Patterns in 960 starting positions I

This blog is the first with the purpose to identify families of FRC starting positions. The idea is to find out what they have in common and try to elaborate potential strategies. I will collect ideas from selected games about pawn structures and piece dispositions, far of the precision of an opening theory.

Which criteria do I classify starting positions?
There are many possible features:
Position of king, difficulty to castle, position of queen, unprotected pawns, etc.
I choose one that I think is the most determining factor to configure initial strategy: position of bishops. There are 16 different positions for bishops from (a,b) to (g,h). I will talk about (a,b) and it is going to be valid for (g,h) configuration.

How many positions am I speaking about?
If 960 is total number of positions and 16 is the total number for bishops configuration then 960/16 = 60 is the total number of positions for each pair of bishops location.
We must find what ID number have those positions. Which it is not difficult.
Given a backrank, for example BBQNNRKR, position identify number , ID, is given by formula:
ID = B + 16Q + 96N where:
B = b-light + 4·b-dark ,
with b-dark=0,1,2,3 if dark bishop is in a,c,e,g respectively
and b-light =0,1,2,3 if light bishop is in b,d,f,h respectively,
so in our case (a,b)=(0,0) then B=0 + 4·0 = 0
Q = 0,...,5 depending on which position queen has in the 6 free squares after have put bishops, in BBQNNRKR case queen is in c, the first free square, then Q=0
N= 0,...,9, Ten possible numbers given that we must choose 2 squares among 5 free squares after put bishops and queen and combinations C(5,2) = 5!/(3!·2!) = 10. Each number correspond to a pair of squares. For example, knights in d,e N=0. There is a table to assign a number to each pair of squares that you may find here https://en.wikipedia.org/wiki/Chess960_numbering_scheme.
Last three squares are for rooks and king, as order RKR is forced it does not determines nothing to calculate ID.
So BBQNNRKR is the position ID=0
The other positions with bishops in (a,b) are now ID = 16Q + 96N, calculating with Q=0 to 5 and N from 0 to 9 they are:

Other positions are a translation of this table after position of bishops, i.e. given B.
You may observe that ID = 16Q + 96N = 16·(Q + 6N) results in an arithmetic progression, 0,16,32,48,64,80,96,..., from 16·0 to 16·59
Now it is easy to look for positions with both bishops in (a,b) squares and look for patterns.
The most easy and common way to start the game is 1.c4, 2.b3 or vice versa, afterwards an usual plan is to break center with d4 getting a 'Maroczy' central structure c4, d4 against e6, d6. Actually, around 50% of games between humans has these opening moves.
The first game that called my attention is Caruana - Kasparov, St Louis 2019, because its pawn disposition with e3, f4 and, joining pawns, development of knights in f2 and g3.
position #784,
Black breaks in d5 instead to play a symmetric defense with f5 more solid but passive. Why did Caruana think that Qe2 was necessary?

Although not strictly lost yet, Kasparov resigned his nasty position.

I will draw 6 from those 60 positions with all possible values of Q and look for different strategies avoiding early b3, c4 for white or black defenses different from symmetric b6, c5. It will be for the next blog.
For selected games I will follow a single rule. No bullets. Neither 3+0, although in this case I will be flexible in games between strong players. Timing of games outside this site is not available.

Q=0
Position #0
After 1.c4 or 1.b3 the first move proposed by module is 1.h4. I already commented this possibility in other blogs Flanks attacks II and Flanks attacks I where I talk about first move 1.h4 when rook is in h1, bishop in a1 and king in g1. Exactly what we have in position #0 and the other positions with N=0 for Q=0,...,4. Not Q=5 , when Queen in h square module first suggestion is different, 1.g4
In this 5+0 game white dares to play 1.h4

It calls my attention how module consider four of five first black moves as ?! Moves that I could also play.

The highest elo game, 3+2, with 1.d4 is...

Interesting the black defense against 1.d4, 1...b5, and amazing the proposed defense , 1...c5 2.d5 c4. Again the advance of 'bishop' pawn as can be seen in my blog Non human 960 openings I

And a last game that if I don't see players elo , I would think that it's a game between two trolls

Q=1
Position #208
In this 3+2 game a non symmetryc defense is presented by a known GM

Notice that the strange move 3.Nh3. I will speak about it in the second part of the blog.
Another defense fighting for the initiative since second move in this 10+2 game. Very interesting the suggestion 6.e5, winning space without fear about open diagonal.

The same defense in this 3+2 game, where a premature castle put white under difficulties. I laughed a lot with proposed 8th move for black, 8...Rg8, that's the less natural move I could think.

Q=2
Position #416
Module proposes 1.b4, c4 or h4 that I can understand, but 1.e3 I do not, except if white looks for Caruana - Kasparov game scheme.
An interesting 3+2 game with 1.h4.

The ?! symbol for the first black move 1...e5 is against all my chess learning.
6.d4 is beyond my understanding

This 10+0 game is the highest human elo non bullet game I could find. Black first moves are the same than in Kamsky game in position #208.

This is the only game played by two moduls with position #416 that was not a draw.

Q=3, queen arrives to f column.

Position #624.
Here a weakness in h7 makes 1.c4 more attractive. Nevertheless the first moves that SF proposes, 1.c4 apart are 1.g4, 1.h4 and 1.f4. The first two moves have an oblique logic when h2 is weak and 1.f4, with the idea to close b8-h2 diagonal is near of scheme of Caruana-Kasparov game,
A 5+0 game with 1.g4 with symmetric defense.

A 2014 120+30 game between two modules. They have a 'low' elo.
At least, after 4th move, symmetric defense is impossible.

White loses the game and module does not detect any mistake, just three inaccuracies.
1.e4 is not among the first moves recommended by module but it could be seen in the next 3+2 game between two GM in the titled arena Dec-22.
The second move is already censored by our plugged friend.

Q=4
Position #832

This 8+0 game has the first moves 1.e4 b6 as in former game and now 2.c4 is the recommended move.

In this another game, white delays the c4, b3 moves until move 7.

2...c5 Unbelievable, only under drugs effects human can play such variation 3.Nc5 Qd5 4.Nb3 Nd6. The question mark after 3.Ng3? is too much severe, it is a move that I bet the most human players would have done.

Black defense was not succesful in this game.

Q=5
Queen is in h column and fight great diagonal h1-a8 with opposite bishop. In these positions recommended move is generally 1.g4. In this family of positions is #80, one of the most critical starting positions for black, specially after 1.g4 as I already mention in my blog How difficult for black are Fischer Random starting positions?
I will take another one position in this family, #176
With 1.g4 a game of your humble narrator.

1...g6 is the first suggestion of module, but 1...c5 is the second.

On the contrary, module dislikes 1...d5 evaluating position with +1.5, too much for first move !

Next blog I will look for the most interesting games with the most frequent scheme 1.c4 c5 2.b3 b6.

If we want to look for positions where bishops be in (g,h) then B = 3 + 4·3 = 15. The rest is the same. It is a translation of former table. In my other blog Non-human-960-openings-iv you may see position #911.