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This is a work in progress. Fischer's positions will be listed in the 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

MalcolmHornewho pointed it out!]. I'll use Stockfish 8 on lichess to indicate possible optimal moves and to make test games.BBNNQRKR[+0.4] 1. f4, d4, b4 Test games #1: 1. f4 f6 2. b4 d5 3. e4 e6 4. e5 fxe5 5. Bxe5 Nc6 (+0.4) #2: 1. d4 b6 2. b3 c5 3. dxc5 f5 4. f3 bxc5 5. c4 e5 (+0.2) #3: 1. b4 e5 2. c4 b6 3. Nb3 c5 4. bxc5 Ne6 5. f3 bxc5 (+0.1)BBNNRKQR[+0.3] 1. d4 Test games #1: 1. d4 f6 2. f3 e5 3. e4 Qf7 4. b3 exd4 5. Qxd4 b5 (+0.3) #2: 1. d4 Nd6 2. Ne3 f6 3. b3 e5 4. dxe5 fxe5 5. c4 b6 (+0.2)BBNNRKRQ[+0.2] 1. g3 Test games #1 1. g3 c5 2. Nd3 Bd6 3. b3 e6 4. f4 Nc6 5. e4 b6 (+0.2) #2: 1. g3 g6 2. c3 c6 3. b3 b6 4. O-O e5 5. e4 Ne6 (+0.2)BBNNRQKR[+0.0] 1. d4, c4 Test games #1: 1. d4 d5 2. c4 dxc4 3. e4 b5 4. b3 c5 5. dxc5 e5 (+0.0) #2: 1. c4 c5 2. b3 e5 3. e4 b6 4. Ne3 f6 5. Nd5 Ne6 (-0.1)BBNQNRKR[+0.2] 1. b3, d4 Test games #1: 1. b3 c5 2. c4 b6 3. e4 e5 4. f4 Nf6 5. fxe5 Nxe4 (+0.2) #2: 1. d4 d5 2. b3 b6 3. Ncd3 e6 4. h4 Ncd6 5. Nf3 Ne4 (+0.0)BBNQRKNR[+0.1] 1. c4, d4, b3 Test games #1: 1. c4 e5 2. e4 c5 3. Nf3 Nf6 4. O-O d6 5. a3 a6 (+0.1) #2: 1. d4 d5 2. b3 b6 3. c4 dxc4 4. bxc4 c5 5. dxc5 bxc5 (+0.1) #3: 1. b3 c5 2. e4 e5 3. c3 b6 4. d4 d5 5. exd5 cxd4 (+0.0)BBNQRKRN1. c4 (+0.13)BBNQRNKR1. b4 (+0.00)BBNRKNQR1. c4 (+0.24)BBNRKNRQ1. d4 (+0.21)BBNRKQNR1. e4 (+0.15)BBNRKQRN1. c4 (+0.22)BBNRKRNQ1. d4 (+0.12)BBNRKRQN1. c4 (+0.29)BBNRNKQR1. c4 (+0.35)BBNRNKRQ1. d4 (+0.20)BBNRNQKR1. d4 (+0.14)BBNRQKNR1. c4 (+0.24)BBNRQKRN1. Ng3 (+0.00)BBNRQNKR1. d4 (+0.34)BBQNNRKR1. Ne3 (+0.11)BBQNRKNR1. b4 (+0.16)BBQNRKRN1. Ng3 (+0.07)BBQNRNKR1. d4 (+0.21)BBQRKNNR1. b3 (+0.29) Nf6 2. Bxf6 exf6 3. d4 Ng6 4. d5 c6 5. d6 c5 (+0.41)BBQRKNRN1. d4 (+0.17) d5 2. c4 dxc4 3. Qxc4 Nhg6 4. Nhg3 b6 5. b3 c5 (+0.01)BBQRKRNN1. Ng3 (+0.42) b6 2. Nf3 Bxf3 3. exf3 d5 4. O-O Nf6 5. Rfe1 Ng6 (+0.58)BBQRNKNR1. c4 (+0.12) c5 2. b3 b6 3. e4 e5 4. Ne2 Ne7 5. f4 O-O (+0.24)BBQRNKRN1. Ng3 (+0.14) c5 2. c4 Ng6 3. b3 b6 4. O-O Nf6 5. Bxf6 exf6 (+0.10)BBQRNNKR1. c4 (+0.23) c5 2. b3 Ne6 3. Ne3 b6 4. Nf5 Kf8 5. d4 Nxd4 (+0.22)These seem to be all BBN- and BBQ-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 :)

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....

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.

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.

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!

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!

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

significantlyif 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.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.

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.

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.

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).