The Divine Move?

I would call that a myoushu (妙手), a »brilliant move«, maybe even »miracle move«. In itself, I don’t think that this could be the narrative focus of a whole manga series, or the highest goal a go player could want to achieve.

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I like to think the divine move isn’t just a move but more so that its something every go player does when they are play the game. Every time they think about the game and show how much they love and care about the game it is a divine move!

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Or maybe… the divine move was the friends we made along the way?

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So does that mean that Yeonwoo’s motivation is Kame no Itte?

https://senseis.xmp.net/?KameNoItte

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This is just my personal way of thinking about it;

Imagine what the spectrum of all possible strategies of Go might look like. (In theory, some multi-dimensional space, but finite dimensional when we restrict to boards of bounded size)

On one end of the spectrum, there is the “random strategy”, which picks random legal moves (equidistributed). When we start playing Go, we start somewhere “near” this point. Of course we don’t play random moves, but we don’t have a grasp of what moves are good yet either.

As we progress our journey and communicate with other people, we may observe that there are increasingly many positions where we agree on what move to play. Intuitively it seems that our strategies are approaching each other. So do these paths converge? Is there a single strategy that we are heading towards? And that is the concept of “divine move” for me.

As a contrast here are some rigorous theoretical points. Under the right ruleset the tree of all game variations is finite, and thus it is possible to calculate which moves lead to an optimal result, although this is not practical of course.

In such a computation we would assume optimal play from our opponent. This means however that in positions where we are behind, i.e. every move fails to win, then every move would be considered optimal. So I believe that further differentiation between moves would be good to define “optimal strategies”, but I don’t know of a rigorous concept right now.

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See also: Divine move in everyone for my take on it and some ideas from others.

Are there any rulesets where the game tree is not finite??

Edit: well besides this one...

[1603.04751] Quantum Go

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Infinite-board Go without stone or point limitation rules~

Or a version of infinite-board Go where one player has to achieve a certain point lead to win, eg. playing until there’s a twenty-point difference.

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Most rulesets have some sort of superko rule, which prevents cycling through previous positions. If playing on a finite sized board, there are a finite number of legal positions and hence a finite number of variations in the game tree.

Japanese rules are a familiar example of a ruleset that does allow cycling and, in principle, an infinite game tree (even on the standard finite board). Under many balanced cycles (like triple ko or eternal life), the game should be eventually declared a no result, so those are still finite. However, there are also unbalanced cycles (such as sending two, returning one) that should not be declared a no result, and instead the game could cycle indefinitely through the same boatd position over and over again (however the game state is meaningfullly changing since one player is getting a net gain in captures). In practice, the player gaining captures should eventually break the cycle when they have enough points to cede that local position to the other player and still win, however, in principle, the players could continue indefinitely to make the score difference arbitrarily large, which could perhaps even be meaningful, if needed to overcome an extremely (and unreasonably) large komi. Of course, these would farcical variations, and one could eliminate these branches from strategic consideration.

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Oh I see. I thought Japanese games end in no result if someone “super-cycles”, but now I’m seeing that it’s more of a de facto rule than part of the ruleset. Cool!

“No results” are a part of the Japanese rules, but it technically requires both players to agree that it is a no result, which players should only agree to if it is due to something like a triple ko (or other balanced cycle).

In unbalanced cycles (like sending two, returning one) the player with the advantage could agree to end the game with no result, but strategically, they should not, and eventually break the cycle.

There are yet other cases, like double ko seki, where one player (maybe the one in a losing position and trying to waste time) could force the game to cycle, but the other player should not accept the no result.

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That would be kamo no itte, though. Kame no itte would be the hand of the turtle.

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Is komi no itte when white wins by fewer than 7 pts?

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蟇の一手

kama no itte, hand of the toad

Admittedly kama is apparently an obsolete reading.

熊の一手

kuma no itte, hand of the bear

駒の一手

koma no itte, hand of the horse

(another archaism)

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Let’s add クモの一手: hand of the spider.

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Other people have already answered better than I could, but just to add my own perspective, I consider “kami no itte” to be closely related to perfect play.

To a first approximation, we could say that Sai is striving for perfect play. Of course, it’s not realistic for any human to achieve, and presumably someone with a deep understanding of the game also understands this to some extent. But Sai probably isn’t much interested in the mathematical definition of perfect play. I think that even in modern times, most pro players aren’t familiar with the fact that there is an objective definition of perfect play (since knowing this is not at all useful to become stronger).

So maybe it’s more accurate to say that they strive to play a game where they don’t make any mistakes, by their own subjective definition of “mistake”. Or maybe they just want to play the best that they realistically can, to achieve their own potential.

And maybe even if they are perfectly aware of how far away real perfect play is, there’s nothing wrong with working towards it as a goal. Even I can think of perfect play as a goal I’m working towards, even though I won’t even reach pro strength in my lifetime.

So I guess what I’m really saying is that Sai’s conception of “kami no itte” fills a similar role for him that “mathematical perfect play” does for me: something to look up towards and be inspired/motivated by.

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The idea of a “perfect move” is fundamentally flawed. You cannot know what future plays your opponent will make. Indeed, the art of good Go playing is to make your opponent’s moves look silly.

Unless your opponent makes a large obvious mistake, games are won with lots of general multipurpose moves that support a well designed overall board strategy.

Isn’t a “perfect move” the one that takes into account all future plays your opponent could make? Of course it is not physically possible to know this move, but such moves certainly exist…

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I still have a problem with the idea of a single best move. You can’t completely evaluate how “good” a move is, until a position is settled or the game is over. You can play the best move assuming your opponent is also making the “best moves”, but that is a HUGE assumption when you are talking about 20+ moves later. An “unperfect” move could later end up being a ladder breaker that determines the fate of a group and the outcome of the game.

A tesuji is a good move that is also in some way unexpected or counterintuitive. This creates an emotional story with a single move, and every Go player has experienced this “tesuji” emotion, from one side or another of the equation.

The divine move as presented in Hikaru no Go is something like the pinnacle of tesuji in an emotional sense. All the moves that come close in the anime reveal deep reading and judgement, and the fact that the move was played says something about the strength and character of the player who saw the move. It’s a shocking and spiritual event. Take that to its limit, and the move becomes super human. The moment of joy and shock that we’ve all experienced when faced with a tesuji becomes a moment of transcendence. The perfection, in a technical sense, is secondary to the story of the move. That’s why Lee Sedol’s move sorta fits the bill, even if it’s “just a trick.”

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