I agree with you about the diagrams you provided. I think that, for a pro, the diagram will look like the one in the middle. For an amateur, it will look like the 3rd one.

But the issue here is not how the graph looks, but where exactly is the flattening/tipping point of the curve.

All I know for certain is my own tipping point - which is probably somewhere around 1-2 hours beyond which my game degenerates into silliness.

I guess what we disagree about is the exact point at which the curve flattens for a pro. You seem to assume that for a pro it would flatten at around 3 hours per game - or at least there is no "proof" that it is otherwise. I assume that it would flatten much later than that, and that a difference between 3 hours and 6 hours would have a noticable effect. Although I also have no proof of that.

I guess without asking some pros, we really cannot easily decide who is right. Anecdotal evidence provided seems to indicate pros side with me rather than with you here. At least with respect to the quality of the game - which is different from winning chances.

So I keep thinking of my idea of asking two pros to play a game with different time limits - one has 3 hours the other 6 hours. If money was at stake, do you think this would be a fair contest? I think not. According to what you say, you would call it fair. It is hard for me to reconcile that.

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Longer time would favor one player. How does this relate to "game quality"? The player with more time may simply steer the game into a direction to exploit the time advantage as a metastrategy. I have a hard time understanding how this does or doesn't affect game quality. I mean, timekeeping is not a rule of go, it is an artifact of the practice of playing the game. The Great Go Player in the Sky would win under blitz conditions, but since her opponent may be a fallible human, the game quality could still be quite low, no matter how much time was given.

I don't know how to judge "game quality." The purported measure in this thread is number of mistakes, but this is only justifiable with the rest of OP's comments if we assume some correlation between novel, instructive play and mistakes under time pressure. This correlation is spurious on its own. You need only consider the advice to DDKs to use their influence for fighting more—their walls have died before and they still feel the sting of that, but we would say it was not the single outcome of that game that mattered, you can still trust me on this, please use your walls for fighting and not enclosing territory; which is to say, the quality of the game is not a reflection on the quality of any particular sequence, result, or application of a concept. If it were so, instruction would be literally impossible.

So what we are left with is the notion that the number of mistakes is itself some kind of measure of game quality. I simply can't agree with that. I have my own games that I found very exciting to review, and pro games that were horribly boring to review, and even though there be none who would say my game had a higher "quality" than the pro game in terms of some gimped notion of perfect play, it doesn't stop me from loving that game and going back to it sometimes to feel some measure of pride at how well I executed a plan—even when part of that execution depended on my opponent's mistakes which they faithfully made. How could amateurs ever muster the psychological force needed to play the next game, being of such low quality?

Bantari, I don't feel like we really disagree that much. I am not making the claim that 3 hours is optimal time for a pro to play. Rather, I claim that we don't know what the optimal time is to produce high game quality for a pro game.

My objection is to the belittling of modern time settings, since I still have faith that the current time setup is able to yield games of high quality. I don't feel that there is sufficient evidence that games from long ago with longer time periods produced higher quality games.

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be immersed

Regarding graph #3, this comment by Kap on the subject of Crazy Stone's blunder in its game with Hajin Lee may be of interest.

Well, ok.
But the underlying assumption of such strategy would be that the player with shorter time would make mistakes which he/she would not make if the times were equal. Q.E.D.

Otherwise, you could apply the same strategy in evenly-timed games.

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- Bantari
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You can still do this, since people manage their time differently (e.g. Go/Kitani).

Well, I can't really disagree with that.
The only thing I have is my gut feeling that the 3 hours are not enough and modern time controls are too short.

All in all, I find it more interesting than a point of contention.

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- Bantari
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Yes. And my feeling is that references here on the forum to "Mickey Mouse time limits", etc., may contribute to your gut feeling

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be immersed

I'm reminded of the episode of The Simpsons in which Homer changes his name to Max Power:

What was to be demonstrated to me is that such mistakes impacted game quality in some non-tautological way (where we don't just define game quality to be exactly the inverse of the number of mistakes^*). For sure, this is my general disagreement.

*_{Math fan alert: presumably in a non-field like the extended reals where we can divide by zero.}

No, they do not.
But common sense does.

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Sure, but still the underlying idea is that one side has less time left on the clock than the other.
And so in complicated situations, the side with less time will likely make more mistakes.
So the side with more time creates complications to benefit from the time difference.

Or am I missing something and this kind of "strategy" works completely differently.

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- Bantari
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I think it is not just the number of mistakes but also their seriousness. If you make 5 big blunders in a fast game, and 5 very subtle mistakes in slow game, I would classify the slower game to be of higher quality. But you are right - we might want to define it first.

Still, this is not a mathematical thesis that we are writing, just a discussion about personal opinions.

The premise is that, in general, given shorter time limits a player will make more mistakes, or more severe mistakes, or both. We already admitted that there might be certain limits beyond which this does not apply. For example: the game can be of the same quality if the time is 2 sec or 4 sec. On the other end, extending time limits from 60 hours to 80 hours might not matter neither.

I am not sure how you see it, to be honest.
What I am claiming that, taking it to the extreme, a 2 min game will be of lower quality than 2 hour game.
If you aagree with that, then we are already in agreement about the principle, we just have to agree on the exact tipping points for the time-vs-quality curve.

If you disagree, I would love to hear your rationale for that.

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- Bantari
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If pros didn't think they could play better with more time they wouldn't play time tesujis (playing a sente move, wasting a ko threat so as not to use up a byo yomi period but basically get double the time to think about the important move).

Don't know how it's "common sense" that 3 hours isn't enough time for a quality game, but ok.

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be immersed

That the quantity of mistakes is not correlated with game quality. If it were so, I would never have made it beyond 30kyu.

I find it astounding how much this thread is discussing whether or not the *human* will play better, and very little is spent on determining if the *computer* will play better. Whether a pro plays slightly stronger or not has to be balanced by whether the computer will play equally, more, or less strongly in the same time period.

I will argue that a human might play slightly better given a day vs. 10s, but a computer will play SUBSTANTIALLY better -- enough that a reasonably fair matchup will become increasingly lopsided in favor of the computer as its given longer and longer to think.

I think it's probably not a stretch to say that it will absolutely play better, given longer time. There are some diminishing returns, but it will *absolutely* play better.

My reasoning is as follows: A purely random MCTS can be proven to (incredibly slowly) converge on the right answer. the "incredibly slowly" is so incredibly slow, that programmers try to speed it up by giving it pattern-based playouts. Essentially, programmers trade off the certainty that it won't miss any successful lines for convergence speed. One has to only 'watch' an AI like pachi work through its initial terrible moves until it finds a decent one to realize that the vaunted speed of computers is *not* at the 1s-10s timescale, and that sufficient playouts are required for a computer to converge on a 'good' move.

humans do an incredible amount of pruning right off the bat.

I would absolutely bet on LSD in a 5s game vs AG. (or at least, the AG of 3 months ago

You underestimate our lack of focus! The real question is, given sufficient thinking time, can we produce higher quality posts?

My bet is that computers can do better.

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be immersed

That's because the question of whether humans play better when given more time is a highly charged one on this forum, so when the topic comes up it tends to dominate the discussion.

I thought I suggested that earlier in this thread (or was it a different thread), and got shot down.