an error tolerance. When only a few (largest) local endgames have to be compared, accurate evaluation is often appropriate.

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 Post subject: Re: Endgame Study
Post #5 Posted: Sat Jun 01, 2019 3:12 pm 
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I'm not talking about approximation. If a certain situation has a point value and you just memorize it, it will naturally yield the same result as an accurate calculation.

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 Post subject: Re: Endgame Study
Post #6 Posted: Sat Jun 01, 2019 3:54 pm 
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Right, but how many shapes are there?:) Yes, some memorisation helps but we will always encounter some shapes whose values we do not know by heart yet. If we study like josekis, 10,000 recalled values would be a start for systematic memorisation. Which accurate sources can we trust? I see ca. 500 known shape values. John mentioned more in some Japanese book but how accurate is it? They cannot have known the new theory for long sequences so I expect mistakes.

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 Post subject: Re: Endgame Study
Post #7 Posted: Sat Jun 08, 2019 6:00 am 
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Sakai 8p is said to have a list of endgame moves and its value, and he still adds them as he sees new moves in actual games, which probably means that there is not yet a comprehensive list of values of all endgame moves. Also, for endgame theory, Mistunaga, 6p pro and a mathematics bachelor from Tokyo Uni, has written a book called "Katsu yose no zetsumyo na tejun".
https://www.amazon.com/Katsu-zetsumyo-t ... oks&sr=1-1
Since this book delves into an academic field on endgame rather than on practicalities, even high dans find the book difficult.

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 Post subject: Re: Endgame Study
Post #8 Posted: Sat Jun 08, 2019 7:08 am 
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I also lack study in endgame. I tried to think of why that is. I came up with:

1.) Most of my games are decided before the endgame. But then again, perhaps this is since I know I’m weak at endgame.

2.) Endgame calculations are less fun than reading sequences. I enjoy the process of visualizing stones while reading. Doing abstract mathematical calculations are not as enjoyable to me. In the latter case, I am playing moves because of relying on a theory - I don’t SEE why it is good for myself. So it’s less fun.

Admittedly, this second one is a lame excuse, but I think it’s true for me.

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 Post subject: Re: Endgame Study
Post #9 Posted: Sat Jun 08, 2019 8:36 am 
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kyulearner wrote:
Mistunaga, 6p pro and a mathematics bachelor from Tokyo Uni, has written a book called "Katsu yose no zetsumyo na tejun".
https://www.amazon.com/Katsu-zetsumyo-t ... oks&sr=1-1
Since this book delves into an academic field on endgame rather than on practicalities


Is this combinatorial game theory or what else?

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 Post subject: Re: Endgame Study
Post #10 Posted: Sat Jun 08, 2019 11:42 am 
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I doubt if this is in anyone's database. https://lifein19x19.com/viewtopic.php?f ... 82#p245682

;)

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 Post subject: Re: Endgame Study
Post #11 Posted: Sat Jun 08, 2019 8:32 pm 
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Kirby, while I perfectly understand the reason for your missing motivation, probably you are aware that reading does not replace evaluation except for the simplest cases. If we only have a few simple local endgames during the latest endgame, we can solve by reading or evaluation. For every other purpose, correct decision-making for local endgame positions during the opening, middle game or endgame phases requires a) a combination of reading and evaluation or b) only evaluation. Global reading without evaluation (other than counting the results) for more than a few local endgames is too complex (already five local endgames each with three available first moves can be too complex for global reading). For the middle game or early endgame, only considering an ensemble of the few clearly largest local endgames by reading in only them is insufficient because the value of playing next elsewhere must also be taken into account so we need evaluation. A monkey jump can be worth ca. 4 to 8 points but by guesswork or only by reading we do not know its value because the first move might be gote and creates an unsettled position.

We can have excuses or good explanations why we might avoid calculations but this results in what you are aware of: weak endgame.

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 Post subject: Re: Endgame Study
Post #12 Posted: Sun Jun 09, 2019 4:50 am 
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Agree with everything you've said, RobertJasiek :-)

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