Once a friend and I were watching two weaker players play go. White had developed a dominant territory in the middle of the board, but some of the border stones had a weakness and could be captured with a tesuji. We watched on the edge of our seats until black found the play, broke into white's center territory, and won the game. My friend congratulated the black player on finding the critical area and the game-winning move.

Of course white had chances earlier to protect that weakness and save the territory, probably winning the game. The tesuji wasn't particularly difficult for us observing, and arguably white's move before was the game-losing move. We usually describe go moves in this way, focusing on the game-losing mistakes. Hajin Lee said on one of her youtube videos that the normal way for pros to review a lost game is to work backwards trying to find the last place where the game was even or winning, to find the game-losing mistake. And for a professional this is a pragmatic way to improve - find what lost you the game so you can win next time.

Mistakes are easier to identify than brilliant plays. The concept of mistake is well-defined: there was another move on the board that gave a better result. But for almost any move any player plays, there will be many many worse moves on the board. What makes a great move? Intuitively it's a move that is better than the "normal" or "expected" move, but normal for who? If you've never seen the two-stone edge squeeze, it's a brilliant tesuji, unexpectedly throwing an extra stone away to turn the fight. But the hundredth time you see it in a problem book or on the board, you know to look for it. It's not brilliant, it's just the right move. In the same way, a move that blows my mind in a professional game might be normal or even unimaginative to another pro.

You might have guessed that the Alphago match put me on this train of thought, especially game 4. At the highest level of professional play, we expect pros to find the best move most of the time. Watching the pro commentary streams, both Redmond and Myungwan regularly predicted the moves of both Lee Sedol and Alphago. Those predictions suggest some consensus that it really was the best, or as close as we can tell. This creates a style of commentary where both players are playing "correctly" until one of them blunders. I feel like describing every move as either "ok" or "wrong" does some injustice to the players and the battle on the board. In some sense every move before the "game-losing move" is a "game-winning move". No one knows what the best moves are, and both players are struggling at each point to find the best play they can.

If god played go against itself, how many of the moves could we predict? Some of the moves would probably look obvious to us, others very surprising.
When fallible humans talk about the moves of other fallible humans (or computers), we do our best to describe the moves in terms we can relate to: dangerous battles, calm preparations, confident finishers. In strictest logic every move falls into two simple categories: winning against even the strongest resistance, or losing. But while we play we don't know which is which. I think a move could be "wrong" for an omniscient observer, but still clever, tenacious, or even brilliant. It is natural and pragmatic to think about game-losing moves. But while we are thinking about what we enjoy about go, I'd like to find a way to emphasize one of the best aspects of the game: the opportunity to play great moves.

Yes, I think this is generally a running theme in most board games at high level. For example, I play chess on a site where I can ask it to analyse the game afterwards, and it gives a number of moves that it considered inaccuracies (around -0.3 to -0.5 pawns), mistakes (-0.5 to -1 or -1.5 pawns -- I forget slightly the upper bound), and blunders (< -1.5 pawns). In general, when playing a decent game at my level, something like 3 inaccuracies and 2 mistakes is reasonably common, which means of the other 30-40 moves I might have played, the vast majority of them were moves the computer considered either optimal or very close to it. However, the game isn't decided by the good moves, it's decided generally by frequency and severity of the bad ones, and I would be very surprised if Go is any different. Certainly from my experience of viewing players and ranks, it seems that people's rank is determined far more by the weakest link in their skills, rather than their strongest.

Does it ever tell you that your move was better than what it expected?

Haha, not yet! Of course, I'm trusting its judgement quite strongly, but then on the whole I'm assuming it's a 3000+ ELO beast and at least knows what it's talking about more than I do. Generally, you can tell who won by who had the lowest "blunder" count, followed by the lowest "mistake" count etc (with the exception of being clearly ahead and then suddenly falling for a checkmate in 1 trap or something)

It would indeed be interesting if the engine was capable of predicting whether we would make a mistake in the next move.
Imagine playing a game with side information stating "59% probability of blundering in this move". Intimidating or eye-opening?

I saw some articles about catching chess cheaters who were using computers to help their play. They had some statistical techniques to know if a player was playing better than expected for their rank. I think it was more an average over many moves thing, rather than looking at individual difficult moves and saying that player shouldn't find this difficult move.

So when two professionals play today, are most of the moves they play optimal? Half? At least some of them will be, certainly by the late endgame I think pros probably play nearly optimally.

Something interesting related to this: for the winning player, there are many moves that will keep them winning, and in some sense the are all equally optimal. For the losing player, no move they make will let them win against the strongest resistance. So what is the best play? Are all the moves equally bad? We usually tell go players not to hope your opponent makes a mistake, but in this case isn't that all you can do?

Both in chess and go, I think the goal is to increase the possibility of error. In chess, if behind, it is common to seek positions where exact play by the opponent is still clearly winning, but where the 2nd or 3rd best moves start to lead towards equality. You try to create complexity that provides as much opportunity as possible for inaccuracies, and resign when the game reaches the point where it's no longer plausible for the opponent to fail to find "good enough" moves to still win.

Magnus Carlsen epitomises this in Chess - he has won numerous theoretically drawn endgames against other top grandmasters by trying to force the opponent to walk as precarious a tightrope as possible - if they walk it, the draw happens, if they wobble too much, he creates enough inequality that he starts grinding out the 40 moves towards a won position etc

Think of a game of tic-tac-toe. You're the circle player:
|b| |X|
| | |a|
|O| |X|

You can play at 'a', but then the X player can play at 'b', and win the game. This is a won game for the X player.

You can play out the game - maybe your opponent will make a mistake. Resigning is fine, too. Either option is equivalent if you are 100% sure that you are in a losing position.

In Go, the difference is that you are rarely 100% sure that you are going to lose. Combine this with the fact that your opponent might also may mistakes, and there is more reason to play out a game that you seem behind in.

In general, to maximize the probability of winning, I think you should play until you are sure that you won't win.

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be immersed

Not as optimally as they think they do. I gather this from being involved in some professional endgame replay tournaments. The players start from an endgame position and finish the game, then change sides and replay the game, adding their scores for each game together. The range in final scores is surprisingly large.

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The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Corollay: DDKs should never resign.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.