Acuteness of openings

Definition 1. An opening is called k-acute (or k-modal) when there are exactly k optimal moves (with close engine evaluations) separated by a sufficiently big gap (in terms of engine evaluations >>0.2) from other moves which are suboptimal, mistakes or blunders.

The initial position is not acute. Engine evaluations are distributed without big gaps between, let's say, +0.3 and -0.6.

Example 1. The Alekhine defense 1. e4 Nf6 is 1-acute (or unimodal).

Indeed, there is only 1 best / optimal move: 2. e5 [Stockfish: ev(2. e5)=+0.5 while ev(2. Nc3)=+0.1].

Example 2. The Scandinavian defense 1. e4 d5 is also 1-acute.

Wow, you can make other openings too and this would be very cool. ( I'm currently trying to exploiting early suboptimal play by opponent ( after playing a -0.2 move after thinking for 20 minutes on move 11 when there was a +2 move and a +1 move.))

Nice, Yigor! Spasibo!

savagechess2k: Yeah, I'll indicate other acute openings as soon as I discover them.

szaszzo66: U are welcome, bro!

It could be useful for the purpose of completing an opening repertoire.

I hope so. Especially interesting are those 1-acute openings where it's difficult to find the unique optimal move.

After a summer of generating useless numbers finally moving in direction of finding information that could effect result of a chess game. Of course whether you are gleaning anymore than looking at how software evaluation at a certain depth varies move to move is doubful. A least have finally realised that it is the variation that is important not the absolute value of a number. Also you have stopped using the sev function, which didn't have any purpose other than generating a number between 0 and 1.

It's not very popular but I think you can add Englund Gambit to your list. =)

TwoMove: LoL Thanks for the compliment but I've not forgotten about sev. I just don't need it here. Though, especially for U, I could introduce the notion of statistically k-acute opening.

That's right, Maria.

Example 3. The Englund gambit 1. d4 e5 is also 1-acute.

Now we need examples of k-acute openings with k≥2.

Initial Position is 20-acute right ?

Well, U could say like that but it's meaningless. It's better to say not acute.

Unrelated but I found out that 1.Nf3 f5 2.h4!? is completely playable and better for white.

More generally, I think that when k >5 we can say not acute.

Ruy Lopez mainline could be a good example for 2-acute unless you're only looking for 2 move openings.

1.e4 e5 2.Nf3 Nc6 3.Bb5 a6

Yes, it's smart to choose those acute openings where it's difficult to find optimal moves.

Wow, Maria, U are great in finding examples.

Example 4 (MariaJose97). Ruy Lopez: Morphy defense is indeed 2-acute (optimal moves: Ba4 and Bxc6).

Nope, in the case of Scandinavian defense, the optimal move is obvious, it's 2. exd5. However, there are openings where it's really difficult to find it. These are often tricky engine-generated moves. I'll give examples later. If U use such an opening against your opponent, U have the great chances to win.