(max/n)-graphs of most popular openings according to Game Explorer

I had a new idea for the systematical study of openings, starting from most popular ones. Let's choose a natural integer n. At each ply, consider the most popular move, let's say, with N master games. Then consider only moves with, at least, N/n available master games. If n=1, U'll obtain the "mainest line" in chess (it's in Sicilian:Najdorf, of course).

Here's how it goes for n=2 and n=3.

1st ply :

1. (n=1) King's pawn (B00) 1.e4
2. (n=2) Queen's pawn (A40) 1.d4

2nd ply :

1. (n=1) Sicilian (B20) 1.e4 c5
2. (n=2) Indian (A45) 1.d4 Nf6 
3. (n=3) King's pawn (C20) 1.e4 e5
4. (n=3) Queen's pawn (D00) 1.d4 d5

3rd ply :

1. (n=1) Sicilian (B27) 1.e4 c5 2.Nf3
2. (n=2) Indian:normal (A50) 1.d4 Nf6 2.c4
3. (n=3) King's knight (C40) 1.e4 e5 2.Nf3
4. (n=3) Queen's gambit (D06) 1.d4 d5 2.c4

4th ply :

1. (n=1) Sicilian:modern (B50) 1.e4 c5 2.Nf3 d6
2. (n=2) Old Sicilian (B30) 1.e4 c5 2.Nf3 Nc6
3. (n=2) Franco-Sicilian (B40) 1.e4 c5 2.Nf3 e6
4. (n=2) East Indian (E00) 1.d4 Nf6 2.c4 e6
5. (n=2) West Indian (E61) 1.d4 Nf6 2.c4 g6
6. (n=3) King's knight:normal (C44) 1.e4 e5 2.Nf3 Nc6
7. (n=3) Slav defence (D10) 1.d4 d5 2.c4 c6
8. (n=3) QG:declined (D30) 1.d4 d5 2.c4 e6

5th ply :

1. (n=1) Sicilian:Modern (B50) 1.e4 c5 2.Nf3 d6 3.d4
2. (n=2) Old Sicilian:Open 1.e4 c5 2.Nf3 Nc6 3.d4
3. (n=2) Franco-Sicilian:Open 1.e4 c5 2.Nf3 e6 3.d4
4. (n=2) Anti-Nimzo-Indian (E10) 1.d4 Nf6 2.c4 e6 3.Nf3
5. (n=2) Nimzo-Indian invitation (E00) 1.d4 Nf6 2.c4 e6 3.Nc3
6. (n=2) King's Indian (E61) 1.d4 Nf6 2.c4 g6 3.Nc3
7. (n=3) Ruy Lopez (C60) 1.e4 e5 2.Nf3 Nc6 3.Bb5
8. (n=3) Slav:modern (D11) 1.d4 d5 2.c4 c6 3.Nf3
9. (n=3) Slav defence (D10) 1.d4 d5 2.c4 c6 3.Nc3
10. (n=3) QG declined:Queen's knight (D31) 1.d4 d5 2.c4 e6 3.Nc3
11. (n=3) QG:declined (D30) 1.d4 d5 2.c4 e6 3.Nf3

 ... to be continued 

How about in game explorer, getting the amount of total games, dividing it by the amount of games that ends up at a certain position, and putting that to the power of the inverse of the amount of half-moves needed to get to that position. So, for Najdorf, that would be [37210 (amount of games that went to the najdorf) divided by 1300762 (total games in database)] to the power of 1/10 (10 moves needed to get to the sicilian najdorf), which is 1.427. Lower numbers imply fewer deviations per move - 1 would be no deviations, doing moves which everyone does, 2 would mean if people did moves which on (geometric) average, half of everyone did, 3 would be 1/3 etc. etc.

Sicilian najforf is not actually the lowest here. The chigorin defence of ruy lopez drops below 1.3 when you're on the line 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. 0-0 Be7 6. Re1 b5 7. Bb3 0-0 8. c3 d6 9. h3 Na5 10. Bc2 c5 11. d4 Qc7 12. Nbd2, which has 3,456 games on the database, 23 half-moves after the initial position. Not sure whether that's the lowest though.

SchuBomb: cool, good systematical idea. My method is much simpler, U just open Game Explorer and see immediately which lines appears with any fixed n.

I don't pretend anything, it was just to have some fun. ECO labels are irrelevant for this purpose but I can indicate them.

I added the 5th ply for n=2; openings with n=3 are coming soon.

Okay let's continue.

6th ply:

• (n=1) Sicilian:Modern (B50) 1.e4 c5 2.Nf3 d6 3.d4 cxd4

A bit lazy, but I'll do it today for n=2 and n=3.