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Sam Trenholme wrote on Wed, Jun 20, 2007 06:21 PM UTC:

OK, I have been doing some thinking about Capablanca chess variants. As discussed before, there are some 126,000 possible Capablanca opening setups, where the bishops are on opposite colors, and where the queen is to the left of the queen. However, looking at all of the Capablanca opening setups which have actually been proposed, I observe that:

All of the opening setups have the king and a powerful (R+N,B+N, or Queen) piece in the center files
All of the proposed opening setups are symmetrical with the rooks, knights, and bishops
All of the proposed opening setups have the rooks either in the corners, or one file closer to the center than the corners.

As it turns out, there are only 72 possible Capablanca opening setups that follow all of the above rules. Of these 72 opening setups, I find that only 15 have been formally proposed as starting setups:

RANBQKBNMR      Aberg                                                           
RMNMQKBNAR      Carrera                                                         
RNBMQKABNR      Bird                                                            
RNBAQKMBNR      Capa 1 (Suffers from 1.Mh3 mating threat)
RNABQKBMNR      Capa 2                                                          
RBQNKMNABR      Grotesque                                                       
RBNMQKARBN      Univers                                                         
RBQNKANMBR      Landorean                                                       
RNBQKMABNR      Embassy                                                         
RQNBAKBNMR      Schoolbook                                                      
NRMBQKBARN      Optimized                                                       
MRNBQKBNRA      Paulovich 1 link
ARNBQKBNRM      Paulovich 2 link
QRNBKABNRM      Paulovich 3                                                     
RNMBQKBANR      Nalls link

All of these, should I note, are perfectly playable, with the exception of Capa 1, and all of these have not had their openings explored nearly enough. Doing some slightly creative math, that leaves us with 56 possible starting setups. Here are some interesting ones, with names that I propose for them:

RNBQKAMBNR      Consulate  
RNQBKMBANR      Finesse
RNQBKABNMR      Notebook
QRNBAKBNRM      Closebook
QRNBKABNRM      Blackbook

Here are three openings setups that are unplayable:

RNBQAKMBNR      1. Mh3 mating threat
QRNBMKBNRA      1. Md3 mating threat
QRNBKMBNRA      1. Mh3 mating threat

Now, if instead of a R+N and B+N piece, we add two colorbound Camel + Bishop (Sage) pieces, and have an 8x10 board, we have 36,000 total possible opening setups (Sages and Bishops on opposite colors, queen to the left of the king). Of those, all of 12 meet the requirements above:

 1. SRNBQKBNRS
 2. RSNBQKBNSR
 3. RNSBQKBSNR
 4. RNBSQKSBNR
 5. SRBNQKNBRS
 6. RSBNQKNBSR
 7. RBSNQKNSBR
 8. RBNSQKSNBR
 9. NRSBQKBSNR
10. NRBSQKSBRN
11. BRSNQKNSRB
12. BRNSQKSNRB

Of these 12 setups, I find 1, 4, and 12 the most interesting.

No, I'm not proposing a new variant. I first need to fully explore the opening in Schoolbook. :)

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