List of 60 Fischer's positions of type BB-: evaluations, best moves and test openings

This is a work in progress. Fischer's positions will be listed by bishops positions +  lexicographical order. By symmetry we can suppose that the king is always at the right-hand side of the board, it reduces our calculations to 480 initial positions [Well, actually not, cuz of asymmetrical castlings, thanks to MalcolmHorne who pointed it out!]. I'll use Stockfish 14+ to indicate possible optimal moves and to make test games. The most popular first moves are taken from the Lichess database.

The common test opening #1 (popular in Lichess database): 1. b3 b6 2. c4 c5 3. d4 cxd4 4. Bxd4 Double English Stairway

1. BBNNQRKR [+0.4] Engine: 1. b4, h4, c4, f4 / Database: 1. b3, e4, c4 / test --> 4...f6 (+0.4)
2. BBNNRKQR [+0.4] Engine: 1. e4 / Database: 1. b3, e4, c4 / test --> 4...f6, d5, f5 (+0.0)
   
3. BBNNRKRQ [+0.7] Engine: 1. g3 / Database: 1. b3, e4 / test --> 4...Nd6, Nc6 (+0.0)
   
4. BBNNRQKR [+0.3] Engine: 1. d4 / Database: 1 b3, e4, c4 / test --> 4...e5 (-0.1)
   
5. BBNQNRKR [+0.3] Engine: 1. c4, h4, b4 / Database: 1. b3, e4, d4, c4 / test --> 4...f5, e5, h5, Nf6 (-0.3)
   
6. BBNQRKNR [+0.5] Engine: 1. d4 / Database: 1. b3, e4, Nf3, d4 / test --> 4...e5 (-0.1)
   
7. BBNQRKRN [+0.5] Engine: 1. c4 / Database: 1. b3, c4, e4, Ng3, d4 / test --> 4...Bxh2 (-0.5)
   
8. BBNQRNKR [+0.4] Engine: 1. c4 / Database: 1. b3, e4, d4, c4 / test --> 4...e5, d5 (+0.3)
   
9. BBNRKNQR [+0.3] Engine: 1. d4, b3 / Database: 1. b3, e4, d4, c4 / test --> 4...Ne6 (+0.2)
   
10. BBNRKNRQ [+0.4] Engine: 1. c4 / Database: 1. b3, e4 / test --> 4...Ne6, Nd6 (+0.2)
    
11. BBNRKQNR [+0.5] Engine: 1. e4, c4 / Database: 1. b3, e4, Nf3 / test --> 4...e5 (-1.1)
    
12. BBNRKQRN [+0.6] Engine: 1. c4 / Database: 1. b3, c4, e4, Ng3 / test --> 4...Bxh2, f5 (-0.1)
    
13. BBNRKRNQ [+0.6] Engine: 1. g3 / Database: 1. b3, e4  / test --> 4...Nf6 (-0.2)
    
14. BBNRKRQN [+0.4] Engine: 1. c4, d4, f3, b3 / Database: 1. b3, e4, Ng3, c4, d4  / test --> 4...Ng6 (+0.2)
15. BBNRNKQR [+0.4] Engine: 1. c4 / Database: 1. b3, d4, c4, e4  / test --> 4...e5 (+0.1)
    
16. BBNRNKRQ
    
17. BBNRNQKR
    
18. BBNRQKNR
    
19. BBNRQKRN
    
20. BBNRQNKR 
21. BBQNNRKR
    
22. BBQNRKNR
    
23. BBQNRKRN
    
24. BBQNRNKR
    
25. BBQRKNNR
    
26. BBQRKNRN
    
27. BBQRKRNN
    
28. BBQRNKNR
    
29. BBQRNKRN
    
30. BBQRNNKR
    
31. BBRKNNQR
32. BBRKNNRQ
33. BBRKNQNR
34. BBRKNQRN
35. BBRKNRNQ
36. BBRKNRQN
37. BBRKQNNR
38. BBRKQNRN
39. BBRKQRNN
40. BBRKRNNQ
    
41. BBRKRNQN
42. BBRKRQNN
43. BBRNKNQR
44. BBRNKNRQ
45. BBRNKQNR
46. BBRNKQRN
47. BBRNKRNQ
48. BBRNKRQN
49. BBRNNKQR
50. BBRNNKRQ
51. BBRNNQKR
52. BBRNQKNR
53. BBRNQKRN
54. BBRNQNKR
55. BBRQKNNR
56. BBRQKNRN
57. BBRQKRNN
58. BBRQNKNR
59. BBRQNKRN
60. BBRQNNKR

These are all 60 BBXXXXXX-positions.

An illustration to the first Fischer's position:

I hope you wrote a program to do it automatically for you, otherwise I'm afraid you'll give up pretty soon :)

Nope, I'm launching it by hand LoL. Hopefully, I'll finish it one day. Nothing presses me. Normally, I have enough free time during this summer. I'm mainly active in the Openings forum though.

1. e4 has finally appeared as the best move in position #6 and a knight move in #7.

In position #9 white has a substantial advantage.

heya Yigor, have you ever had an IQ test ? i scored 127 the other day on a fast online IQ Test....

Hey, Billy! Nope, I'll do it, maybe not today.

thats cool, make sure you find the free one online, it takes about 1/2 hour or more, and some of them ask for money for the results. so find the free ones.

(All right. Meanwhile, position #11 is so bad for black that it can be even refutable. I'll make a test game today.)

P.S. Oops, sorry, something went wrong with my calculations. I'll correct it right now.

I was obliged to bypass a little glitch with the Analysis Board that doesn't incorporate automatically Shredder-FENs and castlings for Chess960 analysis. Obviously, evaluations change (as well as some moves) and I'm incorporating new values. It will be corrected soon.

Yigor: "By symmetry we can suppose that the king is always at the right-hand side of the board. It reduces our calculations to 480 initial positions."

Surely you have to consider all 960 positions, not 480? Castling on the left hand side is different from the right hand side, and this will have an effect on many opening lines.

Ah yeah, right, there are non-symmetrical castlings. Damn, it will complicate my task. Thanks for pointing it out!

Wouldn't it still be 480?

RNKNRBBQ is the same as QBBRNKNR, since Black's position must mirror White's.  If 1.c4 is the best move in the first case, GUARANTEE YOU that 1.f4 is the best in the second one!

Even in cases where Rook distance is not the same on both sides:

RNBBKNRQ is still the same as QRNKBBNR.  Yes, Queenside castling is "longer" on the left and "shorter" on the right in the first scenario, but everything is still symmetrical, and if 1.b4 is best in the first diagram, GUARANTEE YOU 1.g4 is best in the second one.

Cataloging all chess 960 positions is an interesting idea, but I question the method used here.

How long did you let these evaluations run for, and on what kind of hardware?

Many or all of these evaluations would change significantly if you ran them on a dedicated cluster-CPU setup like http://analysis.sesse.net/ 

You would have to run analysis for a whole day on a regular home pc to get the same accuracy a supercomputer gets in minutes.

ThrillerFan: Thanks for your comment. Strictly speaking, it doesn't guarantee that best moves will be the same (even in the case of symmetrical rooks!). This is cuz the pseudo-symmetry doesn't exchange short and long castlings. In your example, the short castling in QBBRNKNR will give *****RK* but U can't obtain *KR***** with the long castling in the pseudo-symmetrical RNKNRBBQ.

I'm doing it just here using the chess.com's Analysis Board at depth d=20. On my comp, it takes about 1 min / position. I make it just for fun and and as a reference for my personal use. I'm not planning to compete with supercomputers.

No, here is what you are mistaking:

QBBRNKNR will have the exact same theory and the same opening move of left-right symmetry as RNKNRBBQ.

So you DO NOT compare short castling of one to long castling of the other.  You compare short to short and long to long.

So, whatever the best move is in the first one, the best move in the second one will be the move of "left-right symmetry".

So, again, not saying these ARE the best moves for both sides, but hypothetically, take the first position, let's say, for argument's sake, that the best first 5 moves for each player is as follows:

POSTION 1:  RNKNRBBQ

POSTION 2:  QBBRNKNR

Position 1 starts 1.c4 c5 2.d4 d6 3.Nc3 g6 4.Nf3 Bg7 5.e3

You have the EXACT SAME GAME in position 2 with 1.f4 f5 2.e4 e6 3.Nf3 b6 4.Nc3 Bb7 5.d3

And so you don't compare "Castle left" to "Castle Left".  "Castle Left" in position 1 is the exact same as "Castle Right" in position 2.

That's why I say you compare Castle Short to Castle Short and Castle Long to Castle Long.  So the flaw in your statement is that Castling Short in the first one is the same as castling short in the second one and all moves are left-right mirror.

So 1.a4 in diagram 1 is the same as 1.h4 in diagram 2.

1.Nc3 in diagram 1 is the same as 1.Nf3 in diagram 2.

So there really are only 480 unique positions.  You just have to mirror all the moves for the other 480.

Here's another way to look at it.  Flip the King and Queen in the starting position of regular chess.  Now 1.d4 in the mirror position is the same as 1.e4 in the normal position.  Castling "short" in the normal position is to White's right.  In the mirror position, it's to White's left, but it's still castling short.  So you are playing the exact same game with left-right symmetry.

The King's Indian Defense, Mar Del Plata Variation, would be 1.e4 Nc6 2.f4 b6 3.Nf3 Bb7 4.d4 e6 5.Nc3 O-O (which is K from d8 to b8, a8 rook goes to c8) 6.Bd2 d5 7.O-O Nf6 8.e5 Nd7 9.Nd1

And the normal position and position where you flip the king and queen are 2 of the 960, but only 1 UNIQUE position.  So there are 480 UNIQUE positions, and 480 mirrors!

Make it even easier for you, let's just say, hypothetically, that you have the following 2 positions:

RNKNRBBQ and QBBRNKNR

And in the first case, after 1.c4 c5 2.d4 d6 3. ... 59.Ke3 Kd6, you have the following position:

WPc4, WKe3, BKd6

If in the second one, you go 1.f4 f5 2.e4 e6 3. ... 59.Kd3 Ke6, you have the following position:

WPf4, WKd3, BKe6

And whatever the theoretical result of the first one is, the same is the case for the second by playing strictly mirror moves of the first.  (By the way, it would be a draw in both cases with best play).