Thursday, October 1, 2009

Capablanca opening setup research

I have done some research about which Capablanca arrangement of the pieces is most ideal.

In the 2000s, we have had many discussions on the Chess Variants server about what makes for the best Capablanca setup. It has been asserted, for example, that all of the pawns need to be defended in the opening setup, and that any opening setup with undefended pawns gives White a sizable advantage.

What I have done is research a subset of Capablanca setups to see if this is true. Since there are some 126,000 setups where the Queen is to the left of the King and the bishops are on opposite colors with the Capablanca pieces, I have reduced the number of setups to six thusly:
  • The rooks must be in the corners. The king must be in the F file. This is to accommodate the software I used for my testing, which only allows castling if these conditions are met.
  • The knights must be in the C and H files, and the bishops must be in in the D and G files. The thinking is this: Since the knights are weaker in Capablanca setups on a 10x8 board than they are in FIDE chess, placing the knights relatively near the center makes them more relevant in the opening and midgame. The bishops are placed near the center just like they are placed in FIDE chess; this is done so that natural pawn development moves (e4, f4) do not hamper the development of the bishops.
  • The Archbishop (Knight + Bishop), Marshall (Rook + Bishop), and Queen may be placed anywhere in the three remaining files.
Here are the six possible resulting setups:
  • RMNBAKBNQR (I call this arrangement “Notetaker’s Chess”; all pawns are defended in the opening array)
  • RQNBAKBNQR (“Schoolbook Chess”; again, all pawns are defended)
  • RANBMKBNQR (I call this arrangement “Narcotic Chess”; the B pawn is undefended in the opening array)
  • RQNBMKBNAR (I call this arrangement “Opiate Chess”; the D and I pawns are undefended in the opening array and White can threaten mate on the first move with Md3)
  • RANBQKBNMR (“Aberg Chess”; the B pawns are undefended)
  • RMNBQKBNAR (“Carrera Chess”; the original 10x8 setup from the 1600s; the B pawns are undefended)
I ran at least 1,000 games for all of these setups. Only games that ended in a Checkmate or a draw were counted; I made sure to have Joker80 play enough games until each of these setups had 1,000 complete games. Here is the win/loss/draw ratio for White with all of these setups:

SetupWinsLossesDrawsGames played
Numbers may not add up to 100% because of rounding

Since we played 1,000 games with each variant, the scores may be off by as much as 2% or so.

In conclusion, we can see that whether or not all pawns are defended is not a relevant factor in White having more of an advantage. The setup with the lowest White advantage (ranbqkbnmr, White advantage 3%) has one undefended pawn in the opening array for each side, and the setup with the highest White advantage (rmnbakbnqr, White advantage 16%) has all pawns defended in the opening array.

ranbqkbnmr appears to be the most balanced setup (3% White advantage); this is followed by rmnbqkbnar (5% White advantage). ranbmkbnqr and rqnbakbnmr both have an 8% White advantage; ranbmkbnqr has fewer draws, however. Both rqnbmkbnar and rmnbakbnqr give White a considerable advantage (12% and 16%, respectively); I am not surprised rqnbmkbnar has a considerable White advantage, since the D pawn near the King is unprotected, and since White can threaten mate on the first move with Md3. However, it is a mystery why White has such an advantage with the rmnbakbnqr, since all pawns are defended in this setup. It would appear undefended flank pawns don’t give White any significant advantage.

For people interested in this research, I have made a 4-megabyte archive with all of the games played in the course of this research here:
I would like to thank H.G. Muller for modifying Winboard and creating Joker80; this software made this research reasonably straightforward to perform.

Edit: Corrected number of undefended pawns in Carrera and Abera opening setups.