6 ms·

Great question. This was foreseen long ago (1500s?); the turn wasting thing is limited by the fifty move rule. A game ends in a draw if no pawn is moved or piec

Great question. This was foreseen long ago (1500s?); the turn wasting thing is limited by the fifty move rule. A game ends in a draw if no pawn is moved or piece captured for 50 moves. Since pieces can only be removed not added and pawns can only move forward, never backward, this proves that cycles are not possible in chess (they certainly would be without this rule of course) See https://en.m.wikipedia.org/wiki/Fifty-move_rule https://en.m.wikipedia.org/wiki/Fifty-move_rule

nextaccountic 5y ago
The rule says a player can claim a draw, but they are not obligated to do. So, if you're a player and want to exhaust the search space, this only helps you if you seek a draw; but perhaps there would be a guaranteed win somewhere if you kept playing (and the opponent didn't claim their draw).
- PeterisP 5y ago
  There's the usual limits where one may claim a draw (threefold repetition or 50 moves without capture or pawn move), but there also are limits where a draw is automatic and should be enforced by the arbiter even if players do not request it (fivefold repetition or 75 moves without capture or pawn move).
pedrosorio 5y ago
Wouldn’t the 3-fold repetition rule also prevent cycles? https://en.m.wikipedia.org/wiki/Threefold_repetition https://en.m.wikipedia.org/wiki/Threefold_repetition
- galdosdi 5y ago
  Yes, definitely. I hadn't remembered that one. You could have much longer chains with the 3 fold repetition rule alone though. I guess both together potentially make it easier on the players and arbiters It seems the 50 move rule is probably older according to Wikipedia (1800s vs 1500s), which is kind of surprising to me, I would have expected the other way around. It's easier to keep track of "moves since last capture/pawn advance" than every board position played so far. Maybe just in theory not in practice. I am a terrible chess player.
  - pedrosorio 5y ago
    You should find it unsurprising that the simpler rule to keep track of came first, right? :)
    - galdosdi 5y ago
      Well when you put it that way I feel silly thinking otherwise haha
- nightcracker 5y ago
  Which begs the question: without the fifty-move rule (only threefold repetition), what is the longest legal chess game?
  - deleted 5y ago
    [deleted]
  - jakeinspace 5y ago
    Let's assume the 50-move rule is automatically applied. We can have 49 moves per pawn move, followed by 49 moves per piece captured. A maximum of 8 pawns (4 white and 4 black, for example) can possibly be advanced over the course of the game to the opposite side (6 squares ahead from their home square). Therefore, it seems to me that the maximum number of pawn moves could involve one player advancing their pawns 4 spaces, followed by the opposing player capturing all those pawns (using pieces rather than pawns, as both moving a pawn and capturing a pawn would be a waste), and then advancing their pawns to the back rank. This would be 8x4 + 86 = 80 pawn moves, plus 8 pawn captures. That's 88 allowances for 49-move knight sequences, plus the initial 49-move knight sequence made from move one. So, with no pawns remaining, and all of black's pawns converted to pieces on the back rank, we have 8949=4361 moves. Now, there are 22 pieces and 2 kings remaining on the board. That puts an upper limit of 22 captures, leading to an additional 2249 allowable moves. All together, that is 11149=5439 total moves. I'm probably off by a few.
    - vitus 5y ago
      > A maximum of 8 pawns (4 white and 4 black, for example) can possibly be advanced over the course of the game to the opposite side (6 squares ahead from their home square). Not so! Pawns move diagonally via capturing, which theoretically could allow white to promote all 8 pawns just in the d column, and black to promote all 8 in the e column (at the expense of various other pieces). edit: of course, you'd run out of pieces first, but you can accomplish something similar by using multiple columns. Sample game start that accomplishes a subset of this (2 pawns promoted from each side, 6 pawns remaining from each side): 1. Nf3 Nc6 2. Ng5 Nb4 3. Ne6 Nd3+ 4. exd3 dxe6 5. Ke2 Qd7 6. Kf3 Qc6+ 7. Kg3 e5 8. d4 e4 9. d5 e3 10. d6 e6 11. d7+ Ke7 12. d4 Kf6 13. d8=R e2 14. Rd5 e1=R 15. Ra5 Re5 16. d5 Rh5 17. d6 e5 18. d7 e4 19. d8=R e3 20. Rdd5 e2 21. Rdb5 e1=R https://lichess.org/wtJoIdT3#42 https://lichess.org/wtJoIdT3#42
- bluGill 5y ago
  3 fold is by mutual agreement, if one side wants to continue they can. At 5 there is no choice
  - anderskaseorg 5y ago
    No mutual agreement is needed. Either player can decide to claim a draw by threefold repetition (§9.2) or 50 moves (§9.3). The only difference with the fivefold repetition and 75 move rules (§9.6) is that those draws are automatic. https://handbook.fide.com/chapter/E012018 https://handbook.fide.com/chapter/E012018
    - bluGill 5y ago
      I stand corrected.
- missblit 5y ago
  The threefold repetition has to be claimed, so the game can legally go on if both players overlook (or ignore) it. There's also the fivefold repetition rule, which draws the game automatically.

nextaccountic 5y ago

The rule says a player can claim a draw, but they are not obligated to do. So, if you're a player and want to exhaust the search space, this only helps you if you seek a draw; but perhaps there would be a guaranteed win somewhere if you kept playing (and the opponent didn't claim their draw).

PeterisP 5y ago
There's the usual limits where one may claim a draw (threefold repetition or 50 moves without capture or pawn move), but there also are limits where a draw is automatic and should be enforced by the arbiter even if players do not request it (fivefold repetition or 75 moves without capture or pawn move).

pedrosorio 5y ago

Wouldn’t the 3-fold repetition rule also prevent cycles? https://en.m.wikipedia.org/wiki/Threefold_repetition https://en.m.wikipedia.org/wiki/Threefold_repetition

galdosdi 5y ago
Yes, definitely. I hadn't remembered that one. You could have much longer chains with the 3 fold repetition rule alone though. I guess both together potentially make it easier on the players and arbiters It seems the 50 move rule is probably older according to Wikipedia (1800s vs 1500s), which is kind of surprising to me, I would have expected the other way around. It's easier to keep track of "moves since last capture/pawn advance" than every board position played so far. Maybe just in theory not in practice. I am a terrible chess player.
- pedrosorio 5y ago
  You should find it unsurprising that the simpler rule to keep track of came first, right? :)
  - galdosdi 5y ago
    Well when you put it that way I feel silly thinking otherwise haha
nightcracker 5y ago
Which begs the question: without the fifty-move rule (only threefold repetition), what is the longest legal chess game?
- deleted 5y ago
  [deleted]
- jakeinspace 5y ago
  Let's assume the 50-move rule is automatically applied. We can have 49 moves per pawn move, followed by 49 moves per piece captured. A maximum of 8 pawns (4 white and 4 black, for example) can possibly be advanced over the course of the game to the opposite side (6 squares ahead from their home square). Therefore, it seems to me that the maximum number of pawn moves could involve one player advancing their pawns 4 spaces, followed by the opposing player capturing all those pawns (using pieces rather than pawns, as both moving a pawn and capturing a pawn would be a waste), and then advancing their pawns to the back rank. This would be 8x4 + 86 = 80 pawn moves, plus 8 pawn captures. That's 88 allowances for 49-move knight sequences, plus the initial 49-move knight sequence made from move one. So, with no pawns remaining, and all of black's pawns converted to pieces on the back rank, we have 8949=4361 moves. Now, there are 22 pieces and 2 kings remaining on the board. That puts an upper limit of 22 captures, leading to an additional 2249 allowable moves. All together, that is 11149=5439 total moves. I'm probably off by a few.
  - vitus 5y ago
    > A maximum of 8 pawns (4 white and 4 black, for example) can possibly be advanced over the course of the game to the opposite side (6 squares ahead from their home square). Not so! Pawns move diagonally via capturing, which theoretically could allow white to promote all 8 pawns just in the d column, and black to promote all 8 in the e column (at the expense of various other pieces). edit: of course, you'd run out of pieces first, but you can accomplish something similar by using multiple columns. Sample game start that accomplishes a subset of this (2 pawns promoted from each side, 6 pawns remaining from each side): 1. Nf3 Nc6 2. Ng5 Nb4 3. Ne6 Nd3+ 4. exd3 dxe6 5. Ke2 Qd7 6. Kf3 Qc6+ 7. Kg3 e5 8. d4 e4 9. d5 e3 10. d6 e6 11. d7+ Ke7 12. d4 Kf6 13. d8=R e2 14. Rd5 e1=R 15. Ra5 Re5 16. d5 Rh5 17. d6 e5 18. d7 e4 19. d8=R e3 20. Rdd5 e2 21. Rdb5 e1=R https://lichess.org/wtJoIdT3#42 https://lichess.org/wtJoIdT3#42
bluGill 5y ago
3 fold is by mutual agreement, if one side wants to continue they can. At 5 there is no choice
- anderskaseorg 5y ago
  No mutual agreement is needed. Either player can decide to claim a draw by threefold repetition (§9.2) or 50 moves (§9.3). The only difference with the fivefold repetition and 75 move rules (§9.6) is that those draws are automatic. https://handbook.fide.com/chapter/E012018 https://handbook.fide.com/chapter/E012018
  - bluGill 5y ago
    I stand corrected.
missblit 5y ago
The threefold repetition has to be claimed, so the game can legally go on if both players overlook (or ignore) it. There's also the fivefold repetition rule, which draws the game automatically.