I've heard it said that some chess 960 positions have a significant advantage for white, usually involving fast attacks against undefended pawns. However, since zugzwang positions do exist, it's theoretically possible that black could have an advantage in some opening setups. Which leads to the question: are there any where he does? If not, are there any that give white less of an advantage than he has in normal chess?

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    I don't think you will get a complete answer because noone has analysed all of the 960 positions, but my conviction is that no, no symetrical undeveloped position is a reciprocal zugzwang. When there is no threat, and when all your pawns are on the second rank, there MUST be useful moves. – Evargalo Oct 7 '17 at 16:45
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    @TonyEnnis you are reversing the burden of proof. I am not claiming that Black as an advantage. You are claiming that White has an advantage (I would probably agree) and that it is proven (that's where I protest). In your arguments, you seem to confuse empirical observation, argument of authority and mathematical proof. The last one is nowhere to be found, and probably forever so since chess softwares make more and more openings lean towards equality... – Evargalo Oct 8 '17 at 17:39
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    Ok, I know that White scores slightly better than Black in chess. We are just not talking about the same thing, but anyway it won't help answering the OP question, so let it be. – Evargalo Oct 8 '17 at 19:41
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    In chess960 starting a game can be tricky, there is no obvious opening. When white starts black has a chance of extra time to analyze the position. It can be an advantage in some cases, however most of the time black's effort is summarized in defending because white had the initiative. – Farhad Oct 9 '17 at 11:32
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    @TonyEnnis "White's advantage is well demonstrated mathematically" except it isn't. There is a common odd misdefinition of White advantage on this website: while it is true that White performs better it is not necessarily true that White can force a win or a draw given the initial conditions (which is the definition of first-move-advantage in game theory). Being X centi-pawns points better implies by no means the first-move-advantage as per definition. – gented Oct 9 '17 at 15:27
up vote 3 down vote accepted

It happens that someone tried to evaluate all 960 positions with an engine. Several positions got a score of 0.00, but none of them offered any advantage for black.

Of course, those conclusions are only the evaluations of Stockfish at 40 plies depth. It is a strong hint, but no definite proof, that Black is fine in the huge majority of 960-chess starting positions, but not better in any of them.

This result matches with the intuition that in a symmetric, non-developed position, with all pawns on the 2d and 7th rank, there is always something useful to do if you are on move: in other words, there cannot be mutual zugzwang.

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    OK, this evidence convinces me. The fact that RBNQKNBR is noticeably more balanced than standard chess is also intriguing. In fact, the only symmetrical starting position with the queen and king on the d and e files less balanced than normal chess is NBRQKRBN. – eyeballfrog Mar 15 at 19:10
  • Isn't RBNQKNBR normal chess? – supercat Mar 15 at 22:51
  • @supercat No. In normal chess the knights are next to the rooks. – eyeballfrog Mar 15 at 23:17
  • @eyeballfrog: [bonks heat]. Of course. Interesting that swapping knights and bishops makes such a big difference, but that's probably because d4 and e4 don't free up bishops. Trying to free up a bishop while creating a pawn center with c4 and f4 will immediately give Black some initiative with f6 or c6, respectively. Using c3 or f3 doesn't give Black the initiative, but doesn't assert pawn presence in the center like d4 and e4. – supercat Mar 16 at 20:24
  • @supercat That's what I thought, too. The fact that white has to choose between central space and piece development rather than getting both at once with 1.e4 and 1.d4 should mean black can be more proactive (and probably go for whichever one white didn't). – eyeballfrog Mar 16 at 22:46

If you accept statistical data taken from games played between computers as evidence, then the answer may be yes.

See this link for the data.

At the time of writing, White scores below 50% in 155 of the 960 positions. A sample of the scores from the RNKBBRNQ starting position is shown below.

Statistics for RNKBBRNQ starting position

Note that the average ratings for both sides are equal, so distortions in expected result due to playing strength should be negligible.

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    According to this screen capture, the average rating of White players was almost 100 points below that of Black players in this particular starting position (quite a feat, btw). As a consequence, in spite of scoring less than 50%, White has actually overperformed by 39 points and Black has underperformed by 37 points. The sample (N=370) might be too small to conclude in either way, but this overperformance seems to show that White actually has a tiny advantage in this starting position as well... – Evargalo Feb 7 at 14:43
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    BTW, the starting position you are referring to is: "the RNBQKBNR starting position"... isn't that standard chess ? – Evargalo Feb 7 at 14:45
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    @Evargalo Good points. It seems I chose unfortunately. Post updated again. – Samantha Feb 8 at 11:00
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    I find that data a little questionable given that it has "RNBQKBNR" (standard chess) scoring at 43% but "RNBKQBNR" (mirror image of standard chess) at 54%. – eyeballfrog Feb 8 at 19:47
  • @eyeballfrog: Engines that know the best moves in standard-chess openings would receive benefits from that which would likely be unavailable in the mirror-image counterparts. – supercat Mar 15 at 22:53

No starting position can have an advantage for black, but it may be that white may not be able to establish a positional advantage like in standard chess. Also, any attack that black can do can be executed by white also (or if not at least stopped by correct play).
As for zugzwang, just as Evargalo said, it just not possible.

I play 960 quite a bit (though it may affect my opening) and have not encountered any such position. Therefore, it probably is just a myth that such positions exist.

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