[960 Balance Analysis] The search for really unfair positions

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glider1001

It's difficult to quantify what we mean by unfair. Suggestions on that would be welcome on this forum. Even in SP518 standard chess, statistics show that white has a slight edge in the probability to win. Is that unfair? I'm approaching the problem from a different angle. Is there even one single position in 960 that is truly unfair to either side, such that their chance of winning is so low that the position is meaningless as a game experience? If we do find such a position, I suspect that Chess960 is we understand it is dead. Chess960 is about playing any and all of the 960 positions. We cannot afford to have even one truly terrible position in the set. Interestingly, we have a genius Chess player that was the originator of Chess960 as we know it today. Bobby Fischer thought Chess960 is the way of the future. Did he feel that Chess960 is balanced as a gut feel? Did he harbour some doubt?

Here is how I can initially test what is a huge scientific experiment, to find that one bad starting position that ruins 960 if there is such a starting position at all!

This graph shows white's win percentage (vertical axis) in the CCRL database of computer chess from April 2010. The database is a tiny sample of 70,000 games but it will have to do in the absence of any other data. Every SP was played, some more than others. The engines were of various abilities and unrealistic limited search depths but at least some different opening moves were played in each SP. Horizontal axis is meaningless other than a data point counter. The graph does not imply that in SP001 white won nearly 70% of the time, just that there was a distribution of SP's with that statistical result:

Note: this data may not be accurate or even correctly collated! It is just preliminary...

There are many many issues with this graph. It may be just plotting the inability of the engines to find more wins for white. Who knows. It is also possible that in some SP's black might actually have a better chance at winning because of a really really deep unavoidable situation of Zugswang!? I doubt it but you never know! At least there is some validity to the data. So far it matches with what people are experiencing as they haphazadly experiment with 960 (that no really horribly unbalanced position has been found). A concern with the CCRL data is that for SP518, these are the stats:

SP518: Draw: 15.5%? White win: 48.6%? (based on 72 games)

Another concern is that there are a few tens of positions where white's win chance is above 60%, the draw chance is around 20% leaving black with a win chance of only 20% (1 in 5). There just isn't enough data and Chess960 needs quality players out there playing it. If it turns out that in 5% of 960 SP's white can win 65% and black win or draw 35% of the time, is that unfair? Sounds ok to me, if that difference is in only present in a few percent of the total set of 960 positions.

Another concern is that do seem to be another small number of SP's where white wins 50% of the time, a draw happened 40% of the time leaving black 10% chance of a win. Again, is that unfair? If it turns out that in 20% of games, white can win 50% and black get's an equal chance at a draw and perhaps even a small chance of win, does it seem fair enough to you? 

All these potentially "unfair" statistics for black could be compensated for in the rules of the tournaments (as they are to some degree today). Matter of fact, I think that if white's clock starts the minute the players are seated, there is a possibility that because black get's to study the position without any cost to his clock (while white has the opening move), that would significantly throw back the odd's to black! It would make it interesting! It feels like the right thing to do from my personal experience. Black get's more initial time and it truly makes game contests interesting and unpredictable. Personally I do not think of a Chess960 game as have an opening. To me it is just a very deep mid game that commences at move one. In that respect of course white's clock should be ticking the moment the players are seated. It put's white in the hot seat!

All we really know is that as yet, there is not one SP that a collection of engines can consistently win at with either colour (100% chance of win). If I take a look at the positions themselves that are most likely to achieve a white win from this data, I can see a trend that could be flawed but never-the-less. The queen and bishops tend to aim at the enemy king sooner rather than later. The enemy king is hemmed as close as possible to the corner (making it liable to smother mates for example). Knights tend to exist in positions where they can get to the enemy king quite quickly. If the king is in the centre, then the problem for black is a queen in the corner that cannot contribute to defense of counter attack. Other situations are that in these positions, there is a pawn advancement that very efficiently allows pieces to develop, yet at the same time, the opponent cannot make that same pawn advancement. It is just a first glance:

White wins 65-66% (max chances): Either the King or Queen are cornered and a Bishop is next to a queen (meaning one pawn can release both those pieces)....

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On the other hand, black's big winning SP's are very difficult to explain, other than problems with the engine's understanding of the SP itself!:

White looses 60-63% (max chance): The queens are cornered? Bishops next to a Queen perhaps?

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BRKNQBRN

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The big warning sign that the data is badly effected by computer misjudgement, is that even in the SP's where white looses more than 60%, the queens are in the corner. Oh well! Back (black?) to the drawing board....

Cheers

glider1001

(I've improved a bit on this analysis of SP080 over at http://chess960jungle.blogspot.com/2011/04/chess960-sp080-buckingham-palace.html) since I wrote this comment back in August 2010:

Ok here is a really classically "unfair" position you would think! It is SP080. White immediately get's the initiative and the tempo and thus can fire his two bishops at black's kingside quicker than a wink you would think! But like anything in Chess960, the game comes down to one of perception! In practical game play we sometimes need to give black some help, and that comes from the fact that SP080 arrives only randomly (thankfully!), and that white will have to think at cost to his clock when it does, while black can examine how to defend this SP while white is thinking. It comes down to remembering some core defensive principals.

Sure it will turn out that in some SP's black is completely on the defense, looking for a draw. Here in SP080 black is just trying to save the position and perhaps counter attack. The point is this. Despite that in some SP's, black will struggle to assert any initiative at all, still black get's to play some really interesting chess. There are 960 positions and so occasionally us Chess960 players are going to have to learn hyper defensive strategies as black. It is just another technique that has to be mastered in Chess960!

Check this line out that black can use in the "unfair" SP080. Black decides to keep his castling options open. He decides that he will build a knight shield in the centre and leave open the possibility of not castling his king at all, leaving it centralised in the centre of the back rank at E8 under strong armoured guard from his knights and pawns. The structure looks like the soldiers standing out the front of the Buckingham palace!

SP080: Black plays the Buckingham Palace Defense (where E8 is the King's bedroom):

Black is using some pretty creative play! Check out other variations in the example that do not work as well for black. What I really like about the setup is the ambiguity about how to play in the centre. As soon as white tries to claim space there, he looses his attack on the long dark diagonal or comes under attack on the long white diagonal. Black is also using the unique ability of the rook pawn as well. If the rook pawn can be deployed proactively, it will be the only pawn that cannot directly cause a pawn island to form in it's master's pawn structure (because if it does, the pawn island was already there!) In Chess960, the rook pawn is the true soldier of honour on the chess board in some SP's!

To summarise, black thinks about king safety in three ways:

  1. Kingside castle perhaps
  2. Centre fortress under guard of the knights developing his king to E8
  3. Queenside castle perhaps under guard of the bishops

I guess there will be a lot more to say on SP080 over the years! It is possible that one day someone will find a killer line where black cannot even draw, but remember that SP080 still has a lot of life in it in the meantime, that there is a lot of challenge and creativity in the SP (especially regarding defensive technique), that black could well find a bullet proof defense after a lot of analysis of this SP, and that in practice, if white makes one slip, black can fight back!

Any thoughts?

Cheers