# Why don't these statistics disprove white's supposed larger (practical?) advantage in chess960?

I've read that, at least theoretically, white has a larger advantage in 9LX as compared to chess. (See appendix.) This seems to be assumed in practice to the point that in some 9LX tournaments, such as the inaugural FIDE 960 world championship, they have players play both colours for any given starting position.

To even begin to talk about that white has more of a practical advantage, I think we should have some statistics that show there is a higher winning percentage change between white win and black win in 9LX as compared to standard. (Then afterwards we see if this increase is statistically significant or not.) But actually 'it's the reverse'! The winning percentage change is lower! See here (and hopefully here later on):

• in standard, white has 23% advantage against black: (39.2-32)/32=0.225, but

• in 960, white has only 14% advantage against black: (41.6-36.5)/36.5=0.13972602739

• (By advantage i mean percentage change between white win rate and black win rate)

In particular those are statistics based on engine games. My thought is that these statistics show how far theory and practice are here given that even engines, under time pressure, do not make the most of the white's 1st move theoretical advantage.

Question: What's going on? What's the basis for all this practical/theoretical advantage in 960 or at least for the both colours thing in 960 tournaments (perhaps it's not about white's advantage or perhaps they're just going on the theoretical advantage given lacking data on practical advantage or something) ?

Guess: Wait I think I just figured it out. Even if in 9LX white has a lower advantage (again, percentage change between white win rate and black win rate), say, in the above case of 14% vs 23%, white still has a higher win rate like 41.6% vs 39.2%. So, like, white's comparative advantage (lower percentage change) to black is decreased, but white's absolute advantage (of higher win rate) is increased...?

In this case I'd like to submit for consideration that comparative advantage be used as a counter-argument to absolute advantage in saying they must play both colours in 960 tournament or something, but I guess I'd save this part for another post and perhaps not on stackexchange.

Appendix on white's theoretical advantage (I actually didn't think I needed to cite because I thought this is why they do the both colours thing)

Another problem with Chess960 is that some positions are more unbalanced than the traditional starting position. While some positions are also more equal, there are a few positions which start with more than twice the "normal" White advantage.

There are some positions where White has a statistical chance to win of more than 60%. That's 6-7% more than standard chess.

• The essence of 960 is the randomness of the piece placement. There is no significant effort to ensure the resulting positions are fair. Hence some positions may favor White more than the "normal" starting position does, while some may actually favor black (haven't seen one, but the possibility exists I think). To control for that, players play both sides, thus canceling any advantage in the starting position for either color. It's the same reason colors alternate in match play, and why color balance is a factor in Swiss and Round Robin pairings. Dec 13, 2021 at 19:45
• @BCLC your appendix is good, but it's worth looking for the statistical evidence (like people publishing tables of evals) rather than just quotes. Dec 14, 2021 at 21:02
• No, e.g., linking the Sesse evaluation instead of the Chess.com article so people don't have to waste time reading a blogpost and can go straight to the data: docs.google.com/spreadsheets/d/…. Computer eval or win-rate is fine but it must be SP-specific, not aggregated, to be useful Dec 14, 2021 at 22:15

For the time being, without being certain one way or the other, I simply challenge the hypothesis:

You could look at eval tables and computer games (or human games, if a sufficient number are available separated by SP) to determine whether the White advantage is greater in Chess960, whether on average (mean, median) or how imbalanced SPs can get. Some limited evidence that the White advantage could be smaller in Chess960: http://www.computerchess.org.uk/ccrl/404FRC/opening_report_by_white_score.html (note the very high position of SP 518 in the ordered list).

• [EDIT: The Sesse evals for the 960 SPs vary from 0.00 to 0.57 and seem to confirm this, as SP 518 is evaluated at +0.22, ranked around 310/960 positions in terms of imbalance.]

As for why "they do the both colors thing" - well, as far as I know, they don't necessarily. There are plenty of Chess960 tournaments (including the actual Chess9LX tournament for example) where they don't swap colors on a given SP against the same opponent.

Finally, I don't believe that, when used, this rule is implemented primarily because of imbalanced starting positions. I believe in general the motivation is something like 'players A and B have just played from SP z, and we don't really understand SP z well enough to know how much of an advantage this really conferred the White player, therefore let them play again with colors reversed'. For example, even if - and it is a big if - we have engines whose evaluation we can trust as much as we do our opening knowledge of SP 518 (the standard chess opening position), it is still possible that humans would find it much easier to play from White than Black, whereas we know very precisely the extent of this inequity in SP 518 thanks to enormous experience of human play from SP 518.

Note also that the rule is more or less automatically implemented in match play in standard chess (the exception being Armageddon).

• Mobeus Zoom, did you perhaps confuse with RNBKQBNR again re the 'note the very high position of SP 518 in the ordered list' ? RNBKQBNR is high but RNBQKBNR (SP 518) is the very last on the list.
– BCLC
Feb 5, 2023 at 21:32
• 2nd this last part is misleading - they are implemented in match play but not all chess is match play. there are many single swiss & single round robin tournaments. why isn't this hypocrisy?
– BCLC
Mar 18 at 7:07

I suspect that we can't really use human (or computer) performance as a barometer of advantage in 9LX games. Standard chess has been studied for hundreds of years, has boatloads of theory, has plenty of heuristics like developing knights before rooks, etc. A lot of this doesn't apply in 9LX. So humans (and maybe engines less so) will consistently play less optimal moves. Imagine you and I race a Ferrari against a Porsche and the Porsche wins. Does that mean Porsche is better? We can't really say since you and I are not professional racers and really didn't achieve peak performance.

I'd guess this applies to neural nets to a lesser degree and to traditional engines even less so.

• and computer performance? computerchess.org.uk/ccrl/404FRC/…
– BCLC
Feb 5, 2023 at 21:33
• computerchess.org.uk/ccrl/404FRC/about.html from your link above suggests these computers have lots of handicaps on them. This is totally acceptable for there purposes, but this is not the cutting edge of chess performance. We haven't built years of chess knowledge, and theory for these 9LX openings. The computers results you linked to aren't even playing at optimal levels. 40 moves in 2 minutes, no opening book, 4 or 5 piece table books, etc. This article tells us nothing about what is the end state/optimal play is. We don't know for classical either but we are closer. Feb 6, 2023 at 13:51