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Posers and Puzzles

Posers and Puzzles

  1. 30 Mar '05 14:01
    What is your least upper bound for the longest possible game of chess?
  2. 30 Mar '05 14:15
    Originally posted by THUDandBLUNDER
    What is your least upper bound for the longest possible game of chess?
    What do ye mean? (least upperbound)
  3. 30 Mar '05 15:19 / 3 edits
    Originally posted by jimslyp69
    What do ye mean? (least upperbound)
    I mean that, using a few criteria, we can estimate it at n, say.
    Then, using a few more, we can lower that estimate.
    The more rules we apply, the more we can lower it.

    To start off, consider the 50-move rule.
    (Assume that the 50-move rule is in fact invoked after 50 moves.)
  4. 30 Mar '05 16:29
    Originally posted by THUDandBLUNDER
    What is your least upper bound for the longest possible game of chess?
    If I understand your question correctly, your asking the maximum numbers of moves that can be done in a chessgame.

    The answer is pretty easy, infinite. Rules like the 50-movesrule do not limit the length of the longest possible game. The problem with this rule (and with the threefoldrepetition rule) is that it needs to be claimed by either one of the players. If none do, the game goes on. (and on and on and on).

    With that out of the way your question would proberbly be, but how long can a game last if one does claim a draw as soon as he/she can. OK then our problem would be the 50-moves rule stating that a draw may be claimed if there where no captures or pawn moves for 100 half-moves. The best thing to do is to start moving with the Knights and on the 50th move you play e2-e3 (or another pawn black or white). You can keep this up for quite a while but eventually you will have to capture and or promote. Enough with the talk lets calculate.

    On a chessboard we've got a total of 16 pawns good for 7 moves each.
    We've got a total of 30 pieces wich can be captured (capture the pawns after they've been promoted.) good for 1 move each.
    Knowing this you should say the longest possible game should last (16x7+30) x 50 = 7.100 moves. But this is incorrect because in order to create passed pawns you need to capture with your pawn which wastes a move. In order to create 16 passed pawns you need to "waste" at least 7 moves. which shortens your game with a total of 7 x 50 = 350 moves. So the longest possible game by your means is 7.100 - 350 = 6.750 moves. (I hope your not playing by the limit of 40 moves in 2 hours).

    Hope this answers your question.

    A more interesting question to my would be. Know we know the longest possible game, what are the number of different games that can be played. I know the result would be a higher number the the total of drops of water on this planet. But still it is limited. I however don't know how to calculate this. (I get stuck on move 2 for white :-)) Has anyone else ever tried?
  5. Standard member Bowmann
    Non-Subscriber
    30 Mar '05 17:16
    Originally posted by Siebren
    6.750 moves.
    That can't be right. Less than eight moves?
  6. Standard member Bowmann
    Non-Subscriber
    30 Mar '05 17:19
    Originally posted by Siebren
    A more interesting question to my would be...what are the number of different games that can be played. I know the result would be a higher number the the total of drops of water on this planet. But still it is limited. I however don't know how to calculate this. (I get stuck on move 2 for white :-)) Has anyone else ever tried?
    10^15,790.
  7. 30 Mar '05 18:00
    Originally posted by THUDandBLUNDER


    To start off, consider the 50-move rule.
    (Assume that the 50-move rule is in fact invoked after 50 moves.)
    Siebren, see above.
  8. 30 Mar '05 19:01
    Originally posted by Bowmann
    That can't be right. Less than eight moves?
    yes six and a threequarter move. ever played a threequarter move? it's when you half finished a half move,.. ahh the English,... :-P
  9. 30 Mar '05 19:02
    Originally posted by Bowmann
    10^15,790.
    Bowmann how is this calculated?
  10. 30 Mar '05 19:03
    Originally posted by THUDandBLUNDER
    Siebren, see above.
    you're rigth I overlooked that one..
  11. Standard member Bowmann
    Non-Subscriber
    30 Mar '05 19:10
    Originally posted by Siebren
    Bowmann how is this calculated?
    You may get a clue when T&B gives you an answer.
  12. 30 Mar '05 21:10
    Hmm.
    So its (maximum possible pieces + pawn moves) * 49 (1less than 50)
    Max poss pawn moves: 72
    All pawns promoted into other pieces 16 + existing pieces 32 = 48
    so its (72 + 48) * 49
    = 5880 moves
  13. 30 Mar '05 21:12
    Originally posted by jimslyp69
    Hmm.
    So its (maximum possible pieces + pawn moves) * 49 (1less than 50)
    Max poss pawn moves: 72
    All pawns promoted into other pieces 16 + existing pieces 32 = 48
    so its (72 + 48) * 49
    = 5880 moves
    Ooops. Slight revision
    Kings can't be taken so that's - 49 * 2
    Also we need minimum piece for check mate. ie one rook so that - 49
    so its 5773 moves folks.
  14. 30 Mar '05 23:38 / 1 edit
    Originally posted by Siebren
    what are the number of different games that can be played. I know the result would be a higher number the the total of drops of water on this planet. But still it is limited. I however don't know how to calculate this. (I get stuck on move 2 for white :-)) Has anyone else ever tried?
    http://mathworld.wolfram.com/Chess.html

    http://www.cs.berkeley.edu/~flab/chess/statistics-games.html
    http://www.cs.berkeley.edu/~flab/chess/statistics-positions.html

    http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A006494
    http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A019319


  15. Standard member Bowmann
    Non-Subscriber
    31 Mar '05 00:26
    Originally posted by Siebren
    Bowmann how is this calculated?
    Very approximately as:

    321^6300 = 10^15,790