Laskerator: Well, thanks for this diplomatic critics. 
I didn't pretend to make a breakthrough in the chess opening theory. However, imho this notion of acuteness is worthy to be formulated. There are definitely situations where the acuteness is not so obvious. I'll bring examples asap.
Acuteness of openings
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Aug 26, 2017
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#42
Aug 26, 2017
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#43
Using software it's not obvious that one line is better than another according to the software ?!
What isn't obvious to me is past move 10 in a game whether using your sev function you will be able to identify the best line, that is in any sense objectively correct.
Aug 26, 2017
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#44
TwoMove wrote:
Using software it's not obvious that one line is better than another according to the software ?!
What isn't obvious to me is past move 10 in a game whether using your sev function you will be able to identify the best line, that is in any sense objectively correct.
Well, engine evaluations constantly fluctuate (from one depth to an other) so sometimes it's not clear which move is better. However, in the case of acute openings, there should be a sufficiently big gap clearly separating optimal and suboptimal moves.
The statistical evaluation (sev) is meaningful only with a big number (let's say, >100) of available games. In principle, it can be calculated for any position if someone has enough patience to generate 100 completed engine vs (the same) engine games.
Aug 26, 2017
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#45
So you agree sev is useless after a certain number of moves?
You can't identify a best line according to software?!, how does your concept of acuteness help you?
Aug 26, 2017
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#46
TwoMove wrote:
So you agree sev is useless after a certain number of moves?
You can't identify a best line according to software?!, how does your concept of acuteness help you?
- Yes, without a sufficient number of master or engine games, sev is indeed useless.
- In the case of k-acute openings, the k best / optimal moves are clear cuz the gap, separating them from suboptimal moves, is big enough and not affected by fluctuations of engine evaluations. That's one of reasons to introduce this notion.
Aug 26, 2017
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#47
DeirdreSkye: The optimality is decided by engine evaluations. If it's useless for U, just don't participate. It's as simple as that. 
Aug 26, 2017
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#48
Yep point 2) is determined by the engine evaluations. How you dress it up with "acuteness" gives nothing.
Aug 26, 2017
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#49
TwoMove wrote:
Yep point 2) is determined by the engine evaluations. How you dress it up with "acuteness" gives nothing.
I tried to answer this question here:
https://www.chess.com/forum/view/chess-openings/optimality-factor
Aug 26, 2017
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#50
DeirdreSkye wrote:
Yes , I won't participate but don't you feel that you have to prove that those that participate aren't actually being misleaded or in best case senario, don't just lose their time?
I'm not defending a Ph.D. thesis here. If this notion is useless, this thread will fall into oblivion, that's all.
Totally useful to me. Especially when I turn on SF to exploit the " strange " decision of my opponent on move 10. ( I should know which moves are suboptimal )
Aug 26, 2017
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#52
Dear Yigor,
I think you have postulated a correct scientific term for what experience already taught us over the centuries. Would there not have been a massive amount of theory already, this would have been a major breaktrough. However there are libraries full of opening theory from which clearly follows that some openings are ''sharper'' or have a lower acutity number for that matter.
To name an example, the preference of a vast majority of the chess population for the Spanish Game/Ruy Lopez over the Spanish four knights game.
For the former, after 3.Bb5 black has the choice out of two moves that are clearly better than the other options, namely 3...a6 and 3...Nf6. For the latter, after 3.Nc3 Nf6 4.Bb5 black has the choice out of no less than four moves that are clearly better than the rest, namely 4...Bb4, 4...Bc5, 4...Nd4 and even 4...Bd6 (since there is no known ''refutation'' of this shit-move)
Even though for black the Ruy Lopez is harder to play in practice than the four knights, it is by no means better and over-use of the Ruy-L may even lead to a practical advantage for the four knights user.
I would advise you to study a few sharp openings like the Ruy Lopez, a few Sicilian lines like the Svesnikov, the Nimzo-Indian including a few sidelines, the Italian game and the Italian two knights (4.Ng5). These are all openings with a relatively low acutity number, however the Nimzo-Indian being a d-pawn opening will have a little higher acutity.
If you like to immerse yourself into opening theory after applying yourself about the existing theory I think you would do best to try and search for novelties. Often newly discovered moves start a line with a low acutity, so as to pose a new and difficult problem for the opponent. I look forward to reading your work 
Belgrade gambit might be 2 acute
Sep 3, 2017
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#55
One additional example in 2 plies: the Anglo-Lithuanian defense 1. c4 Nc6.
https://www.chess.com/forum/view/general/list-of-all-400-legal-openings-in-2-plies-master-games
Here the unique optimal move 2. d4 is neither forced nor so obvious.
Sep 3, 2017
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#56
BluemanisBack: Thanks for your detailed comment about acuteness! 
Sure that it's basically just a reformulation of already known things. 
Sep 3, 2017
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#57
zinkelburger wrote:
Belgrade gambit might be 2 acute
Actually, no, Stockfish 8 on lichess indicates 5...Nb4, 5...Bc5, 5...Nxe4 and 5...Bd6 as close to be optimal moves and there is no a clear gap between optimal and suboptimal moves.
Sep 8, 2017
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#58
Phoenyx75 has indicated an example, called Immortal Draw (a remarkable game played in 1872), where each move starting from 4. Kxf2 is 1-acute.
https://www.chess.com/forum/view/general/the-search-for-a-perfect-game
https://chess.stackexchange.com/questions/346/is-there-a-perfect-game
Sep 9, 2017
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#59
One more example of 2-acute position in Alekhine defense:
There are 2 optimal moves 3. c4 and 3. d4 separated by a sufficiently big gap from all others.
With all due respect to everyone participating, I must take pfren's side (though perhaps with a more diplomatic tone )
You can already see from the examples of k-acute you have gathered where this is going to go: forcing positions are highly k-acute (any gambit opening; the Ruy Lopez after ...a6 when White wastes time with anything else other than Bxc6 and Ba4; etc) as are situations which are highly tactical (for instance, a middlegame situation where one side has sacced a piece for an offensive).
So, the conclusion of this work is going to be what is already known: if you want to increase you opponent's chances of erring, you fight for the initiative. How sharp and how aggressive you can get away with, depends on your opponent's level.
To use the previously mentioned example: you don't play 4. Ba4 against the Ruy Lopez because you know it's a 2-acute situation. You play that because you are using common sense and general chess principles (instead of relying on an engine's analysis tree).
Also, if you want a practically meaningful definition of 2-acute, you need a way higher treshold than 0.2. Take the Alekhine's, for example; if your opponent plays 2. Nc3 instead of 2. e5, you haven't won yet nor have you even gained the upper hand. So saying that the Alekhine's is a 1-acute opening is just plain wrong. And once you increase the treshold to where it "should" be, you'll notice there are no situations where k-acuteness exists in the opening phase, outside of gambits (where finding the best move is usually fairly straightforward) and downright mistakes by the opponent.
I was pretty nuanced in my posts, however I don't write an entire essay to enforce my opinion 😉