Chess 960 or much more?

Bobby Fischer, one of the most brilliant and controversial chess player of 20th century has stated that he was not interested anymore in classical chess. The heavy opening preparation in standard chess has become a burden to creative chess. Today, opening preparation is reaching easily the 20th move in some top level games. We can state safely that :

The deeper the chess opening knowledge is, and the more likely draws will be.

This is why Fischer turned his attention to shuffle chess. Chess 960 or Fischer random chess is the alternative to classical chess that should put aside opening preparation. For those who are not familiar with it, below a link to wikipedia :

http://en.wikipedia.org/wiki/Fischer_Random_Chess

It is interesting to notice that the people that have won the Mainz Chess 960 Open are very strong classical chess players (Aronian, Svidler, Bacrot...). This shows that even though opening preparation is very important, it is still chess thinking that matters. And for the moment, the best chess thinkers are still within the top classical chess players.

Looking further into this, I realized that there is a large number of additional starting positions already in chess 960. Instead of making the classical mirror symmetry over the middle of the board line, one could make a central symmetry over the center of the board (point in green in the diagram). The diagram below shows the standard starting position with the central symmetry. Suddenly the fact that the black king position is swapped with the black queen makes the position even more equal. Castling king side with black will finally feel the same way as when castling king side with white.



There is no reason not to play this position. And this position could be considered part of Fischer random chess. By the way, it will not be anymore chess 960 but 960x2=1920 because every chess 960 starting position has a dual position with a central symmetry. Chess 1920 is funnier and more complex. It can also be called Fischer random chess extended.

So while thinking about this, I discovered on the board another interesting position.



Basically I am extending shuffle chess to different sides. I do not know if this is new. I called it Mixed Shuffle Chess or Mixu-Chess. Mixu-Chess is chess starting positions with pieces of opposite side colors standing on the same side of the board. I shall remark that in this first diagram castling is still possible (the Fischer way) but in other positions, it won't be.

Is the position neutral enough to be a possible new starting position ?
It seems that White has a small edge. My computer estimates it to between +0.2 and +0.5.
So this might make a difference for two strong computers playing each other but for most humans it won't. It might be fair and may be exciting to let such positions be played as draw odds. White starts but if there is a draw, black wins.

Actually the question is also fully relevant to chess 960 or chess 1920 : are all 960 or 1920 starting positions equal enough ?

I would not be surprised if in some of them White has some edge.
Below a couple of other Mixu-Chess starting positions :


This rook based Mixu-Chess position is considered very equal by the computer. Below a rather weird Mixu-Position, also quite equal :


However the following very interesting position that could be called Mixu-Chess Extended (because of the central symmetry used like Chess 1920), White seems to have an edge (+0.5).



Finally, my chess wandering brought me to a new chess variant : Cubic Chess. The idea of using the central symmetry allows some very interesting starting positions. Below an example of cubic chess :




The computer says that white has a slight edge but I do not believe here my computer assessment. In Cubic-Chess, the position of the pieces can vary inside the starting cube as much as wanted provided it gives equal chances for both sides. There is a total of about 1.3 billion of possible starting positions in cubic chess, however probably only a very small part of it is really equal. It might be that cubic chess is only playable with draw odds although it is very difficult to assess this.

There are many other possible starting positions that can be equal enough. May be in the future when 32-men tablebases are available, precise equal starting positions can be generated just before the match starts. And the players would discover the board. This would allow to discover the large continent of chess possibilities that is today only being investigated in chess studies.

I will be posting some mathematical analysis of chess possibilities in the future.