Height of an opening

 Beware: silly trolls rode around!

I started to divide the height in 2 parts (for white and for black) as suggested by Atos.

Main line in Ruy Lopez:

1.e4 (h=2+0) e5 (h=2+2) 2.Nf3 Nc6 3.Bb5 a6 (h=2+3) 4.Ba4 Nf6 5.O-O (h=5+3) Be7 6.Re1 b5 (h=5+5) 7.Bb3 d6 (h=5+6) 8.c3 (h=6+6) O-O (h=6+9) 9.h3 (h=7+9) Na5 10.Bc2 c5 (h=7+11)

1st main line in French (Winawer, Advance) :

1.e4 (h=2+0) e6 (h=2+1) 2.d4 (h=4+1) d5 (h=4+3) 3.Nc3 Bb4 4.e5 (h=5+3) c5 (h=5+5) 5.a3 (h=6+5) Bxc3 (h=6+6) 6.bxc3 (h=8+6) Ne7 7.Qg4 O-O (h=11+6) 8.Bd3 Nbc6 9.Qh5 Ng6 10.Nf3 Qc7 [17= 11+6]

I've given this topic a little bit of thought, and have come up with the following:

FIRST THOUGHTS.

Can it be guaranteed that any position can only have one HFZ value, regardless of any transpositional sequence of moves used to obtain that position.

Consider the following (rare) scenario: Game 1 has pawn exchanges but no piece exchanges, Game 2 has no pawn exchanges but does have piece exchanges. Game 2 also has pawn promotions which reclaim the lost pieces. eventually, after x amount of moves, Game 1 and 2 end up with the same position. I would say, that for a given position, its value for HFZ should be the same, regardless of the sequence of moves used to obtain the position. The values used for pawn moves, exchanges, castling, castling by hand, pawn promoting, etc, should all be 'fine tuned' so that every position has a unique HFZ regardless of how it occurred.

If the same position can have different HFZ values depending on how that position was obtained, Then it seems to me the HFZ value has lost some of its relevance.

SECOND HOUGHTS.

What practical use can be obtained from the HFZ?

What information can it give us?

In the opening, if there is a large difference between the HFZ value for black compared to the value for white. That would suggest one of the players was using a hypermodern opening (very few central pawn moves) compared to the other player.

With chess playing programs, apart from such things as material, and piece mobility etc, It may be that chess engines could benefit from using different heuristics depending on the nature of opening used.

I think calculating the HFZ value in a computer program would be very easy and fast compared to determining equivalent information by studying the position of all the individual pieces in a position. So the HFZ value MAY have some use in chess engines.

I would imagine the HFZ value to have less and less relevance as the game progresses through middle to end game. I'm guessing HFZ values for black and white would get closer as the game progresses. So a computer programme may use something like: HFZ divided by (some function of ply) in its evaluation function. So the HFZ value would have less effect as the game progressed.

This is all typical of the random thoughts that manifest in my brain. Sorry if I've bored you with a load of drivel.

Hey Malcolm, now I calculate only relative heights and distances between positions with the same pawn bases. It's quite useful in classification theory of openings.

For example, Tennison <-- Blackmar-Diemer <-- Van Geet: Berlin gambits form a tower in HFZ metric. The height of Van Geet: Berlin above Blackmar-Diemer is 1 (e5 pawn instead of e4) and the height of Blackmar-Diemer above Tennison is 2 (e4 pawn instead of e2).

http://www.chess.com/forum/view/chess-openings/blackmar-diemer-and-other-ed2e-gambits

i still don't understand, how to determine the height ?

can be explained ?

Please give me an opening position and I'll explain U how calculate its height.

1.e4 (h=2) c5 (h=4) 2.Nf3 d6 (h=5) 3.d4 (h=7) cxd4 (h=9) 4.Nxd4 (h=10) Nf6 5.Nc3 a6 (h=11) 6.Bg5 e6 (h=12) 7.f4 (h=14) Be7 8.Qf3 Qc7 9.O-O-O (h=17) Nbd7 10.g4 (h=19) b5 (h=21)

1.e4 (h=2) e5 (h=4) 2.Nf3 Nc6 3.Bb5 a6 (h=5) 4.Ba4 Nf6 5.O-O (h=8) Be7 6.Re1 b5 (h=10) 7.Bb3 d6 (h=11) 8.c3 (h=12) O-O (h=15)9.h3 (h=16) Na5 10.Bc2 c5 (h=18)

you said that distance of Najodrorf and Ruy Lopez after 10 moves is distance(Najdorf,Ruy Lopez) = height(Najdorf) + height(Ruy Lopez) - 2 x height(CIS) = 21+18-2x9 = 21 and CIS value is 9.

Why if distance(Ruy Lopez,Najdorf) ? whether the value of CIS remains ?