10557 Players currently online!
Man vs. Machine - good luck!
Turn-based games at any time!
Vote for the best move to win!
Do you have what it takes?
Backgammon, Yatzy, and more!
Sharpen your tactical vision!
Get advice and game insights!
Learn from top players & pros!
View millions of master games!
Your virtual chess coach!
Perfect your opening moves!
Test your skills vs. computer!
Find the right private coach!
Can you solve it each day?
Bring it all together!
Beginners, start here!
Make friends & play team games!
News from the world of chess!
Search all Chess.com members!
Find local clubs & events!
Who's the best of your friends?
Read what members are saying!
I heard that Chess960 is called like this because 960 means all positions of this type of game. But how was this number calculated?
Wikipedia can explain it better than me:
"Each bishop can take one of four positions, the queen one of six, and the two knights can assume five or four possible positions respectively. This leaves three open squares which the king and rooks must occupy according to setup stipulations, without choice. This means there are 4×4×6×5×4 = 1920 possible starting positions if the two knights were different in some way. However, the two knights are indistinguishable during play (if swapped, there would be no difference), so the number of distinguishable possible positions is half of 1920, or 1920/2 = 960. (Half of the 960 are left-right mirror images of the other half, however Chess960 castling rules preserve left-right asymmetry in play.)"
Though calculating this number is related to permutation, the link you provided was not as useful for my question, although it can be very useful for students of high school math.
Wikipedia can explain it better than me:
Interesting, but what about i start with the knights? Using the same logic, each knight can take 8 and 7 squares, the queen six, the bishops depends where the other pieces stay. How we do it now?
I sat down & did this calculation several months ago & managed to make it tally - this is how I reasoned it out...
L.S.Bishop ...... 4 squares (4 permutations in total)D.S.Bishop ...... 4 squares (16 permutations in total)Queen ........... 6 squares (96 permutations in total)Knight-pair ..... 10 possible pairings on 5 squares (4+3+2+1)
This leaves 3 squares for king & rooks but since the king must always have a rook on either side (otherwise, how do you castle?), there's only 1 permutation of this.
Gives 960 possible arrangements of pieces!
* Because one knight is indistinguishable from the other, if you start with the knights, all possible permutations are 7+6+5+4+3+2+1 = 28 instead of 8 x 7 = 56 !
Edit: If you start with all permutations for the knights, it seems as if the calculation doesn't work because 960 can't be divided by 28 but you have to take into account that when both knights are on different-coloured squares, there are 9 permutations of bishops, whereas when the knights are on same-coloured squares, there are only 8 permutations of bishops.
Much better to start with the bishops
Thinking well, it should be renamed to Chess959, since 1 of 960 positions is the standard.
Unless it's actually left out (is it?) why not count it?
It is counted. 1 X 960 = 960.
@wafflemaster, i believe that the original idea of Chess960(or Fischer Random) was a attempt to rupture with the classical chess, avoiding all the openings well-known in the standard position. So, it should be Chess 959.
Either the classic position is or is not allowed in 960. This is the only thing that determines whether it's counted or not.
Chess 1 (normal chess), vs Chess 960 (variations which include normal chess).
Rooks need not be on opposite sides of the King at start. Indeed one or both could be in the end castling position at game's start. Some sites have the rule of plunking the K on top of the R to achieve the castling move, others have you lift and replace the K, still others have differing methods.
sftac, I havn't played a great many games of 960 but I can't remember one in which both rooks were on the same side of the king at the start. Also, the calculation doesn't come out correctly unless you assume that the king is always placed between the rooks.
If what you say were true, it would be called Chess 2880 instaed so I really have to challenge your claim!
In Chess 960 the king is always between the rooks, this allows kingside and queenside castling similarly to regular chess.
Chess960 is not the only option for random chess. It is always possible to allow any possible starting position for the pieces on the back rank. Then it is even possible to have both bishops starting on the same color.
A little combinatorics.
About any possible position with the pieces on backrank, would be also possible the 2 rooks on the same side(especially with king on the corner), making castling impossible. It wouldn't be the best way to play chess IMO.
Its called Chess 960 because in the year 960bc, the guy who was playing black was a sore loser; and every yr he came back and said,"let's try it this way"; it took him 960 yrs to finally win a game; ya know, like the Red Sox!
by Aquarius550 5 minutes ago
Playing 1. e4 as White
by ylblai2 7 minutes ago
9/3/2015 - Keres - Petrosian
by vahid13661366 14 minutes ago
Who do you think was the best chess player of all time?
by joshuameain 19 minutes ago
How do you earn points in chess.com
by Daniel-Gong 26 minutes ago
Chess In Eastern New Mexico
by Phythalion 36 minutes ago
Post You're Chess Sets
by PhantomCapablanca 40 minutes ago
Kings Gambit Accepted, Three Pawns Variation
by batgirl 42 minutes ago
How High Rated Did I play?
by Aquarius550 45 minutes ago
What side do you like to put the chess clock?
by alex-rodriguez 46 minutes ago
Why Join | Chess Topics |
Help & Support |
© 2015 Chess.com
• Chess - English
We are working hard to make Chess.com available in over 70 languages. Check back over the year as we develop the technology to add more, and we will try our best to notify you when your language is ready for translating!