Values of moves

Bill Spight · Post by **Bill Spight** » Wed Sep 19, 2018 10:19 pm

Pio2001 wrote:For me, a score is something like "Black wins by 4.5 points", or "White wins by 25.5 points".

Many sports have a scoreboard that shows the score or scores before anybody has won or lost.

Correct me if I'm wrong, but I assume that you mean Black's points minus White's points, including territory and dead stones present in the local region, not including komi or handicap compensation, the local region being defined as a given set of intersections... What Robert Jasiek calls the "count" in a "locale".

I cannot vouch for Jasiek's usage. Berlekamp introduced the term, count, for the non-final value of a game or independent go position. When I was learning about the endgame, books simply called that territory, but these days sticklers in the West prefer to use territory only for final values; so I use count in self-defense.

daal · Post by **daal** » Wed Sep 19, 2018 10:36 pm

Bill Spight wrote:I don't like this diagram. It relies too much on words and numbers to be understood...

More words I say! More words and diagrams like the examples that you and pio2001 offered of sente vs. gote positions. They are precisely what makes the diagram halfway intelligible to people like me.

mitsun · Post by **mitsun** » Wed Sep 19, 2018 11:19 pm

Bill Spight wrote:
Code: Select all
             Start = 4
               / \
       sente  /   \  reverse-sente
             /     \  value = -4
            /       \
           4         0
I don't like this diagram. It relies too much on words and numbers to be understood, and makes it look like a sente is a gote. There is no branch indicating a White reply.

Yes, on reflection I do not like it either. As you say, the left branch makes it look like B invested a move, when in fact he did not. Better to keep the node and single branch.

Code: Select all

             Start = 4
               / \
       sente  /   \  reverse-sente
             /     \  value = -4
            /       \
           S         0
            \
             \
              \
               \
                4

RobertJasiek · Post by **RobertJasiek** » Wed Sep 19, 2018 11:53 pm

Pio2001 wrote:I assume that you mean Black's points minus White's points [...] What Robert Jasiek calls the "count"

The count of a settled (local) position. Counts of unsettled positions are derived from counts of subsequent positions.

mitsun · Post by **mitsun** » Thu Sep 20, 2018 12:31 am

Here are the graphs for the two positions Bill provided as Go diagrams earlier. The node counts and branch move values are for the gote assumption, with probability 50% for every branch.

Code: Select all

    
                o 5.25                  o 2.75? really 3       
               / \                     / \
              /   \ -2.75             /   \ gote -1.25,
             /     \                 /     \ really sente
            /       \               /       \
           8         o 2.5         4         o 1.5
                    / \                     / \
                   /   \ -2.5              /   \ -1.5
                  /     \                 /     \
                 5       0               3       0

Bill demonstrated that the W branch is local gote in the first graph and local sente in the second graph. Is there an easy way to see this from the graphs? I guess the contradiction in the second graph is that the gote count of the starting position (2.75) is less than a terminal position (3) which B can always guarantee reaching, by treating the W move as sente.

John Fairbairn · Post by **John Fairbairn** » Thu Sep 20, 2018 2:55 am

Can I remind people that the starting question of this thread, virtually unanswered, was: What is the easiest way to determine a rough value of a move in order to compare alternatives. I am more interested in "ballpark" than "correct."

We seem to have descended, rapidly and predictably, into counting how many angels can dance on the head of a pin. Angels are, admittedly, a step up from fleas, but in my view of the angelology only the archangel Bill has the right to stand on the pinhead. Although one other angel is surreptitiously trying to claim equal status, it is evident that the other angels don't really know what the archangel knows and don't even understand each other. In short they haven't earned their wings yet.

Does this matter? Well, one celebrated example in real life of the folly of counting angels was the fall of Constantinople when the Byzantine courtiers argued over the meaning of sente while the Turks were left undisturbed to plot their successful invasion of the city.

I don't mind being the barbarian at the gates and so will attempt to give daal an answer to his question. It's something I call the principle of affected areas. I gleaned it from Japanese books, but I have mangled it horribly since then, and have no idea whether it is truly useful. It's certainly not correct but might possibly be called ballpark. I don't know the origin of that American term but I assume that it refers to being in a baseball stadium and making a stab at guessing how many spectators are there. My method is more akin to being on the moon and guessing how many people are in all the ballparks together. Still, I do fondly believe it contains the germ of an idea that could work for daal.

daal wanted to know how to decide on whether to play A, B or C above. I assume he regards A as sente, however tentatively, for both sides, B as sente for Black but a gote area for White, and C is gote for Black (only fleas and angels worry about reverse sente). In real life I expect he would play in the order A, B, C. But (because of the inescapable angelic chatter) he would harbour some doubts as to whether he should be playing C first. He therefore wants a method that would enable him to feel less guilty about harbouring those doubts and that would once in a while actually let him play a better move. Failing that, a method that would enable him to see some sense in pro play would not go amiss.

(I hope I'm not being too intrusive, or wide of the mark, with these speculations, daal.)

To be more precise, daal would like to know whether he can play the triangled stone below and be sure that White will answer at A, or should he worry that White might ignore it and play something like the square-marked monkey jump, in which case he should revert to B. There are some tactical nuances, of course, but barbarians don't worry about things like aji that can bite you in the bum. We have two Shredded Wheats for breakfast.

The principle of affected areas, as shown below, tells us. An SDK certainly, and possibly even a DDK, can easily surmise that if White ignores Black and plays the monkey jump, Black can jump into the new triangled point and (because White then has to worry about the safety of his entire group) set off a sequence that leads to something like the square-marked stones being played in sente (with some filling in round the edges towards the end of the game), so that Black can return to the lower side to answer the monkey jump. We can then easily visualise, again without precise calculation of tactics, that the triangle-marked stones will appear on the board. The marked areas are the "affected" areas and we can see that the area in the upper right is bigger then the one in the lower left, so Black is justified in starting at A and not worrying about the monkey jump.

I will leave daal to work out a case where his A may be sente locally but the resulting affected area is not as big as the monkey jump area below, and so he needs to play C (e.g. he can stick a white stone somewhere in the top right corner so that it makes a Black invasion less profitable).

Now another aspect of what daal was asking about, which seems to have been mostly ignored, is that we would like to know how to choose between big moves at any stage of the game, and not just the endgame - and not even just the boundary plays.

Below is an example from real life. For those who want to see the whole game it is from the Oza on 2017-07-13, Takao Shinji playing Son Makoto.

White has just played move 96 to end a ko in the top left. Black needs to add a move at A to save his group. But he demurred and played B. The principle of affected areas, used in a ballpark way, can tell us why.

If we count the affected area in the upper left if White plays there first, it is about 20 points. It is, however, quite easy to see that Black should be concerned about what may happen on the centre right. He has a couple of stones stranded there on the right, and his group in the centre is not yet quite sure of life. It seems obvious there is some urgency in the area and just by inspection we can see the potential Black area affected if White plays there first ("affected" because Black would have to answer - a non-urgent area is where there are e.g. miai and so can be shared whoever goes first) could easily exceed 20 points. If we want to be a little more serious about this but still avoid doing lots of arithmetic, we can even apply QARTS theory. Black has a one-eyed group in the centre that's not safe so we count up to -10 for that, and a no-eyed group on the right so we count -15 for that. Combined, that gives us a but more than the 20 or so affected points in the upper left.

LeelaZero even agrees with the pro players, with the small exception that it would prefer to start at C. It rates A, B and C as all very close to each other, but B or C do rank marginally ahead of A. But, even if A had emerged ahead of B and C in this bot ranking, we can see at the very least that the pro not playing at A was not a typo and was not a blunder, but was a rational choice.

As I said, I have mangled this method horribly. I have never made any attempt to refine it as I so rarely play, so I don't know for certain whether it is refinable. Even if refined, I don't expect it to be anywhere accurate enough to satisfy the angels.

Just in case, the angels are getting too exhausted at flapping their wings in irate consternation, I do understand your aims. I just don't have the time to share them. Or to put it another way: I do like Abba's song; I just can't play it as well as I'd like.

I have a dream, a move to play
To help me cope with anything.
If you see the wonder of a boundary play,
You can fake the future even if you fail.
I believe in angels, something good in this thermography.
I have a dream.
When I know the time is right for me,
I'll play sente.
I have a dream, a fantasy,
To help me through reality...

RobertJasiek · Post by **RobertJasiek** » Thu Sep 20, 2018 3:26 am

John Fairbairn wrote:The principle of affected areas

Instead of a principle, it is your assumption of avoiding continued mutual reduction.

Kirby · Post by **Kirby** » Thu Sep 20, 2018 4:01 am

As a side note, I'm reminded of an endgame heuristic I heard awhile back:

Play moves on "higher" lines first. So if you have endgame moves on the 3rd line, 2nd line, and 1st line, a rough heuristic is to start with the 3rd line moves, then move on to 2nd, then do 1st line moves.

The basic idea is that the "higher" line moves result in claiming more points.

Bill Spight · Post by **Bill Spight** » Thu Sep 20, 2018 4:32 am

mitsun wrote:Here are the graphs for the two positions Bill provided as Go diagrams earlier. The node counts and branch move values are for the gote assumption, with probability 50% for every branch.
Code: Select all
    
                o 5.25                  o 2.75? really 3       
               / \                     / \
              /   \ -2.75             /   \ gote -1.25,
             /     \                 /     \ really sente
            /       \               /       \
           8         o 2.5         4         o 1.5
                    / \                     / \
                   /   \ -2.5              /   \ -1.5
                  /     \                 /     \
                 5       0               3       0
Bill demonstrated that the W branch is local gote in the first graph and local sente in the second graph. Is there an easy way to see this from the graphs? I guess the contradiction in the second graph is that the gote count of the starting position (2.75) is less than a terminal position (3) which B can always guarantee reaching, by treating the W move as sente.

The final 5 and 3 provide lower bounds for the original counts.

The count of the position on the left lies between 8 and 5; the count of the position on the right lies between 4 and 3.

daal · Post by **daal** » Thu Sep 20, 2018 10:41 am

John Fairbairn wrote:Can I remind people that the starting question of this thread, virtually unanswered, was: What is the easiest way to determine a rough value of a move in order to compare alternatives. I am more interested in "ballpark" than "correct."

Thanks for the reminder. I had almost forgotten that I had asked the original question precisely because I am so bad at counting correctly.

Does this matter? Well, one celebrated example in real life of the folly of counting angels was the fall of Constantinople when the Byzantine courtiers argued over the meaning of sente while the Turks were left undisturbed to plot their successful invasion of the city.

Just quoting this because it is so much fun.

I don't mind being the barbarian at the gates and so will attempt to give daal an answer to his question. It's something I call the principle of affected areas. I gleaned it from Japanese books, but I have mangled it horribly since then, and have no idea whether it is truly useful. It's certainly not correct but might possibly be called ballpark. I don't know the origin of that American term but I assume that it refers to being in a baseball stadium and making a stab at guessing how many spectators are there. My method is more akin to being on the moon and guessing how many people are in all the ballparks together. Still, I do fondly believe it contains the germ of an idea that could work for daal.

I think so too. What I especially like about this idea is that the term "affected areas" is easy to intuitively grasp and remember to apply. As to "ballpark," my uncorroborated feeling is that it allegorically refers to the area where a ball is in bounds, i.e., within a large but not exactly defined region. I wonder if they should introduce komi for different sized baseball fields... Now there's a task for our friends!

(I hope I'm not being too intrusive, or wide of the mark, with these speculations, daal.)

Not in the least.

The principle of affected areas, as shown below, tells us. An SDK certainly, and possibly even a DDK, can easily surmise that if White ignores Black and plays the monkey jump, Black can jump into the new triangled point and (because White then has to worry about the safety of his entire group) set off a sequence that leads to something like the square-marked stones being played in sente (with some filling in round the edges towards the end of the game), so that Black can return to the lower side to answer the monkey jump. We can then easily visualise, again without precise calculation of tactics, that the triangle-marked stones will appear on the board. The marked areas are the "affected" areas and we can see that the area in the upper right is bigger then the one in the lower left, so Black is justified in starting at A and not worrying about the monkey jump.

(;AB[dc][dd][ce][ef][dg][eh][hb][gb][ga][gc][bi][ch][eb][ea][bh][dh][fa]AW[fc][fd]
[fh][hh][ci][ge][fb][ic][ia][ib][ha][hd][gd][di][ei][fi][hc]TR[bi][bh][ch][dh][ei]
[gb][di][eh][fi]SQ[fa][ea][ga][ha][ia][ib][ic][hb][fb][gc][gd][hc][ci]SZ[9])

I really appreciate this kind of explanation. An easy to follow and nicely illustrated text.

Now another aspect of what daal was asking about, which seems to have been mostly ignored, is that we would like to know how to choose between big moves at any stage of the game, and not just the endgame - and not even just the boundary plays.

Indeed. I hadn't dared bring it up again what with so many move values beginning with a decimal point, but yes, in fact the reason I originally posted had less to do with endgame, and more to do with how to establish priorities.

Below is an example from real life. For those who want to see the whole game it is from the Oza on 2017-07-13, Takao Shinji playing Son Makoto.

I don't know how much I will learn from it, but I have memorized the first 100 moves. Btw, Go4Go calls Takao's opponent in this game Sun Zhe.

As I said, I have mangled this method horribly. I have never made any attempt to refine it as I so rarely play, so I don't know for certain whether it is refinable. Even if refined, I don't expect it to be anywhere accurate enough to satisfy the angels.

I am curious to hear their take on it though...

Knotwilg · Post by **Knotwilg** » Thu Sep 20, 2018 11:17 am

I'm not of the gospel type, I like to understand things. I will neither worship Bill for saying things I don't understand, neither will I diabolize Robert for doing the same. I admire both for scanning the horizon and building theory. Bill has been more zealous in explaining things - I assume Robert keeps that for his book. I see mitsun and others as those who try to bridge those early developments with what is being traditionally understood - "barbarians" if you like. John, you never answered my question whether my attempt at building that bridge was even moderately successful, so I assume it wasn't.

I'll keep it here (but will continue studying modern endgame theory, now that my interest is raised)

John Fairbairn · Post by **John Fairbairn** » Thu Sep 20, 2018 12:57 pm

Btw, Go4Go calls Takao's opponent in this game Sun Zhe.

The Nihon Ki-in normally gives Son Makoto but the web site (though never the yearbooks or other publications, in my experience) adds the Chinese as an alternative. He comes from in Yokohama (i.e. Japan) and was raised there. His surname is common in China as Sun, but even if it ultimately came from there it's also got a long standing in Japan (Son is the usual reading but Mago also occurs).

Makoto is unusual - Satoshi or Tetsu would be the more common readings.

I don't know whether he has any recent Chinese connections or not, but I usually stick with the readings of the organisation a player works for.

There have been a few cases of Taiwanese Chinese pros (both Nihon Ki-in and Kansai Ki-in) in Japan getting a bit uppity about their names being read as Japanese. Even Go Seigen went through a phase of this. Editors sporadically attempt to pacify them, but then tend to lapse back. And some editors jump before they are pushed - sometimes wrongly. I think some of the website entries may fall under this category.

Edit: I decided to do a bit of digging about his origins. I found many Japanese references to him and none give Sun Zhe as a reading. Some, of course, give no reading at all, but an unusually high proportion do, as it is obviously seen as an unusual name (but so is Ichiriki Ryo and many others). Then it is invariably Son Makoto. It is the "Makoto" part that is seen as unusual and for that reason this portion is often given in hiragana (i.e. 孫まこと rather than 孫喆). The unusualness is not so much the kanji but the reading, although the kanji itself is classed as uncommon (because it is more usually written as 哲). There is absolutely nothing "Chinese" about this. Indeed the what stands out is the pure Japanese word Makoto rather then the common Sino-Japanese Tetsu (Satoshi wuld also be pure Japanese).

I also found local newspaper references to when he was a child prodigy in Kanagawa. There was no mention there that places him or his family in Taiwan or China, as you would expect as part of the usual journalistic "colour."

The Nihon Ki-in site (and only in its recent version) therefore appears to be the only source of a Sun Zhe reading, and even then not as the main reading. Knowing, further, a little bit about how this site is put together, I'm prepared to postulate that there was some automatic translation involved, and as Sun Zhe does exist as a Chinese name it may have crept in via this route. I could find no Chinese site that laid claim to Son as one of their sons (pun half intended

, and in fact his nationality (if mentioned) was listed as Japanese there.

Negatives don't prove much, so I can't unequivocally say he does not have Chinese connections or a personal preference for a Chinese reading, but common usage very, very strongly favours Son Makoto, and there is absolutely nothing countervailing I can see so far that supports using Sun Zhe.

All of this must, of course, be seen in the context that Japanese name readings in general are a complete dog's breakfast.

Bill Spight · Post by **Bill Spight** » Sat Sep 22, 2018 10:02 am

mitsun wrote:Here are the graphs for the two positions Bill provided as Go diagrams earlier. The node counts and branch move values are for the gote assumption, with probability 50% for every branch.
Code: Select all
    
                o 5.25                  o 2.75? really 3       
               / \                     / \
              /   \ -2.75             /   \ gote -1.25,
             /     \                 /     \ really sente
            /       \               /       \
           8         o 2.5         4         o 1.5
                    / \                     / \
                   /   \ -2.5              /   \ -1.5
                  /     \                 /     \
                 5       0               3       0
Bill demonstrated that the W branch is local gote in the first graph and local sente in the second graph. Is there an easy way to see this from the graphs? I guess the contradiction in the second graph is that the gote count of the starting position (2.75) is less than a terminal position (3) which B can always guarantee reaching, by treating the W move as sente.

Is there an easy way to see this from the graphs? Yes, indeed, as you have actually shown.

Let me repeat the graphs without the calculations.

Code: Select all

    
                o A                     o C      
               / \                     / \
              /   \                   /   \ 
             /     \                 /     \ 
            /       \               /       \
           8         o B           4         o D
                    / \                     / \
                   /   \                   /   \ 
                  /     \                 /     \
                 5       0               3       0

When we play the gote strategy for A in the four copies, we get these four results: 2*8 + 5 + 0 = 21. The sente strategy for Black yields these four result: 4*5 = 20. Black does better with the gote strategy, so we can use those results to find its territorial count: 21/4 = 5¼.

Using the graph we would first find the count of B, which is (5+0)/2 = 2½, and then find the count of A, assuming it to be gote, which is (8+2½)/2 = 5¼. OC, we can see at a glance that the count of A, assuming it to be sente, is 5, which is less than 5¼, so we conclude that A is gote. Using the graph gives us more information, and may be quicker.

When we play the gote strategy for C in the four copies, we get these four results: 2*4 + 3 + 0 = 11. The sente strategy for Black yields these four result: 4*3 = 12. Black does better with the sente strategy, so we can use those results to find its territorial count: 3.

Using the graph we would first find the count of D, which is (3+0)/2 = 1½, and then find the count of C, assuming it to be gote, which is (4+1½)/2 = 2¾. OC, we can see at a glance that the count of C, assuming it to be sente, is 3, which is greater than 2¾, so we conclude that C is White sente. Using the graph gives us more information, and may be quicker.

----

Suppose we wish to find a general rule to find out whether such a position is sente or gote. Let's relabel the graph with letters.

Code: Select all

    
                o A          
               / \           
              /   \          
             /     \         
            /       \        
           a         o B     
                    / \      
                   /   \     
                  /     \    
                 b       c

The result with the gote strategy is

2*a + b + c

The result with the sente strategy is

4b

Taking gote as the default, we get this rule:

Code: Select all

    
                o A          
               / \           
              /   \          
             /     \         
            /       \        
           a         o B     
                    / \      
                   /   \     
                  /     \    
                 b       c   

A is White sente if and only if 4*b > 2*a + b + c.

Noting that we can subtract b from both sides of the inequality, we get

Code: Select all

    
                o A          
               / \           
              /   \          
             /     \         
            /       \        
           a         o B     
                    / \      
                   /   \     
                  /     \    
                 b       c   

A is White sente if and only if 3*b > 2*a + c.

Now tell that rule to a regular go player. :scratch:

Archibald MacLeish wrote:A poem should be wordless
As the flight of birds. . . .

A poem should be motionless in time
As the moon climbs. . . .

A poem should not mean
But be.

Bill Spight · Post by **Bill Spight** » Sat Sep 22, 2018 10:53 am

To be kind to regular go players, especially if they have learned to count in the usual way (deiri), we can make the rule slightly less poetic.

Code: Select all

    
                o A          
               / \           
              /   \          
             /     \         
            /       \        
           a         o B     
                    / \      
                   /   \     
                  /     \    
                 b       c   

A is White sente if and only if b-c > 2*(a-b).

b-c is the deiri value of B, and a-b is the reverse sente value of A (if it is a White sente). Regular go players have already learned to multiply reverse sente values by 2 to compare them with gote. What this says is that A is sente if and only if its threat is greater than its reverse sente value.

Converting to O Meien's values, we get

Code: Select all

    
                o A          
               / \           
              /   \          
             /     \         
            /       \        
           a         o B     
                    / \      
                   /   \     
                  /     \    
                 b       c   

A is White sente if and only if (b-c)/2 > a-b.

And if we note that B need not be gote, we get this definition.

Given position P and players A and B:
Position P is sente for player A if player B's reply to player A's play from position P gains more than player B's play from position P.

That's the correct version of O Meien's definition.

RobertJasiek · Post by **RobertJasiek** » Sat Sep 22, 2018 9:44 pm

Bill Spight wrote:A is White sente if and only if (b-c)/2 > a-b.
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Given position P and players A and B:
Position P is sente for player A if player B's reply to player A's play from position P gains more than player B's play from position P.

That's the correct version of O Meien's definition.

What slightly wrong definition does O give?

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