Sunday, May 29, 2016

Part 11: Reactions worldwide and prize giving

[NL Versie]

Reactions and prize giving

After the end of the fifth and last game, the final outcome of the Google challenging match is: AlphaGo defeats Lee Sedol by 4 - 1. A result that only a small minority (< 10-15%)  of the more than 280 million people worldwide who watched this match online, would have predicted in advance. 

AlphaGo deeply impressed Go players from all over the world with rock-solid, balanced, profound, sometimes unexpected, new and really wonderful, brilliantly effective moves in these games. 

During the post-match press conference Lee Sedol said: "I am sorry because the challenge matches have come to an end. I also feel sorry because I wanted to gain a victory, but was unable to do so. In this match, I started out in the first half feeling that I had the upper hand. But, the fact that I still lost makes me think that it showed my inadequacies, yet again.... Yes, I think it was a match that once again exposed my inadequacies. Although there are many reasons to feel sorry on a personal level, I really want to give my deepest thanks to everyone who cheered for me and encouraged me. I will try harder to show an ever-improving Lee Sedol. Thank you".

And later on he added: "I like to say a few more words. It was regrettable but I enjoyed it. This is not a defeat of human beings, it clearly showed my weaknesses but not the weakness of humanity. Once again I would like to thank DeepMind for this wonderful opportunity". 

Though Lee Sedol has lost this match, he fought like a tiger, as best he could under the enormous pressure and media attention. And he stayed true to himself in spite of everything, accepted his mistakes and didn't lose his respect and humility.

Answering a question about whether the five games might have changed his understanding of the game of Go, Lee Sedol responded: "Basically, I don't necessarily think that AlphaGo is superior to me. I believe there is still more that a human being can do to fight against the AI program. That's why I felt a little bit regrettable because there is more that a human could have shown during this match".

And to a question about his experience of play against AlphaGo as compared to his playing against professionals: "Obviously playing AlphaGo is different from playing human professionals and the style that it uses and also the ambiance, everything was completely different from what I was used to and in the beginning I was having difficulty getting used to that. If I had the opportunity to play AlphaGo again I'm not sure if I would be able to win and catch up to AlphaGo. What concerns Go skills, I don't think AlphaGo is superior but when it comes to psychological factors I think, yes, that AlphaGo is definitely superior. AlphaGo is not intimidated by strong wonderful moves".

Demis Hassabis summarized the match: "It has been an absolutely mind-blowing and overwhelming week for our team. I thank Korea for welcoming us with so much passion, warmness, and enthusiasm for the game and for this match.  I would like to express my immense admiration for Lee Sedol's unbelievable fighting spirit and the creative genius he demonstrated throughout the whole match. How able he is to close up his abilities and his skills.  We have seen incredible games of Go and there will be some moves that will be discussed for a long time: move 37 in game 3 and move 78 in game 4. And of course in today's game which was the most exciting game of all".  

He continued: "I hope and think that the popularity of Go has increased around the world, especially in the West because of this match. It has been on the front paper of all the western papers and news outlets as well as of course in Asia. We have been told that more than 100 million people have been watching the match. The deepest and most profound game that mankind has ever devised which is Go". And after expressing his pride and thanks to the DeepMind team: "Many thanks to Lee Sedol for this greatest, once in a lifetime event of our lives". 

David Silver, head of DeepMind's AI development team, added: "everything that happened during this match exceeded our expectations. In terms of the enthusiasm on the spot this is really a profound moment for all of us".

Commentator Chris Garlock, who commented all games of the match live together with Michael Redmond (9p), remarked: "This match has triggered unprecedented global attention to the game of Go. We could not have asked for a more wonderful or generous gift to this game. The five historic and beautiful games of this once-in-a-lifetime challenging match will be studied over and over again in the years to come, launching what I'm sure is going to be a new era in the most ancient of games. I'm really looking forward to that". 

Lee Sedol concluded: "Enjoyment is the essence of Go. I do wonder whether I've always been enjoying the game but I do want to admit that yes, I did enjoy the games against AlphaGo. Creativity of human beings and also all the traditional and classical beliefs that we have had, well I've come to question them a little bit based on my experience with AlphaGo. So I've more studying to do down the road ...". 

This has been a most exciting, fascinating, instructive and downright breathtaking match. And though AlphaGo has been able to win with clear figures, there is a lot of thought in each of the five historic games and the explanation of the why and the how of many moves. 

In the fourth game, Lee Sedol played a brilliant move that has been identified worldwide as: "Lee Sedol's masterpiece", "a God's play", and "Lee Sedol just fought the 1000 years history of Baduk" by several top Go profs. At least one game in which Lee Sedol stunned and crushed AlphaGo, and managed to set the program straight! 

Prize Giving Ceremony

During the prize-giving ceremony, Hong Seok-Huyn, chairman of the Korean Baduk Association and president of International Go Federation, thanked the AlphaGo team for their wonderful program and congratulated Lee Sedol for his fighting and putting up such a brilliant match against AlphaGo:  "He sincerely, truly showed us the ingenuity and intricateness of a human being during the past week to the entire korean people". 

He continued: "There have been over 30 million views of the korean live stream of the match. Whether they play Go or not, they paid their attention to this Google DeepMind match and not just for the game of Go but also were mesmerized and also surprised by the extremely high level of AlphaGo".  

Then he handed the official honorous 9p certificate to David Silver as a special gift from the KBA in recognition of AlphaGo's extraordinary and remarkable skills in the game of Go during this match. Therefore, the program officially is the youngest 9 dan pro in the history of Go. 

Finally, he presented one more special gift from the KBA to both Demis Hassabis and Lee Sedol: a glass artwork designed by a Korean Go fan who was inspired by the 78th move of the fourth game (the design incorporates the patterns of the move).  

Demis Hassabis handed over an envelope and a framed photo of the playing room of the match to Lee Sedol. Then, Lee Sedol signed --live-- with a marker the Go board they used for the five games, as a special present to the AlphaGo team, and handed this to Hassabis. A players autograph signature on a Go board has the very special meaning to appreciate your opponent's achievements, in this case by the entire DeepMind team behind AlphaGo.

Reactions by the public

Prior to the match a club player said: "if AlphaGo wins, the glow of the game is a little played out don't you think?". Reactions among Go players worldwide are essentially the same: the vast majority is beaten up and still can't believe it, others are still with complete amazement, incomprehension, bewilderment and wonder. All process in their own way the stunningly strong, aggressive, forcing and constructive style of AlphaGo's playing. It is almost like a new kind of heavy tooth pain and many shall just have to become used to it. 

Journalist for the Korean Times Baek Byung-yeul stated: "The historic five-game go match between Korean grandmaster Lee Se-dol and Google's AI program AlphaGo has placed the ancient board game under the spotlight". Also, the worldwide sales figures of Go books and material have exploded during the period of the match. For example, the biggest Korean supermarket Lotte Mart sold over 60% more Go sets in the week preceding the match, as compared to the same period last year. Auction, the Korean equivalent of eBay,  saw a similar increase in the sales of Go games with more than 40%. Alladin, a local Korean online bookshop, recorded a 150% rise in it's sale of Go books.  

China's top player Ke Jie, who currently has the highest Elo Go rating of the world, claimed during the match that he would be able to defeat AlphaGo, but that he rejected playing against the program because he was afraid that AlphaGo "would copy his style". As the match was proceeding he noted however, after careful analysis of the first three games, that it was most likely that he would have lost. 

Many top Go players considered AlphaGo's unorthodox style of playing as apparently questionable and dubious, and had their doubts regarding some moves by which they initially were perplexed and totally amazed but that did make a lot of sense afterwards. And about one unexpected fact all top profs did agree on: AlphaGo's play undeniable has been greatly strengthened in comparison with the Fan Hui match. 

So the most spectacular, remarkable and pioneering match in the history of the most ancient of games has come to an end: the Google DeepMind challenging match where AI program AlphaGo  defeated top Go professional Lee Sedol (9p), who has been at the top of the world league for more than fifteen years.

Recently, Yang Jae-ho the secretary general of the Korea Baduk Association, has asked Google for a rematch between the world top-ranked Go player Lee Sedol and AlphaGo, according to The Korea Times: "We want the return match to happen in around three months. We don't know if Lee will accept the rematch. If he doesn't, we will look for another top player". A spokesman of the KBA told the Korea Times however that the proposal was made without discussing the matter with the association. Google has made no decision yet.

Impact of the Match

What worldwide long has been regarded as the most outstanding grand challenge for artificial intelligence, namely mastering the game of Go by computer programs, may have become a closed down chapter with this match. A chapter of searching for more than half a century, inventing new algorithms, translating go principles into manageable concepts for computers, and the development of ever improving programs with only one single goal: playing without handicap against humans without completely being swept off the Go-board.

AlphaGo's overwhelming wins are and will be seen internationally as a landmark moment for (and a breakthrough in the history of) artificial intelligence. Apart from the enormous increase in the global interest for playing Go, with AlphaGo's justified successes and complete triumph at Go, also the worldwide attention on applying AI algorithms to the most complex problems has grown exponentially. 

And to quote Michael Redmond (9p) after Lee Sedol lost the third game of the match: "I think it is fair to say that it beat Lee Sedol at his own game. What I see in AlphaGo is the potential when it plays new moves as it did in the 2nd game, it's potential to inspire Go players to perhaps study a different type of opening moves. I think we could have a revolution of the years coming up with AlphaGo helping us, giving us a boost to start it. I like to characterize today by my believe that the AlphaGo team created a true work of art".

The after-effects of this incredible and historic match will undoubtedly last a very long time. The shock is big also to non Go players: this is the first computer program ever that has managed to defeat one of the strongest Go profs of the world in a level-playing game. 

Sunday, May 1, 2016

Part 10: Review of Game 5: AlphaGo unfamiliar with common tesuji in ultimate moyo game (The historic match of deep learning AlphaGo vs. Lee Sedol)

[NL Versie]

Review of Game 5:  AlphaGo unfamiliar with common tesuji in ultimate moyo game  

Professional  Kwon Gap-yong (8p), who also has been a mentor to Lee Sedol, said before the game: "Lee has already learned that AlphaGo tends to make strange moves when it faces unfavorable conditions. Lee will have more of a chance of winning the final match if he makes key moves that are difficult to read".

In the fourth game, Lee Sedol exposed some of AlphaGo's weaknesses in judging the amount of aji in the program's center moyo. When analyzing the game afterwards with his team, in the exhilaration of victory, Lee Sedol must have concluded that AlphaGo's moyo treatment had been far from optimal and could be put through the mill once again this last game of the match.   

AlphaGo starts off with a probing move (yosu-miru) to see how Lee Sedol will answer (circle in Dia. 1). On that basis white will determine if and how to complete the joseki in the bottom right. 

Dia. 1:  Game 5, after white 12 (circle, Lee Sedol is black) 
Black replies calmly, then plays tenuki to prevent white from making a double extension to the right (circle in Dia. 2). Lee Sedol presents AlphaGo with a choice: clamp and allow black to attack the three white stones in the bottom right, or try to fight and prevent black from connecting underneath?

Dia. 2:  Game 5, after black 17 (circle, Lee Sedol is black) 
AlphaGo chooses to clamp and makes a base for it's three stones in the upper right (see Dia. 3). Then both sides cut and AlphaGo ends in sente as Lee Sedol connects his attacking stones underneath (circle in Dia. 3).

Dia. 3:  Game 5, after black 25 (circle, Lee Sedol is black) 
Black gets a rather large and secure corner in exchange for white's strong and balanced group at the right edge. After moves on the left, where Lee Sedol builds a solid group and white makes a well-balanced extension from the bottom left corner (Dia. 4), AlphaGo plays to make influence towards the center and to build potential in the bottom left quarter of the board (circle in Dia. 4).

At this point, it is completely unclear how many points white's move is worth (how much it could add up to) but in any case this move works well with white's other stones on the board.  And pushes Lee Sedol to prevent that AlphaGo will play nobi or keima downwards to further build it's moyo. 

Both Lee Sedol and AlphaGo play a very solid opening and after move 40 (circle in Dia. 4) the outcome of the game appears completely open from their opposing moyo and territory strategies.

Dia. 4:  Game 5, after white 40 (circle, Lee Sedol is black) 
Lee Sedol avoids that AlphaGo will foreclose the bottom right corner and extends his corner (Dia. 5). AlphaGo calculates that it's three stones have enough aji to make a fight meaningful. The program apparently is unfamiliar with a  common tesuji (also known as the 'tombstone squeeze': you offer two stones, subsequently throw in another one, in order to rob the opponent efficiently from the inner liberties).

This tesuji frequently occurs in the games AlphaGo originally has been trained on, so it is quite incredible that the program didn't learn to handle this tesuji correctly. AlphaGo looses points here (as well as ko threats), apart from the unnecessary waste of options to utilize the potential aji  of it's three white stones (Dia. 5).

At this point in the game, Demis Hassabis tweeted: "AlphaGo made a bad mistake early in the game (it didn't know a known tesuji) but now it is trying hard to claw it back... nail-biting". He added later: "The tesuji itself appears quite often in pro game records, thus it is most likely learned through the 'policy' network. I personally feel AlphaGo should be aware of the tesuji itself, but Lee Sedol's follow-up move was probably better than expected by AlphaGo". He bites his nails and hopes that AlphaGo very soon gets a chance to make things right again (Dia. 5). 

Dia. 5:  Game 5, after black 59 (circle, Lee Sedol is black) 
Fortunately for AlphaGo, it played these moves in territory already more or less realized by Lee Sedol, and it has a few sente moves on the outside that might come in handy later if white wants to make points there. 

Dia. 6:  Game 5, after white 70 (circle, Lee Sedol is black) 
White especially focuses on influence and, after a few moves in the upper right corner, a battle develops for AlphaGo's meanwhile firm center moyo (Dia. 6). 

Lee Sedol invades to pressurize AlphaGo further in the upper left corner and to reduce AlphaGo's potential center moyo at the same time (triangle in Dia. 6). However, AlphaGo plays a beautiful and effective response which turns around the flow of the game immediately. Now, Lee Sedol is put himself under very high pressure (circle in Dia. 6).

AlphaGo's move prevents black's invading stone to connect easily with black's group to the left, prevents an escape of the invading stone to the center to make eventually a base there, forces the invading stone towards white's strength top right, and firmly contributes to it's built up sphere of influence in the center. Moreover, the idea is that if Lee Sedol tries to live, AlphaGo can exert huge pressure on him to become strong on the outside (to reinforce it's moyo even further, see Dia. 6). 

Dia. 7:  Game 5, after black 81 (circle, Lee Sedol is black) 
There's no other choice for Lee Sedol than to create a base. But in exchange AlphaGo gradually continues the work on it's moyo (Dia. 7). AlphaGo keeps pushing Lee Sedol's group and ends in sente, then builds further on it's moyo at the bottom side (triangle in Dia. 8). 

Dia. 8:  Game 5, after black 91 (circle, Lee Sedol is black) 
In a complex middle game Lee Sedol is forced to find efficient ways to prevent AlphaGo from cashing in it's entire moyo. The question is whether AlphaGo can make enough points in the center to outweigh Lee Sedol's already secured territory in the corners (Dia. 8).

Black has about 70 points secured territory, white has about 30 points together in the upper left corner and it's center moyo. Taking 7.5 komi into account this means that white can only win this game if the program gets at least 35 points in the bottom left corner and edge (without giving black any extra compensation for this). Alternatively, white has to find ways to collect additional points in the center. This crude estimate suggests that the game in this position is still open and undecided.

Dia. 9:  Game 5, after white 122 (circle, Lee Sedol is black) 
The game is developing slowly as Lee Sedol first somewhat contains AlphaGo's center moyo, and then creates  a group in the bottom left (Dia. 9). With white's calm responses initially some strength is built though it is unclear what white does want with this. After AlphaGo's extension (circle in Dia. 9) it becomes clear, however, that Lee Sedol has to make a base with his group at the bottom side (or must connect). And that white is trying to lock up black.

Dia. 10:  Game 5, after white 136 (circle, Lee Sedol is black) 
Black connects his group underneath with the right corner and gains some extra points while white builds some force and meanwhile significantly reduces black's influence at the lower right. Then, AlphaGo plays a magnificent split move and nice counter attack (circle in Dia. 10) that adds burden on black and let's white stones working together optimally. 

It is difficult for black to decide what is the best strategy in this position. Lee Sedol can't afford to give up his center stones and at the same time has to minimize white's center moyo as much as possible. AlphaGo's strength at the lower side is being used primarily to keep pressure on Lee Sedol with a range of possible cut actions.

Dia. 11:  Game 5, after black 183 (circle, Lee Sedol is black) 
A comparison between Dia. 10 and Dia. 11 shows that black succeeded to neutralize both white's potential on the left and a significant part of white's center. However, in exchange white gets about 15 secure points as compensation. Whether these are enough for AlphaGo to win the game is unclear, especially as Lee Sedol has still opportunities to further reduce white's potential (both on the left side and in the center). The difference is estimated to be a few points at most for the benefit of AlphaGo (Dia. 11). So, despite Lee Sedol's great moyo reduction skills, it is still deep learning AlphaGo that is ahead due to the sufficient compensation it got along the way. 

What complicates this position is that black's territory is almost defined while white has opportunities to score some additional points at different locations on the board. Lee Sedol's only chance is to restrict AlphaGo's potential as far as possible with smart and effective reduction moves.

For the top Go-profs who comment live on this game, it is hard to say where Lee Sedol perhaps played a lesser move. Even so, AlphaGo managed somehow to get things right after it misjudged Lee Sedol's tesuji earlier in the game. Overall, the flow of the game as well as the way of play of both players looked very well-balanced, constructive and profound.

Dia. 12:  Game 5, end position after white 280 (Lee Sedol is black) 
In the next 100 moves, Lee Sedol unfortunately is not able to catch up his disadvantage of about 2 points. A few minutes before the game is finished, Lee Sedol leaves the Go-board when AlphaGo plays a move that is clearly non-optimal: a sign that the program estimates it will win this game anyhow. Despite the fact that Lee Sedol is ahead on the board, he would loose with about 2.5 points, taking into account AlphaGo's komi (7.5 points).

When he returns, Lee Sedol plays another couple of moves and then resigns after move 280 (final position, Dia. 12) with just less than a handful of endgame moves left. It is the first time in this match that a game has been played until so late in the endgame. And has ended with such a small difference in points.

So this has been another amazing, inspiring, and historic game in which differences in playing strength between the world's top Go-prof Lee Sedol and deep learning program AlphaGo were hard to detect.

With this result, the final outcome of the match is: AlphaGo defeats Lee Sedol by 4 - 1. A result that only a small minority (< 10-15%)  of the more than 280 million people worldwide who watched this match online, would have predicted in advance. AlphaGo has impressed all Go players worldwide with rock-solid, deep reading, sometimes unexpected and really wonderful, effective moves in these games.

During the post-match press conference (never seen so many press and media gathered together), Lee Sedol said: "I am sorry because the match comes to an end". And answering a question about whether the five games might have changed his understanding of the game of Go, Lee Sedol responded: "Basically, I don't necessarily think that AlphaGo is superior to me. I believe there is still more that a human being can do to fight against the AI program. That's why I felt a little bit regrettable because there is more that a human could have shown during this match".

Hassabis stated afterwards: "I am speechless about this most exciting experience we have had so far. AlphaGo made a mistake early in the game because it missed a tesuji. But got itself back into the game. This is by far the most exciting and stressful one of all the games of the match". 

It took Lee Sedol about four games to slightly figure out AlphaGo's way of play: the first two games Lee Sedol probably lost by making a bad strategy decision, the third game Lee Sedol lost due to a fatal mistake already early in the opening, and with the knowledge of the fourth game, it is highly probable that Lee Sedol would have followed other tactics. And would have had a significantly greater chance of winning this match.

A more extensive report of the press conference after the end of the fifth and last game of this match, with more detailed reactions of Lee Sedol and Demis Hassabis, will follow later.

In this fifth and exciting last game of the Google DeepMind challenging match, deep learning AlphaGo played an impressive and very balanced moyo-building game. Even though Lee Sedol had substantial (secure) territory already early in the game and though he was able to thwart most of AlphaGo's moyo plans, the program succeeded in getting enough compensation along the way to stay ahead by a margin of just a few points. And to maintain this small advantage during the second half of the game.

[Part 11: Reactions worldwide and Prize giving]

Friday, April 29, 2016

Part 9: Review of Game 4: Lee Sedol's brilliant move reveals weaknesses AlphaGo (The historic match of deep learning AlphaGo vs. Lee Sedol)

[NL Versie]

Review of Game 4:  Lee Sedol's brilliant move reveals weaknesses AlphaGo

After Lee Sedol went under in the match against AlphaGo with three successive losses, and after his mental succumb under incredibly high psychological pressure yet early in the third game, the main question is what Lee Sedol still has up his sleeve when trying to defeat AlphaGo.

And how unimaginable resilient, persistent, and believing in himself Lee Sedol must be, after the new sledgehammer blow of the third game, to try to collect himself, to show that he is able to deliver, and to prove all humanity is right?

The opening of the fourth game is the same as that of the second game (in which Lee Sedol had white also) up to move 12. Lee Sedol response to AlphaGo's probe move (yosu-miru) in the bottom left corner is aggressive (triangle in Dia. 1), attacking both the black stone on the left and black's probing move. 

Dia. 1:  Game 4, after black 25 (circle, Lee Sedol is white) 
Lee Sedol forces AlphaGo to make a choice but the program simply plays somewhere else (tenuki, circle in Dia. 1). With a shoulder hit black first wants to see how things develop in this area before deciding how to answer white's double offensive (triangle in Dia. 1).

Dia. 2:  Game 4, after black 35 (circle, Lee Sedol is white)
Lee Sedol concentrates on taking territory in the edges and bottom corners while AlphaGo conquers the upper side and builds influence in the center (Dia. 2). Lee Sedol follows the amashi strategy: the amashi player takes territory in exchange for influence, and hopes to withstand the outside power and attacks later.

Dia. 3:  Game 4, after black 47 (circle, Lee Sedol is white)
When Lee Sedol tries to neutralize AlphaGo's strong center influence (triangle in Dia. 3), AlphaGo completely ignores his move and plays another shoulder hit at the right side (circle in Dia. 3). Again, black wants white to answer before deciding about attacking white's center group.

When black cuts off the four white stones in the upper center (triangle in Dia. 4) and white extends (circle in Dia. 4), a complex and ambiguous fight develops. AlphaGo heightens the tension and forces Lee Sedol to act with his center stones to prevent that black cashes in the influence built in the center. 

After white's extension (circle in Dia. 4), black's stones on the middle right comes under very severe pressure. How is black able to involve these stones in the game without weakening it's earlier investments in the center?

Dia. 4:  Game 4, after white 64 (circle, Lee Sedol is white)
AlphaGo's last move (triangle) cuts off the white group in the center.
Since multiple important and large-scale fights make it much harder for AlphaGo to judge the board position correctly, these are the ideal and complex battles to initiate for Lee Sedol.

Where to play next, is a matter of 'looking' forward at least 20-25 moves in this ambiguous fight in the center and right edge. Lee Sedol's fabulous intuition and immense skills in assessing all options and starting points in such explosive positions, are herewith invaluable (Dia. 4). Both AlphaGo and Lee Sedol have to rely on a very crude estimate of how the position may develop gradually.

Black decides to leave his stones at the middle right hand side and further strengthens his moyo to increase the pressure on white to the very maximum. For Lee Sedol it seems virtually impossible to do something  sensible with his center stones. After he cuts to make the position more complex (triangle in Dia. 5), AlphaGo answers confidently and seals off any escape routes towards the center (circle in Dia. 5).

Dia. 5:  Game 4, after black 73 (circle, Lee Sedol is white)
Although black has substantial weaknesses at both moyo edges, the white center stones appear to cooperate rather loosely and creating a living group is there out of the question. Also, to escape is not an option for white with such a majority of black stones awaiting him (center and bottom). Moreover, the aji of black's group in the middle right complicates an eventual white escape (Dia. 5).

In short, it looks like this once more will be a major victory for AlphaGo: white's position seems completely hopeless. But then Lee Sedol puts forward a completely unexpected, wonderful, and brilliant move that suddenly sets the entire board on fire.  All white center stones are activated at once and do cooperate effectively by exploiting the aji in black's center moyo in all conceivable means (Dia. 6).

Dia. 6:  Game 4, after white 78 (circle, Lee Sedol is white)
Lee Sedol's move just dropped out of the sky, both for all live commentators and the many top Go-profs that closely followed the game.  It unites all Lee Sedol's power, skills, perseverance, creativity, intuition, willingness to fight and to seek reprisal for all frustration and powerlessness in the previous three games. When seeing this move during the live commentary in China, top Go-prof Gu Li (9p) described Lee Sedol's move 78 (triangle in Dia. 6) as a "God's move". 

With black 79, AlphaGo fails to play the best response and what happens is a sequence of moves that the program calculated as the strongest answers. In exchange for it's group lost on the right, AlphaGo just gets a poor sente move that the program also could have played immediately (Q13 in Dia. 7).

Dia. 7:  Game 4, after white 94 (circle, Lee Sedol is white)
Commentator Michael Redmond (9p) showed that instead of black 79 much better responses were possible than AlphaGo actually played in the game. In the end, AlphaGo has to give up the stones in the middle right, so that Lee Sedol not only has secured his group and largely destroyed black's center moyo but in addition cashed in a pile of points on the right. 

With move 110 (circle in Dia. 8), white secures his relatively weak stones in the center by attacking the black group on the left (center). In this manner, white creates enough options to connect with the group in the bottom left in case of emergency. 

Direct comparison of Dia. 7 and --more than thirty moves later-- Dia. 8 immediately demonstrates that white has achieved the unimaginable: it is as if white's invading center stones were able to escape through an invisible tunnel (David Ormerod). Lee Sedol efficiently utilized the aji in black's center that he correctly estimated 25 moves earlier.

Dia. 8:  Game 4, after white 110 (circle, Lee Sedol is white)
With this successful center fight, Lee Sedol takes a clear lead. The South Korean live commentators cannot hide their excitement when it becomes clear that Lee Sedol --after three hours into the game-- probably will notch a win. 

There is nothing left to AlphaGo other than to secure it's group on the middle left and to allow that Lee Sedol meanwhile connects his center group --in sente--. Then white further erodes black's center by connecting the three white stones on the upper side. Black's entire moyo has been neutralized (Dia. 9).

AlphaGo tries to catch up with active play but Lee Sedol plays magnificently sharp. An example of this is Lee Sedol's counter move in Dia. 9: white ignores black's threat at the bottom right corner and plays a larger counter threat (circle in Dia. 9; that also prevents black's sente moves in this area). 

Dia. 9:  Game 4, after white 136 (circle, Lee Sedol is white).

Another example is Lee Sedol's ignorance of a big endgame move by AlphaGo (triangle in Dia. 10) which he replies with an even more binding move (circle in Dia. 10).

Dia. 10:  Game 4, after white 146 (circle, Lee Sedol is white)
About twenty moves later, AlphaGo threatens with a pointless dame point to cut off white's meanwhile large center group (triangle in Dia. 11). In response, Lee Sedol plays a big endgame move settling his group at the same time (circle in Dia. 11). If AlphaGo would have played here first, the program would have gained several points --in sente--. Thus, with this move (triangle in Dia. 11) AlphaGo in fact resigns.

Dia. 11:  Game 4, after white 168 (circle, Lee Sedol is white).
Obviously, AlphaGo's logic is not optimal anymore at all since it plays many forcing moves generated by the meager potential that the opponent might make a mistake (Michael Redmond). After playing a handful of doubtful moves and several mistakes that even lost additional points, AlphaGo resigned (Dia. 12).

Dia. 12:  Game 4, end position after white 180 (Lee Sedol is white). 
Dia. 12 shows the final position after Lee Sedol's move 180, nearly five hours into the game, at which AlphaGo resigned after it's notion that the probabilities of winning this game were falling below it's critical threshold of 10% for resignation. At this point, AlphaGo is behind at least 5 points (komi included) and therefore needs to make more than ~20 points in the bottom center area (without Lee Sedol getting any compensation for that) in order to catch up.

Even though Lee Sedol played under ultra-high pressure for more than one hour (from move 90 on), using his last byo-yomi period up to the max each move, he was able to maintain and solidify his advantage built up in the middle game. This is the first time that AlphaGo lost a game against a top professional Go player (in the official match games without handicap). Lee Sedol's great victory is an extraordinary and historic achievement which has led to the deepest respect and admiration from all over the world.

A Korean Go-pro stated: "Lee Sedol just fought the 1000 years history of Baduk and I am proud of him". An Younggil (8p) concluded that the game was "a masterpiece for Lee Sedol and will almost certainly become a famous game in the history of Go". 

Lee Sedol's win against AlphaGo shows --and does prove for the first time-- that deep learning AlphaGo does not play perfect all the time and sometimes has severe problems in judging correctly complex middle game positions. Despite the considerable pressure, Lee Sedol could play his own game and exposed a clear glimpse of AlphaGo's weaknesses.

During the press conference afterwards, the public and press were wild with enthusiasm and chanted: Lee Sedol!” ”Lee Sedol!” “Lee Sedol!. Several minutes flashing recorded a radiant, visibly overjoyed and genuinely pleased Lee Sedol: "I have never been congratulated so much just because I won one game. Winning this game is still valuable, the drive behind the win today is the trust and the compassion of you all. This one win is so valuable and I will not trade this for anything in the world". 

After the game Lee Sedol answered a question about his mental condition: "after loosing the first three games and thus the match against AlphaGo, I could not say that there was no psychological shock ... but it was not to the extent that I would have to stop playing the ongoing match because at any moment of the game, I really enjoyed the game. I can tell you that I've not retained any severe damage and I'm very happy to say that I won this single game".

And asked what Lee Sedol was thinking when he was played his brilliant move (move 78, Dia. 6): "I thought I would be able to gain some profit quite easily but that wasn't the case. It became more difficult than I had expected and at that point in time, at time of 78th move, that was the only move that I could see, there were no other moves, no other placement that I could think of. That was the only place I could place my stone, it was the only option for me, so I put it there. So I am quite humble for all the praise that I'm getting for that".

Demis Hassabis said: "AlphaGo made a mistake around move 79 but it realized it's mistake only after the 87th move, when it was too late to recover from. AlphaGo thought it was doing very well at the start of the complex center fight but was pressured by Lee Sedol in some mistakes. It is because of the incredible fighting spirit Lee Sedol showed that a creative genius like him is able to find out and exploit any weakness of AlphaGo. The loss by AlphaGo is very valuable: we will look at all the statistics and are looking forward to learn from these weaknesses and fix these problems".

David Silver, Google DeepMind's team leader, added: "We have designed AlphaGo to learn by itself by repeating self-plays. But such an algorithm must have holes in it that we cannot know about. Lee was able to push AlphaGo to expose such a weakness".

Lee Sedol concluded: "I believe AlphaGo has two weaknesses: when I made an unexpected move, AlphaGo responded as if the program had a bug, indicating that the machine lacked the ability to deal with surprises. Furthermore, AlphaGo finds it more difficult to win the game when it has black as opposed to when it has white. Therefore, I would like to ask Demis Hassabis and David Silver: 'would it be possible for me to take black in the last game instead of drawing lots?'". The answer was: "yes, it's fine"

This fourth game of the match was decided by Lee Sedol's profound and fabulous move in a complex middle game fight that forced deep learning AlphaGo to a sequence of mistakes. After this, the game was completely turned around and AlphaGo was unable to defend against all weaknesses exposed in it's center position. After three successive losses against the program, this game Lee Sedol clearly outperformed AlphaGo for the first time: a great and historic achievement by Lee Sedol.