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More about the Leela Zero Go-Playing Program

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Manji Inoue, Living National Treasure, Pottery Exhibition at Storrier Stearns Japanese Garden, 270 Arlington Dr., Pasadena, CA 91105, November 17-18, 2018

Last week I went to my Japanese go club, the South Bay Ki-in, located in the New Gardena Hotel, 1641 W. Redondo Beach Blvd., Gardens, CA 90247; (310) 327-5757 with another member, Kevin Carr, who brought Leela Zero, a go-playing computer program to the club on his laptop computer. I explained all this earlier and wrote that I would elaborate about the matter this week. More on that later.

Yesterday, I went online to Wikipedia to research Leela Zero. The following is what I found out.

Leela Zero is a free and open-source computer go software program released on October 25, 2017. It was developed by Belgian programmer Gian-Carlo Pascutto, the author of the chess engine, Sjeng, and the go engine Leela. According Wikipedia…

"Leela Zero’s algorithm is based on DeepMind’s 2017 paper about AlphaGo Zero. Unlike the original Leela, which has a lot of human knowledge and heuristics programmed into it, Leela Zero only knows the basic rules and nothing more.

"Leela Zero is trained by a distributed effort, which is coordinated at the Leela Zero website. Members of the community provide computing resources by running the client, which generates self-play games and submits them to the server. The self-play games are used to train newer networks. Generally, over 500 clients have connected to the server to contribute resources. The community has provided high quality code contributions as well.

"Leela Zero finished third at the BerryGenomics Cup World AI Go Tournament in Fuzhou, Fujian, China on 28 April 2018.

"Additionally, in early 2018 the same team branched Leela Chess Zero from the same code base, also to verify the methods in the AlphaZero paper as applied to the game of chess. AlphaZero’s use of Google TPUs was replaced by a crowd-sourcing infrastructure and the ability to use graphics card GPUs via the OpenCL library. Even so, it is expected to take a year of crowd-sourced training to make up for the dozen hours that AlphaZero was allowed to train for its chess match in the paper."

That is all that Wikipedia has to say about Leela Zero. Not much. When AlphaGo beat the top professional players some time ago, I sent an email message to the DeepMind team inquiring about the program and did not receive any response. (Lest the reader think me hopelessly naive to make that effort, I should explain that I only did this because a friend asked me to do so.) At that point, I just forgot about the matter. But I think that there are a number of aspects about this AI program that are interesting and worthy of analysis. At some point I hope to do that.

I am also willing to play the program, but I have not had that opportunity. When I get around to that, I will report on it here.

Now, I continue analyzing the Meijin title match. By the way, I saw this game the day after the complete game record was printed in the Asahi Newspaper. That is on November 2. (I realize that this sounds strange, because the game was played on November 2! However, it was played in Japan, which is a day ahead of us. So, when I saw the game record it was November 3 there.) In the newspaper article, the editors recommended the reader to visit the website: www.ashi.com/igo. I recommend that as well, although unless the reader is fluent in Japanese, I am not sure how much can be understood. One thing I can point out is that at the bottom of the homepage there are two oblong boxes. The one on the left has directions written on it that say that clicking on it will take the reader to a commercial site that costs a fee to view. The box on the right takes the reader to a free site. And that site is loaded with features, including the game commented on by professionals, videos of players and historical background information.

43rd Annual Best of Seven Meijin Title Match, Game 7

White: Cho U 9 dan

Black: Iyama Yuta, Meijin

Played on November 1 and 2, 2018.

Komi: 6 1/2 points

271 moves. White wins by 4 1/2 points.

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Figure 1: Defying the Conventional Wisdom (1-30)
Those interested in replaying the game move by move can click here to do so.

The off-beat corner enclosure of Black 3 and 5 was played three times in this match. In Games 1 and this one by Iyama and in Game 4 by Cho. The opening in Game 4 started almost exactly as this one, except that Black 1 was played on the star point. There is a psychological aspect to this. The players are very close in strength, so fighting spirit impels them to use the other’s strategy against the opponent.

White 6 through 12 is one of the most common joseki, played over many decades, so the possible variations have been worked out to a great extent. Since it is a joseki, the result is equal, so both players want to use it in order to stabilize their game in a whole board sense.

Here is where things get strange. In response to the attack on the corner of Black 13, White answers with the pincer of 14. In recent years, White usually replied with a knight’s move corner enclosure two points above 25. I suppose that White wanted to neutralize the power of Black’s corner enclosure in the lower right. But then White follows up with the sequence through 30. This position has many weak points, so White will not be able to fight strongly in this area. And more than that, it is not really effective thickness, either.

Another thing about this is that Black invaded the upper left corner with 15, leading to the joseki through White 22. White is building thickness in the center, so that one would think that in response to the invasion of Black 23, White would block at 25.

All of these factors are very strange. No doubt, my perception of the game is not advanced enough to critique these tremendously strong players. I remember years ago asking Yang Yilun 7 dan what the meaning was of some moves that top players made in a match game. "I don’t know," he replied. "These really strong professionals make moves that I can’t understand." So how could I be expected to figure them out? (When I finally work out the way to access the Japanese analysis online, I will be able to offer better work. But at this time, I am unable to even create my own diagrams. Again, it is suggested that the reader go to www.asahi.com/igo to see the analysis there.)

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Figure 2: Territory Versus Thickness (31-60)

Black 31 finishes up the joseki in this corner. At this point in the game, Black has taken all four corners. According to the go proverb, this is fatal. (If you lose four corners, the game is lost.) However, as Takemiya Masaki proved with his patented "Cosmic Go," the center of the board can turn out to be bigger than it seems. Perhaps Cho was trying to prove the same thing. That is a dangerous strategy to use in a critical game like this one. Especially against such a formidable opponent as Iyama.

White plays the checking extension of 34 to cover the thinness of the position in the lower left corner while undermining Black’s lower right corner enclosure.

But Iyama continues on the territorial quest with the invasion of Black 35. With the moves through 45, Black gouges out White’s position on the upper side. In exchange, White gets powerful thickness in the center. The problem is that Black has no weak stones for White to aim at attacking in order to put that thickness to good use. All that White can do is to make the attachment of 46 to try to start a fight.

The moves through White 58 seem like an impromptu joseki devised by the players at the board. It would be interesting to see the time each of them took for each move. Of course, since the form of corner enclosure that Black set up there was used three times in this match, the players may have researched the possibilities in study groups earlier.

Anyway, Black 47 through 59 create thickness to counter White’s on the upper side. Black might also get a chance to secure the corner later on. Black’s thickness also can be used to attack White’s thin group in the lower left.

White 60 sets up a large territorial framework (moyo). Note the point that was occupied. In the past, this kind of move was described as a "good guess." The move aims to work in coordination with the White positions on the upper, lower and left side, but it is impossible to determine exactly which point in this general area would be right for that purpose. So how does a player come up with the move to play? By choosing the one that makes the best shape. Here, White 60 seems to be balanced with the White stone to the left of 40 on the upper side, the stone four points to the left of 34 on the lower side, and the stone below 32 on the left side.

Large territorial framework games are notoriously difficult to count accurately, but here goes.

Black has 20 points in the upper right and upper side, 10 points in the upper left corner and 10 points in the lower left corner. Plus, whatever points will be gained in the lower right.

Total: 40+ points.

White has approximately 10~15 points in the lower right and left sides. Plus the komi. The question is whether White can consolidate 20~25 points in the center. This seems feasible, but Black will make an attempt to neutralize White’s large territorial framework in the center. During that process, each side will strive to prevent the other from attaining their goal, while taking more territory than the other at the same time.

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Figure 3: Black Plays Simple and Easy Moves (61-90)

Black 61 is a solid, conservative move. It puts more pressure on White’s group in the lower left, but does little to counter White’s large territorial framework in the center. I had expected Black to play on the point to the left of 64. Black 61 indicates that Black believes the game is comfortably under control.

In response, White 62 attempts to extend the large territorial framework to the greatest extent possible.

Unconcerned, Black makes the extension to 63 to securely take territory on the right side.

White 64 goes all-out to enlarge the large territorial framework. White’s position is thin, but White aims to next play on the point one point above Black 63 and one point to the left of that. A White move on that point works ideally with White 62 (being a knight’s move from that point) and White 64 (being a large knight’s move from that point). The problem is that White will be hard-pressed to get that move in. White is playing all-out while Black keeps comfortably ahead by playing simple and easy moves.

But then Black plunges deeply into White’s large territorial framework with 65. Does this seem risky to the reader? And what is the purpose of this move?

First, the move is not risky at all. In fact, it is a probe (in Japanese, yosu-miru) to test White’s response. If White attacks this stone too vigorously, White’s surrounding positions can come under attack, such as the group in the lower left corner. The move also aims at the cutting point two points above 84. That is why White counters with 66. Rather than having to capture a Black cutting stone in a ladder, the stone can be captured in a loose net (geta).

However, White has to protect the cutting point after all with the move of 70. The sequence that follows shows White walking a tightrope to keep all White’s stones working together, while Black takes the opportunity to make thickness through 87 to control the flow of the action.

Note how Black 85 defends both of Black’s groups above and below. This is the most effective way to play and the reader is urged to tuck this technique in the reader’s memory for use in similar situations.

Black 89 moves even deeper into White’s large territorial framework, but there is nothing White can do about it because of the thinness of White’s two stones in the center. Instead, White plays the knight’s move of 90 to give support to those stones from a distance. This move also begins to isolate Black’s stones to the left.

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Figure 4: Black Lives Easily (91-120)

I thought that Black would play 91 one point below this. Shows how much I know. But this is the value of studying the games of top professionals. When you guess the next move and compare that to the course of the play, you get insight into what you need to do in order to improve.

Here, I now see that Black 91 coordinates well with the stone below 111. That connection is more important than what I believed: that Black should try to connect with the group in the lower right. What Iyama perceived and I did not was that Black’s group can live easily independently. That leaves the Black group in the lower right the freedom of action that will allow it to develop even more profitably.

White attaches at 92 in response. This might seem to be a severe move, but it appears to violate a go proverb: Do not attach against weak stones. Rather, it proves that Black’s stones are not weak at all. Black counterattacks with 93 and White does not have any good follow-up move. White temporizes by exchanging 94 for Black 95, then switches to play the attachment at 96.

This follows still another go proverb: If one wants to attack on the left, first play on the right. In Japanese, this is called motare, or a leaning attack, i.e., a player leans on the opponent’s stones on one side to gain leverage to attack on the other side.

Naturally, Iyama knows exactly what is happening and attaches at Black 97 to secure the life of the group here. With the moves through Black 109, the group has two eyes. Then, instead of answering the White atari of 110 by connecting at 92 to make unequivocal life, Black pushes at 111, which indirectly does the same thing.

However, in the midst of this sequence, Black even has time to go back and play at 103. Again, this demonstrates that Black is in control of the tempo and pace of the game. All that White can do is to respond with the makeshift sequence from 104 through 118 to draw things out.

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Figure 5: Closing Up Shop (121-150)

It might be hard to believe, but the game has already entered the endgame. In Japanese, this is called the oo-yose, that is, the large point-value stage of the endgame. Black defends at 121, but then ignores the forcing move of White 122. Many amateur players would connect in reply at the point above 121, but playing Black 123 is better. Let me explain why for the benefit of kyu players.

Say that Black answers White 122 by connecting at the point below this. White then blocks at the point above 123. This forces Black to make life for the group by playing at the point two points above 123 and one point to the left. This is painful for Black, being pushed around by White. And for what? Is it worth it to save the two Black stones?

Even after Black plays at 123, White does not cut at the point above 121. Why not? Because that move is only worth 5 points (the two black stones and the points they occupy, plus the point above and to the right of 122). At this stage of the game, 5 points is too small. Look at the move that White plays next instead: the block at 124. This captures a Black stone and the points surrounding it. Surely it is obvious that this move is bigger than capturing Black’s two stones.

However, Black hardly notices this. Jumping into White’s large territorial framework (moyo) with Black 125 is a very big move, much larger than 5 points. Actually, White’s position here can hardly be called a large territorial framework anymore. Not only that, but Black adds insult to injury by capturing a White stone with the moves through 133.

White captures Black 131 with the moves through 136, but this is practically meaningless since Black gets in the moves at 135 and 137 at the same time. These might be called equivalent options, that is, basically the size in terms of points. From here on, that is all that is left on the board. For instance, when White extends at 138, Black 139 is worth about the same.

By the end of this figure, the oo-yose is over. That is, the point value of the endgame moves that are left on the board are of a smaller size now. Pop quiz: Can the reader evaluate what that point value is?

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Figure 6: A Ko in the Endgame (151-180)

Black connects at 151. As stated before, this move is worth 5 points. So that is the value of the endgame points on the board in this position.

What this means is that the board can be counted accurately. Professional players do this continually over the course of a game, and here both sides knew within a point or so exactly what the score was.

Black plays 163 through 167 to reduce White’s territory, but also to challenge White to try to capture the stones. This can only be done with White 172 through 178. The end result is that a ko is produced.

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Figure 7: Winning and Losing a Ko (181-210) Black 185 takes ko at the marked stone; White 188, same; Black 191, same; White 194, same; Black 197, same; White 200, same

The ko fight builds in intensity in this figure. But this is a fairly straightforward ko fight. There are no serious complications that must be taken into consideration.

Consequently, a swap (furi-kawari) occurs, with White winning the ko in exchange for giving up four stones in the lower left with the moves from 182 through 204. This is almost an equal result for both sides. But in regards to this outcome, White is satisfied to ends in sente and can block at 210.

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Figure 8: Playing Out the Last Moves (211-240) White 238 captures at the point of the marked stone

It should be clear by now that the game is over. Even amateurs watching on the sidelines in Japan must have known that. The players just finished out the game as a formality. Cho, playing White, must have just been sitting back with a warm glow inside himself, knowing he had just won the Meijin title. Facing him across the board, Iyama played the moves out to avoid resigning directly.

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Figure 9: To the Bitter End (241-271) White 256 captures ko at the point of the marked stone; White 264 connects at 253; Black 271 connects below 265

There is nothing left to analyze. Cho was now the new Meijin, while Iyama could only look back over the chances lost over the course of the match with chagrin and regret.

271 moves. White wins by 4 1/2 points.

Those who wish to comment on the opinions expressed here may send their thoughts to info@GoWizardry.com. The most interesting responses will be addressed in future postings.

Robert J. Terry

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