960 random thoughts

Yeah, I get the feeling some players feel like "if we both started from square one..." idea.  The best 960 players would of course still be the best standard players.  Not the exact order, I'm talking 1500s will be better 960 players than 1300s etc.  Largely because the endgame and strategy (and of course tactics!) are all the same.

It doesn't take an expert to see that opening memorisation reduces the skill factor.  Someone who's been playing for a couple of weeks could figure that out.

I think some of you are being rather condescending to beginners here.  In fact, in one respect I think beginners are a better judge of whether 960 or chess is "best".  We've been playing for so long that we are surely blinded to some of chess's faults.  And we, having invested time and effort in studying opening theory, are surely biased to some degree.

Orange Honda:

"Didn't say it very clearly in the last post... what I mean is although the ideas are interesting it's not clear if you (Eberulf) are presenting these ideas from a theoretical standpoint, as in outlining the extent of what 960 positions offer in terms of novel strategic ideas or more from a players point of view where the random starts level the playing field as far as memorized openings and opening theory."

Most recenly I've been saying the former - that there will be many more board configurations than occur in standard chess. I think my example with the knight on D3 should indicate that for anyone who reflects on it for a moment.  Its not a question of what's possible in standard, because any board configuration would be  theoretically possible no matter how unlikely it is.  So the question is the number of board configs weighted by probability.  But I've been trying to find a college math or statistics paper that analyizes 960 from this standpoint, and also that possibly shows that there is structure in these additional configs, because if the'yre just random then no new theory for 960 is possible.   

Benko the colloborator with Fischer on 960 was actually a math prof and was the one who determined there were 960 starting configs (found that out yesterday).  But that would have been pretty trivial for a math prof, so was hoping there was another paper by him analyzing 960 more in depth along the lines outlined above.  Haven't found anything yet.  Have also been googling "Chess960 university department abstract references conclusion mathematics statistics".  (No luck yet.)

But regarding the second of your alternatives above, sure, it levels the playing field regarding opening theory.  But it goes beyond that - I'm thinking regardless of what a player knows of openings in standard, there is this deep intuitive knowledge shared among every player of standard chess, regardless of ability, regarding that standard opening config, and regarding the types of board configurations that can evolve from it.  You could say that the types of configs that can evolve from it are unlimited, but that is true I believe in only a theoretical sense.  But there are types of players (perhaps me and others) who will excel at 960 instead of having to continually fight this intrinsic knowledge among opponents of that standard opening config.  

"In either case there are two basic points I had in the back of my mind.  First is, the more I think about it, I see all the fundamental middlegame strategy for 960 is the same as standard chess.  What it has is novel openings and unique middlegames.  The second is, due to your experience with standard chess you may not realize how deep and novel certain positions in standard chess can be.  For example how knights aren't uncommon on d3.

In short 960 doesn't seem as novel and unexplored as you may think and standard may not be as shallow as you may think.  They're actually pretty similar.  It's biggest appeal would be to GMs who have memorized countless middlegame positions.  For these players it's the most different.  As I look at some 960 games and ideas I'm realizing to a player like me it's actually a very similar game.  All the familiar advantages are there, simply break them down and configure my pieces around them."

I have to repeat this - your online profile doesn't show you as having played 960. (At least not three days ago it didn't - of course you could have hammered out a few 960 games in the interim which would be a good thing.)  And also your assertion that knights on D3 are common.  Why would you just assert that without any sort of proof.  When I remarked on it earlier at least I observed that it takes one white knight at least 4 moves to reach it and the other 3 whereas in 960 20-25% of the board configs can  hit it on the first move.  I don't currently have a premium membership but did at one point. It might be possible to use the chess.com DB here to resolve this.

But perhaps all online forum debaters should be required to actually  play a chess match against each other to determine whose ideas are most valid.  It looks like your game of choice is bullet or blitz and mine is currently 960, so who knows.

[Anyone know how to break up a chess.com quote block.]

that is a good theory. the bias would come into play in many cases. yet someone who is "tactically toothless" (saw that phase in a book the other day and had a good laugh) might be even but not enough to decide..  .. what about someone who does tactics puzzles for a long time and never plays a real game? that would seem a legit way of testing.

I do agree that 960 does have its place.(and I like to play 960 myself!) I just dont think that normal chess should be "dead" to anyone whos just starting out. 

from what Ive seen the real starting position for chess seems to be the most dynamic. if anyone sees 960 position that is ripe with more ideas than the normal way please let me know.

I've been fiddling with analyzing 1,014,000 pgn games this weekend. So I counted the number of times a white knight was on any square at any point in any of the games. I get 17,811,398 knight appearances total. 959,372 of those are on d3. d3 is the 17th most common square for a knight to appear on.

Could you list the entire distribution -

1

2

...

17 D3

18

etc.

Also, how were those pgn games selected.

Also, how many games of those 1 million plus did a knight land on D3.  (Previously I speculated it would be 1 out of 1000 in the early part of the game, so also what % landed on D3 within the first 10 moves.)

More on d3:

I tracked down the first post mentioning d3 (#58 I believe), when it was talked about happening "early in the game."

I redid the counts for the first 10 moves. I get 10,172,933 white knight placements, 12,269 of them on d3, which is the 25th most common square.

Extending that to the first 20 moves I get 15,601,197 white knight placements, 266,407 of them on d3, which is the 21st most common square.

@Eberulf: I don't know how the games are selected. It's the Million Base available from http://www.top-5000.nl/pgn.htm. It's got 1.74 million games, but my bare bones pgn reader was only able to parse the first 1,014,000 games. Give me a minute on the full list.

Formally there are 960 starting positions, but in actuality there is less because for example the two Knights or the two Rooks are the same piece so if one Knight is on c1 and the other one is on h1 the position is the same regardless of which Knight is on which square. (Hope that this makes sense.) Also I think that it is accepted that Bishops should be placed on squares of different color and that configurations with Bishops on same color squares are not utilized. 

ichabod801:

"I redid the counts for the first 10 moves. I get 10,172,933 white knight placements, 12,269 of them on d3, which is the 25th most common square."

10,172,933/12,269 = 1271

Me [post #58]:

"And aside from the minimal number of moves necessary,  can one even imagine the scenario where that move [white ND3] would occur.  Early in the game it must happen in 1 game out of 1000 or something."

For the whole game:

1. f3 (17811398)
2. c3 (17120035)
3. b1 (11222747)
4. g1 (7912743)
5. d2 (4244367)
6. d4 (3709381)
7. e2 (3188681)
8. e5 (1705193)
9. e4 (1663084)
10. b3 (1659241)
11. g3 (1537614)
12. d5 (1213869)
13. c4 (1202536)
14. e3 (1181305)
15. b5 (996069)
16. g5 (974348)
17. d3 (959372)
18. f4 (866372)
19. a4 (778164)
20. c5 (619908)
21. h4 (610951)
22. f5 (597956)
23. c2 (566350)
24. f1 (560219)
25. a3 (541917)
26. e1 (531996)
27. d6 (477962)
28. f2 (466940)
29. d1 (440327)
30. c6 (388081)
31. h3 (379509)
32. g4 (325908)
33. h2 (325364)
34. e6 (283796)
35. c1 (258843)
36. b6 (250621)
37. a5 (248439)
38. f6 (245731)
39. g2 (227182)
40. b4 (219439)
41. h5 (216446)
42. c7 (157757)
43. b2 (145179)
44. a2 (136078)
45. e7 (132228)
46. d7 (117829)
47. g6 (115248)
48. f7 (115060)
49. b7 (95807)
50. h6 (85825)
51. a7 (66904)
52. a6 (62491)
53. g7 (48160)
54. a8 (45951)
55. c8 (43740)
56. h7 (43359)
57. e8 (38083)
58. d8 (37375)
59. h1 (28245)
60. f8 (28063)
61. a1 (26473)
62. h8 (23023)
63. b8 (16589)
64. g8 (9410)

The 960 count takes into consideration that knights and rooks are interchangeable, and that bishops are on different colors (and that the king is between the rooks). Without any restrictions and treating the knights and rooks as unique, there are 40,320 ways to arrange the back rank pieces (8!)

My numbers don't really correlate to games. They don't even really correlate to positions, because any position with two knights in it is counted twice, and positions without knights aren't counted at all. I would have to program a different analysis. I just threw those numbers up because they were easy to get out of the data I've been collecting this weekend. Which took 2 1/2 hours to run after I programmed it.

ichabod801:

Thanks for that - it seems like it basically confirmed that one specific comment I made I mention above but I'll have to look more into it, as well as that site.  But thanks a lot for the info.

10,172,933/12,269 = 1271

wrong

10,172,933/12,269 = 829

I accidently used the previous value of 15,601,197 for the numerator.

But anyway something like 1/4 in 960 vs 1/829 in standard.  (1 out of 4 because any 960 starting config with a white knight on either of 2 squares can hit D3 on first move and there are 8 squares so approx 25% but maybe slightly less even though its a logical first move.

if there are 10,172,933 knight moves in the first 10 moves and it takes on average 3.5 moves for a white knight to even reach D3 its probably going to only hit it once in that first 10 moves if at all  So that would come out to 1 game out of 829.  (But my specific comment was regarding the white knight and I don't know if your results measured that. 

--------------------

Wait - thats not right - your the math prof you can take a stab at it I guess.  I'll come back to this thread later.

Well How Very Bizzar

For another high level game where the Knight lands on d3 see Perlis-Tartakower here (just appeared on the chess.com front page):

http://www.chess.com/article/view/move-order-to-oblivion-amp-studying-games

I think it is more like it that a beginner or an intermediate player is not likely to put a Knight on d3; strong players do. (It's often not a bad field for it all.)

"And aside from the minimal number of moves necessary,  can one even imagine the scenario where that move [white ND3] would occur.  Early in the game it must happen in 1 game out of 1000 or something."

As it turns out I was wrong, though: its 1 out of 252 games in which the white knight lands on D3 in the first 10 moves.  That's in comparison to 1 out of 4 games in chess960.  So, 63 times more likely in 960 (64 squares,  63 times more likely - interesting  coincidence.)

(Ichabod801 - if you're still reading this thread you could just load that DB file into ChessDB and it takes half a minute to run a query. 4 minutes to load though.)

Where's the fun in that?