You don't both the 50-move rule and the 3-fold repetition to prevent an infinite game of chess. It's impossible to have an infinite game of chess without repeating positions (there are only a finite number of positions), and it's also impossible to have an infinite game of chess where you move a pawn or capture a piece every 50 moves. *Either* rule prevents an infinite game of chess. You just need both rules so the arbiter can go home before his/her retirement.
Another point to note is that it is perfectly legal to repeat a position more than three times and keep playing. A player must elect to take the draw, it is not automatic. The only rule that prevents infinite length games is the 75 move which is like the 50 move rule but takes place automatically and need not be claimed.
fburton8> Yep, the key point is that the 3-fold repetition rule applies to positions not moves. But he said it has to happen three times _in a row_ which doesn't have to happen; they can do a four-cycle forever.
Note that a repeated "board state" does not mean simply "all the same pieces are on the same squares as before". The FIDE rules state that for a board state to be considered the same, it has to fulfill all these requirements: 1) All the same pieces (or more precisely the same types of piece) of the same color are on the same squares (it doesn't matter if two of the same-colored same type of pieces swap their position with each other, eg. to black knights can swap their positions with each other, and it's still considered the same). 2) It's the same player to move. 3) All the possible moves are the same. (This refers to castling rights and en passant right, which may differ between the two otherwise identical positions, making them "not the same board state". Note that a hard pin or an impossible castling (because of a king ending in check or passing through a checked square) does not affect the possible moves. They are still considered possible in this regard.) An interesting question is that, considering the above definition, what is the theoretical maximum number of times that the same _visual_ arrangement of pieces on the board can repeat without the three-fold repetition rule kicking in. (The answer is surprisingly large.)
Once with en passant possible for whoever's turn it is to move, four more times (twice with each player to move) without en passant, but with castling possible on both sides for both players, four more times for each of four more castling states, until no castling is possible, for a total of 21. The position could then occur a 22nd time with either player to move, which would be the third occurrence of one of the previous board states, and would draw the game. Note that there can't be another occurrence with en passant possible with the other side to move, because that would mean another pawn has moved, and even though there are four possible castling states for each side, you can't get all four of them in one game, because once castling becomes impossible on one side, it can't become possible again. For example, if the castling state is KQkq, and White loses the right to castle kingside so that it becomes Qkq, it can never be Kkq, KQq, or KQk in the same game.
@@Jivvi Indeed. The same visual position can theoretically repeat up to 21 times without the three-fold-repetition rule kicking in. Curiously, not many chess software implements three-fold-repetition checking to this level of accuracy. In many of them if you start playing in a manner that deliberately goes through all the 21 visual repetitions, many chess programs will declare it draw sooner (usually much sooner) than that. There are some notable exceptions though. Also, basically no chess engine bothers to make the check to that level of accuracy (because there really isn't any need. It has no effect on playing strength or validity, but on the contrary not doing the checking to that level of accuracy saves time.)
The answer is borderline impossible to calculate because of how many moves get added to the equation with every passing move. It's easy to start with when there are only 20 legal moves at the start for each player, but the number and calculation gets astronomically more complex the further into even a single game, let alone all possible games and moves.
There is a 75 move rule as well. It's like the 50 move rule, except instead of allowing a player to claim a draw, after 75 moves (without moving a pawn or capturing a piece), the ARBITER can go in and declare a draw. So (at least in tournaments), if neither player wants to admit a draw, an arbiter can still intervene eventually.
It doesn't require an arbiter. Rule 9.6 says: "9.6 If one or both of the following occur(s) then the game is drawn: a. the same position has appeared, as in 9.2b, for at least five consecutive alternate moves by each player. b. any consecutive series of 75 moves have been completed by each player without the movement of any pawn and without any capture. If the last move resulted in checkmate, that shall take precedence." So, after 75 moves without a capture or pawn movement, the game is over. Regardless of an arbiter present.
@@AbiGail-ok7fc Which means in practice, after 50 moves one of the player has to claim the draw, while if it was 80 such moves (no capture and pawn move) and ended in checkmate then the player can appeal and the result become a draw.
@@AbiGail-ok7fc Yes but a pattern like that requires that someone both notices it and has the desire to bring it to attention. And that means an arbiter. Players would have already chosen the 50-move rule if they noticed and wanted to bring it to attention.
I've always thought he says "if you happen, thanks for watching" (like, if you happen to be watching, thanks). Is it possible (I'm not a native speaker)?
an absolute honour working with you! We are editing away on our video about Hugh Alexander and we are very happy to announce that Grandmaster Simon Williams aka GingerGM will do the analysis of Hugh's brilliant win against Botvinnik.
3 fold repetition isn't when a sequence of moves is repeated three times, it's when a POSITION appears three times. And it is not necessary that they be consecutive.
Not really, it's actually quite easy as it's usually as they also said in the video when one tries to claim a draw while the other player does not. If one insist of playing on he or she won't repeat moves so it's not needed to remember, but if they do it's usually really quick.
8 pawns each with 6 forward moves possible each result in 6*8*2=128 pawn moves. There are 30 capturable pieces, 15 on each side, thanks to the pawns promoting and still being capturable later. (You can promote all 16 pawns on the board with collaborative capturing of enemy pieces to help the pawns change files and shuffle past opponent pawns. This is also how you can get 18 queens on the board.) The 50 move rule limits us to 49.5 (both players take 49 turns and only one of them completes their 50th turn, since a turn is both players moving. With 49.5 turns each time before we do an irreversible move (move pawn or capture) we cannot forget after our last capture, we still get 49.5 moves before end of game, so we can sneak in an extra +.5 before we multiply by 49.5. Then the game could end by a player triggering the 50 move rule as a bonus last last move. AND WE GET ((128+30+1)*49.5)+.5=7475 turns, so black would end the longest possible game by triggering the 50 move rule. That is 14950 total piece moves if you count each player's turns separately.
in the last few years two new rules were added: 75 move rule (which is similar to 50 move rule) when 75 moves have been made with a pawn being moved or a piece being captured, it has to be a draw regardless of whether its declared of not, similarly 5 fold repetition, when you reach the same position 5 times it becomes a draw regardless of whether its declared or not
And the reason that rule was created is because computer analysis found a condition in which a player could force a win in more than 50 moves but still be claimed as a draw by the other player because of the original 50-move rule.
to be technical, it's not three same moves, it's that the same position repeats three times that makes the draw. often it's result of consequent identical moves but this need not be the case. EDIT: this is addressed later on in the video
My favorite part about the 50 move rule is that there are positions which if played out lead to a forced checkmate after more than 50 moves without pawn moves or captures, so there are positions which are draws even though one player could win if this rule didn't exist. There are positions where 500 moves can be played between pawn moves/captures, but if allowed to continue play, one player can force a win!!!
It's so funny that the need for this would arise. I'd just use my own human power of choice in a situation where a game was regressing infinitely. Either a social appeal to my opponent, or an appeal to the laws of physics in the form of a table flip.
The rule is not a sequence of moves that repeats 3 times. It is a position (including same conditions, such as player to move, castling abilities, en passant possibility) that occurs three times.
Small addendum to 3-fold repetition rule. All 3 times when the position occurs on the board it has to be the same side on the move. I acctually remember interesting casus from the tournament when one player declared a move and claimed 3 fold repetition draw. It was true that after declared move would be played, the position would repeat for the third time, but this time it would be his opponent on the move, whilst previous two times it was him on the move. In consequence claim was denied he had to play declared move, which cost him a pawn and later he lost the game.
I remember when you briefly mentioned the rules that prevent an infinite game of chess on the Numberphile video about Shannon's number, so it's really nice to see you expand on that here. Lovely video--thanks to Rune and his team for this!
Funnily enough, the game at 0:58 is a win for Black. Rather than bouncing back and forth between the same two squares, Black can zigzag backwards until the Queen forks the King and Rook, then capture the Rook. From there it’s a won Queen vs. Pawn endgame with the Knight preventing any stalemate resources for White.
T Perm glad you mentioned this! I was thinking the same! Truly crazy to think about the idea that there could be a forced win with 65 precise moves in a theoretically “drawn” endgame. There are variations on the Queen v Rook endgame that can take more than 50 moves as well
Remember a move is made of a white and a black turn. Each player has 50 turns which is probably enough for all endgames. The rule is to avoid a situation where a player is in a winning possition and doesn't know how to mate, this will waste everybody's time. You should figure out mate patterns on your preparation, not in the board with an opponent.
Threefold repetition is based on board state and not move sequence. Your "infinite game" would end after the black knight moved back to its home square for the second time, since the starting postition, the middle position, and the end position would all be the same.
You should talk about the proof by backward induction that chess is a solvable game. I.e. either white can force a win, white can force a draw or black can force a win. Though the solution is not known since there is an absurdly high number of possible chess games. Regardless of how fast computers get we will never have enough memory to store the solution because there isn't enough matter in the universe.
@@jasondoe2596 That's an interesting way to think about it. A solution to chess is an endgame table worked all the way back to the starting state of the game.
@@thatunnamedredshirt We're not talking about regular mathematical induction but backward induction. Imagine all possible chess games as part of a tree with its root node being the starting state of the game. If you go to the deepest node (the longest possible game under the modern rules) you will find several leaf nodes with one parent. The leaf nodes each represent one of three scenarios: white wins, black wins or draw. Now take the parent node and look whose move it is, if it's white's move and one of the leafs is a win for white then parent is reduced to a white wins node and the leafs discarded since we assume both players are playing optimally. The same logic applies for black wins and a draw. If you reduce the tree all the way back to the root node you get a solution for chess where both players play optimally. Either white can force a win or a draw or black can force a win. The other player isn't able to do anything about it assuming optimal play.
The 3-fold repitition counts only the position. It doesn't matter if it's in sequence, if the same position repeats 3 times, it's a draw. Which is sufficient to prevent an infinite game, because there's finitely many positions on a chess board and you'd eventually exhaust them and have to repeat positions if the game is not to conclude in mate or draw by insufficient material. HOWEVER, the 50 move rule was created to prevent drawn endgames to drag out "forever", because even with 3-fold repitition can lead to quite long sequences of moves being prepeated. For instance, a rook and king vs a rook and knight endgame is in most cases theoretically a drawn endgame, but it can still drag out for quite long without a mate. To prevent such cases, the 50 move rule was invented to put a hard limit on how long a chess game can go on without anything happening.
this is the first time I heard the name bu I discovered this sequence quite a while ago in an unexpected place. I was playing around with infinite nested fraction. The fraktion starts with a 1 at the top of the numerator then you put division line and put the next number below, which is 2. Then the way to grow the fraction is by putting a "bigger" division line below and do the same below as you did above but with increasing numbers as you go down. Where thue-morse sequence comes in is if you instead structure it a product of all the integers but to the power of either 1 or -1, the sequence of -1 and 1 would be the thue-morse sequence.
That's kinda a weird way of putting it. Rather, it takes affect whether or not the players want it. If no one notices something, how can it be enforced?
@@hamsterfromabove8905 The game is officially over at that point, whether the players notice or not. So even if someone "wins" after that, it doesn't count. They can play on, but the game is over.
The repetition of moves rule does not require that the moves be consecutive, only that the position be repeated three times with the same player to move.
Photographic position rule prevents thus because if a position comes on a board 3 times (doesn't matter if its in a row or not), a player can claim a draw
Three-fold repetition refers to the position, not the sequence of moves. If a position occurs three times at any three points in a game, the game is drawn.
Occasionally the 50 moves rule is rescinded to (say) 75 or even lifted entirely, consider the "white to move and mate in 500+" puzzle where eight pieces are onboard including the two kings and white's first move is queen takes black queen.
It wasn't imaginary. That's how the rule used to be before the 1890s. Same deal with sequential repetition in shogi, until that too was changed, but much later (in 1983).
Assuming we're in a tournament, the game organizers can declare a draw, regardless of any repetitions, if it's clearly obvious each player is beyond the 50 move rule, as score must be kept. This happens in kid's tournaments sometimes especially if the time for the next round is approaching. No master-level players would do this, as one player almost always claims a draw as soon as the 3rd position arises, or the 50-move rule applies. Keep in mind the 50-move rule is cumulative; that is, if not claimed on the 50th move, it can be claimed on 51st, or 52nd, etc, (so long as no pawns move or no captures take place. Either of those would restart the count. The same goes for repetitions.) Also, games are timed, so that tends to make infinite games unlikely.
I knew you guys were somewhere special at the outset by the lighting and the background. But wow, I was really surprised. So cool that it’s Alan Turing’s old haunt. I think he put ads in the Times seeking crossword geeks and chess players. Everyone must read Simon Singh’s The Code Book. The section on Bletchley Park is phenomenal.
The construction of the sequence is amazingly similar to one way of making the dragon curve. If we say a 0 is a left turn and a 1 is a right turn, starting with a left turn the sequence can be built by adding a left turn and then going backwards along the previous step inverting each position. So the first step is a 0, then you add a 0 to the end and run backwards inverting it so 001, then again 001 0 011, etc, 0010011 0 0011011. So one very long curve would be 001001100011011000100111001100011001100011011100100111001101100010011000110110001001110011001110011000110111001001110011011
POintless discussion. First read, the rules: Article 9.2: The game is drawn upon a correct claim by the player having the move, when the same position, for at least the third time (not necessarily by a repetition of moves): a. is about to appear, if he first writes his move on his scoresheet and declares to the arbiter his intention to make this move, or b. has just appeared, and the player claiming the draw has the move.
It interesting, that according to endgame tables some positions are winnable, but require much more moves than 50. For example there is a position Queen and Knight against Rook, Bishop and Knight that requires 517 moves to win. Also if I recall correctly there is Queen and Knight against Queen endgame with 529 moves to win. Obviously no human player can make such an analysis behind the board.
Yes, that's the entire point. If your opponent can't figure out or isn't able to checkmate, then they don't get to have a win. But you also can't win. So its a draw.
This is similar to superko rules in go. There is positional superko, where the board state cannot repeat, and situational superko, where the board state cannot repeat with the same player to move, which have subtle differences in various pathological game states.
He says that the 50 move rule isn't sufficient, but I think it is. The boardstates rule is also sufficient. Could he have meant that they are individually sufficient, but they have both just to have more potential options so that the game doesn't drag on for days?
1:31 The repetition must not be in sequence. Any 3 repetition during the game gives the right to draw. Even more, the figures must not be the same figures, rooks or knights may have swapped their places, still validating for repetition.
Yeah, I was thining the same thing.. This rule alone would make an infinite game inpossible but they could become insanelly long so that is the reason for the 50 move rule..
No, you are quoting a different rule, that's the point of this video. The previous rule was a sequence of moves which is repeated 3 times in a row is a draw. The NEW rule is a repetition of position 3 times is a draw, with no rules regarding whether they are in a row at all.
@@philipmorse-fortier5499 Yes, exactly! They actually discussed this later. Still I left my hasty comment there, for those who don't dear to watch to the end.
If you want to dip into crazy chess rules, as far as the rules limit you, you can promote the king's pawn into a rook and provided that rook and the king haven't moved yet, don't castle out of, through, or into check, you can castle across the board toward the enemy. The king would still move his standard 2 moves. I've only seen it once and it didn't help the player, more just showboating.
I did some research into this and it appears that a couple of people wrote about the possibility of castling that way because it technically satisfied the wording of the requirements for castling in the FIDE rulebook. It was a loophole, one that was fixed in 1970 and has been an illegal move ever since. It has never been played in a tournament.
It's more than just the position. You can have the same position three times with the king on e1 and a rook on h1, but it's not a threefold repition i.e. if castleing was a legal move the first 2 times, but due to some Kf1 Ke1 manouver the right to castle is lost (same goes for en passant, obviously)
At 6:50 Just to throw a spanner in the works I believe that the three fold rep has to be claimed by one of the players.. I'm not 100% sure but I reckon if both players so choose they can legally ignore the rule. Similarly the same thing may well be true of the 50 move rule.
It's very easy to set up a an infinite game of chess. It's possible for the game to wind down to just the two kings. At that point, unless one of them messes up big-time, they will usually end up chasing each other around the board indefinitely, and they can do so with many moves before repeating one.
1) In fact, with just the two kings, it's _impossible_ to mess up unless you violate the rules :P 2) Many moves, but not _infinite_ moves. There's a finite number of board states, so eventually one will reappear.
Also, officially there is a 75 move limit. If no piece was taken and no pawn moved in 75 moves then the game is a draw, irregardless of what the players want.
When checkmate is no longer possible it is an automatic draw. But even disregarding that, before Euwe it would have been thought that eventually you would have a repeating sequence of moves in this case, and thus a draw. Clearly positions will repeat, but as Euwe showed, not necessarily sequences of moves.
Actually, the players can't play forever, even if they wanted to: From the FIDE Handbook: www.fide.com/fide/handbook.html?id=171&view=article "9.6 If one or both of the following occur(s) then the game is drawn: the same position has appeared, as in 9.2b, for at least five consecutive alternate moves by each player. any consecutive series of 75 moves have been completed by each player without the movement of any pawn and without any capture. If the last move resulted in checkmate, that shall take precedence." while the 3-fold repetition and 50 move rule are "upon a correct claim by a player having the move".
"The game is drawn, upon a correct claim by the player having the move, when the same position, for at least the third time (not necessarily by sequential repetition of moves)" 3 fold repetition wiki
Wait, how does the 50 move rule not prevent an infinite game? Pawns can only move so many spaces before getting promoted, and there’s only a finite number of pieces that can be captured.
No, we still can't have a infinite game even if we don't claim a draw because for that reason we have 5 fold repetition and 75 move rule which forcibly terminates the game
That's also correct. Any length that is a power of 2 will give two different sequences of that length, which when replaced by 0 and 1, will give the original sequence.
Just a little precision about the "threefold repetition" rules. You sais @ 1:30 that it has to repeat 3 times in a row. And it is not exactly correct. The players can claim a draw if : the same position occurs three times, or will occur after their next move, with the same player to move. It doesn't have to be in a row.
If someone askes "but why showed it is not" then sorry they corrected it later on to waste time. The 3 move repetition rule does not exist anymore. 50 move rule is also automatically a none inifite rule You have to capture or move a pawn within 50 moves, thus at one point you ran out of pawn/moves and things to capture and game ends.
This video is about the old rule. We say "The rule was..." and explain the old rule and the problem with the old rule. We then describe the new rule at the end of the video.
even though that with the 3 move repetition must be claimed to make the game a draw, if the same move is repeated 5 times, the arbiter must stop the payers and make the game a draw. Likewise, if the same position is repeated 5 times or no player have moved a pawn or captured a piece in 75 moves, the game must end in a draw
I feel like this sequence is somehow connected to the dragon curve. I wonder if there is a nice mathematical relationship between them. I would also appreciate a longer video explaining the proof. Not every step was explained, and I'm somewhat struggling to fill in the gaps
The Threefold rule is not a sequence of moves, it's the same position being repeated three times...so it doesn't matter how you get to that position. Nice to see a video though!
No. That information needs to be forefronted since the video is called "The Infinite Game of Chess" and implies an error in chess as constituted now instead of previous flawed rules.
Many such positions have been found using computers to construct "endgame tablebases" (Google'able term). The longest known sequence that leads to a win (with perfect play from both sides) is over 500 moves long. Since several such positions have been discovered, and more will be in the future, but all are pretty much impossible to calculate by unassisted humans, it has been decided to keep the practical 50-move rule. (However, correspondence chess, which is often computer-assisted, apparently allows to claim such victories.)
the problem is that to get an infinite game neither play can be trying to win and have to only be playing move they know wont get them anywhere. also most ppl who are playing with these kind of rules (the little known ones) are always playing with a timer anyway... so yea its not really and issue.
wtf? its just longer sequence then 4 moves, thats it. There will not be infinite long sequence on finite chess board hence you cant infinitly play chess just by having rule of draw when 3 times same sequence. Also there are rules that forces you to take piece or move pawn with 50 moves so it makes those sequences smaller. (Sometimes it even makes diferent outcome on games coz someone forgot how to win in 50 moves and so on exapmple ending with knight bishup in 50 forced draw + some exceptions of needing more then 50 moves exist but rule is stil 50 coz theres very small chance of having those boards and coming up with solutions on the spot while defending position corectly). (and theres 75 move for referee)
This is close to being the most unimportant and trivial video on youtube. It is almost 9 minutes long but could have been explained in under a minute. In any game or sport, of course, there is made a limit to how long a game can last, or else it wouldn't work at a high level. So to the question "Can there be an infinite game of chess?" - "No, because there are rules." That is the answer and it is very simple.
I don’t understand what is meant by odd position. There are to ones in position 1 and 2. Taking the first digit to be zero. So the double digits are on an even number and an odd number? Eg position number 1 and 2
Video title: Infinite game of chess
Video length: under 10 mins.
Me: Hmm, something is wrong
Great vid! :]
Just loop the video
Auro Cords did you just solve the Halting Problem!?
Each move takes half as much time as the previous
Just play it backward, backwards and forwards again ... then mirror that total order, and you have your building blocks.
Supertask, infinite game in finite time.
You don't both the 50-move rule and the 3-fold repetition to prevent an infinite game of chess. It's impossible to have an infinite game of chess without repeating positions (there are only a finite number of positions), and it's also impossible to have an infinite game of chess where you move a pawn or capture a piece every 50 moves. *Either* rule prevents an infinite game of chess. You just need both rules so the arbiter can go home before his/her retirement.
Yep, the key point is that the 3-fold repetition rule applies to positions not moves.
Another point to note is that it is perfectly legal to repeat a position more than three times and keep playing. A player must elect to take the draw, it is not automatic. The only rule that prevents infinite length games is the 75 move which is like the 50 move rule but takes place automatically and need not be claimed.
@@Draz0000 Accepting that, do some (most?) online platforms enforce the 3-fold repetition constraint automatically?
@@fburton8 At least on Lichess, if a position is repeated 3 times, there will appear a button named "claim draw".
fburton8> Yep, the key point is that the 3-fold repetition rule applies to positions not moves.
But he said it has to happen three times _in a row_ which doesn't have to happen; they can do a four-cycle forever.
Note that a repeated "board state" does not mean simply "all the same pieces are on the same squares as before". The FIDE rules state that for a board state to be considered the same, it has to fulfill all these requirements:
1) All the same pieces (or more precisely the same types of piece) of the same color are on the same squares (it doesn't matter if two of the same-colored same type of pieces swap their position with each other, eg. to black knights can swap their positions with each other, and it's still considered the same).
2) It's the same player to move.
3) All the possible moves are the same. (This refers to castling rights and en passant right, which may differ between the two otherwise identical positions, making them "not the same board state". Note that a hard pin or an impossible castling (because of a king ending in check or passing through a checked square) does not affect the possible moves. They are still considered possible in this regard.)
An interesting question is that, considering the above definition, what is the theoretical maximum number of times that the same _visual_ arrangement of pieces on the board can repeat without the three-fold repetition rule kicking in. (The answer is surprisingly large.)
Once with en passant possible for whoever's turn it is to move, four more times (twice with each player to move) without en passant, but with castling possible on both sides for both players, four more times for each of four more castling states, until no castling is possible, for a total of 21. The position could then occur a 22nd time with either player to move, which would be the third occurrence of one of the previous board states, and would draw the game.
Note that there can't be another occurrence with en passant possible with the other side to move, because that would mean another pawn has moved, and even though there are four possible castling states for each side, you can't get all four of them in one game, because once castling becomes impossible on one side, it can't become possible again. For example, if the castling state is KQkq, and White loses the right to castle kingside so that it becomes Qkq, it can never be Kkq, KQq, or KQk in the same game.
@@Jivvi Indeed. The same visual position can theoretically repeat up to 21 times without the three-fold-repetition rule kicking in.
Curiously, not many chess software implements three-fold-repetition checking to this level of accuracy. In many of them if you start playing in a manner that deliberately goes through all the 21 visual repetitions, many chess programs will declare it draw sooner (usually much sooner) than that. There are some notable exceptions though.
Also, basically no chess engine bothers to make the check to that level of accuracy (because there really isn't any need. It has no effect on playing strength or validity, but on the contrary not doing the checking to that level of accuracy saves time.)
The answer is borderline impossible to calculate because of how many moves get added to the equation with every passing move. It's easy to start with when there are only 20 legal moves at the start for each player, but the number and calculation gets astronomically more complex the further into even a single game, let alone all possible games and moves.
@@LucianDevine Given the rules for 3-fold-repetition it's perfectly possible to calculate. The number of possible moves has nothing to do with it.
@@DjVortex-w Ah, I thought you meant like the maximum number of board states until total until 3 fold repetition kicks in, not just those pieces.
There is a 75 move rule as well. It's like the 50 move rule, except instead of allowing a player to claim a draw, after 75 moves (without moving a pawn or capturing a piece), the ARBITER can go in and declare a draw. So (at least in tournaments), if neither player wants to admit a draw, an arbiter can still intervene eventually.
It doesn't require an arbiter. Rule 9.6 says: "9.6 If one or both of the following occur(s) then the game is drawn: a. the same position has appeared, as in 9.2b, for at least five consecutive alternate moves by each player. b. any consecutive series of 75 moves have been completed by each player without the movement of any pawn and without any capture. If the last move resulted in checkmate, that shall take precedence." So, after 75 moves without a capture or pawn movement, the game is over. Regardless of an arbiter present.
also there is a slimier rule for 5 fold repetition
@@AbiGail-ok7fc Which means in practice, after 50 moves one of the player has to claim the draw, while if it was 80 such moves (no capture and pawn move) and ended in checkmate then the player can appeal and the result become a draw.
@@AbiGail-ok7fc Yes but a pattern like that requires that someone both notices it and has the desire to bring it to attention. And that means an arbiter. Players would have already chosen the 50-move rule if they noticed and wanted to bring it to attention.
For those who enjoy rules-lawyering, the "Rule 9.6" which Abi Gail referred to is from www.fide.com/fide/handbook.html?id=208&view=article
"... if you have been, Thanks for watching" Bring warmth to my heart
Additya Si i just came to read this comment. i dont even know what a video is.... is it something you can hold?
I've always thought he says "if you happen, thanks for watching" (like, if you happen to be watching, thanks). Is it possible (I'm not a native speaker)?
I thought it was “if you’re happy, thanks for watching”
Me who was listening while making dinner: :/
The sentence is cut off on purpose after 'been', any specific reason he says it this way?
My stile of playing:
- What do you do with your sword when you see an orc?
- Draw?
- Agreed!
an absolute honour working with you! We are editing away on our video about Hugh Alexander and we are very happy to announce that Grandmaster Simon Williams aka GingerGM will do the analysis of Hugh's brilliant win against Botvinnik.
5693.5!
3 fold repetition isn't when a sequence of moves is repeated three times, it's when a POSITION appears three times. And it is not necessary that they be consecutive.
Not a position, but a BOARD STATE, i.e. position and castling and en passant rights.
youd have to have a great memory to claim a draw then
Not really, it's actually quite easy as it's usually as they also said in the video when one tries to claim a draw while the other player does not. If one insist of playing on he or she won't repeat moves so it's not needed to remember, but if they do it's usually really quick.
You can try to claim a draw whenever, but if the claim is incorrect, time can be deducted from your clock.
8 pawns each with 6 forward moves possible each result in 6*8*2=128 pawn moves. There are 30 capturable pieces, 15 on each side, thanks to the pawns promoting and still being capturable later. (You can promote all 16 pawns on the board with collaborative capturing of enemy pieces to help the pawns change files and shuffle past opponent pawns. This is also how you can get 18 queens on the board.) The 50 move rule limits us to 49.5 (both players take 49 turns and only one of them completes their 50th turn, since a turn is both players moving. With 49.5 turns each time before we do an irreversible move (move pawn or capture) we cannot forget after our last capture, we still get 49.5 moves before end of game, so we can sneak in an extra +.5 before we multiply by 49.5. Then the game could end by a player triggering the 50 move rule as a bonus last last move.
AND WE GET ((128+30+1)*49.5)+.5=7475 turns, so black would end the longest possible game by triggering the 50 move rule. That is 14950 total piece moves if you count each player's turns separately.
in the last few years two new rules were added: 75 move rule (which is similar to 50 move rule) when 75 moves have been made with a pawn being moved or a piece being captured, it has to be a draw regardless of whether its declared of not, similarly 5 fold repetition, when you reach the same position 5 times it becomes a draw regardless of whether its declared or not
breathless792 that s not true
it was 1 july 2014 when those rules became official.
And the reason that rule was created is because computer analysis found a condition in which a player could force a win in more than 50 moves but still be claimed as a draw by the other player because of the original 50-move rule.
to be technical, it's not three same moves, it's that the same position repeats three times that makes the draw. often it's result of consequent identical moves but this need not be the case.
EDIT: this is addressed later on in the video
4:40 "And we can prove that this works as well!"
"Well... WE can't, you can"
"I can..."
That's how I feel in every math class. 😂
Is it Christmas again.
Video from you.
I really like how you put the explanation in the description! It helped me follow the video.
The title slide says "Math as Chess" in morse if anybody was wondering.
captions be like: "I've recruited a chestnut"
My favorite part about the 50 move rule is that there are positions which if played out lead to a forced checkmate after more than 50 moves without pawn moves or captures, so there are positions which are draws even though one player could win if this rule didn't exist. There are positions where 500 moves can be played between pawn moves/captures, but if allowed to continue play, one player can force a win!!!
I almost left a nitpicky comment about the threefold repetition rule as you first described it. Glad I decided to watch the video to the end first.
It's so funny that the need for this would arise. I'd just use my own human power of choice in a situation where a game was regressing infinitely. Either a social appeal to my opponent, or an appeal to the laws of physics in the form of a table flip.
I agree.
50 move rule
Glad you see another video from you, I hope to see a lot more this year.
The rule is not a sequence of moves that repeats 3 times. It is a position (including same conditions, such as player to move, castling abilities, en passant possibility) that occurs three times.
Small addendum to 3-fold repetition rule. All 3 times when the position occurs on the board it has to be the same side on the move. I acctually remember interesting casus from the tournament when one player declared a move and claimed 3 fold repetition draw. It was true that after declared move would be played, the position would repeat for the third time, but this time it would be his opponent on the move, whilst previous two times it was him on the move. In consequence claim was denied he had to play declared move, which cost him a pawn and later he lost the game.
Three fold repetition occurs when any position occurs three times. It doesn't have to be in a row.
I remember when you briefly mentioned the rules that prevent an infinite game of chess on the Numberphile video about Shannon's number, so it's really nice to see you expand on that here. Lovely video--thanks to Rune and his team for this!
Very happy surprise to see this James.
Funnily enough, the game at 0:58 is a win for Black. Rather than bouncing back and forth between the same two squares, Black can zigzag backwards until the Queen forks the King and Rook, then capture the Rook. From there it’s a won Queen vs. Pawn endgame with the Knight preventing any stalemate resources for White.
I know that you are busy, but I wish you would make more videos.
Yaay I've been waiting for this for ages 😍
50 moves rule is kind of restrictive. There are solutions to endgames, that take more moves.
yes, but those are very rare to find and difficult to solve. For practical purposes the 50 moves rule is ok.
we are not all supercomputers man sheesh
imagine unironically pointing out impracticalities on a math channel
T Perm glad you mentioned this! I was thinking the same! Truly crazy to think about the idea that there could be a forced win with 65 precise moves in a theoretically “drawn” endgame. There are variations on the Queen v Rook endgame that can take more than 50 moves as well
Remember a move is made of a white and a black turn. Each player has 50 turns which is probably enough for all endgames. The rule is to avoid a situation where a player is in a winning possition and doesn't know how to mate, this will waste everybody's time. You should figure out mate patterns on your preparation, not in the board with an opponent.
Bletchley Park is the best possible location for you to shoot a video. Great to finally see a new one.
Threefold repetition is based on board state and not move sequence.
Your "infinite game" would end after the black knight moved back to its home square for the second time, since the starting postition, the middle position, and the end position would all be the same.
You should talk about the proof by backward induction that chess is a solvable game. I.e. either white can force a win, white can force a draw or black can force a win.
Though the solution is not known since there is an absurdly high number of possible chess games. Regardless of how fast computers get we will never have enough memory to store the solution because there isn't enough matter in the universe.
Yeap, it's the exact same process used to create "endgame tablebases". And, indeed, we'll never have enough space for a 32-piece tablebase.
@@jasondoe2596 That's an interesting way to think about it. A solution to chess is an endgame table worked all the way back to the starting state of the game.
We have the algorithm, we just cannot run it... That's still "solved" in my book :P
(Too bad we don't have access to the solution!)
Wouldn't this be the pigeon hole principle? I fail to see how induction applied?
@@thatunnamedredshirt We're not talking about regular mathematical induction but backward induction.
Imagine all possible chess games as part of a tree with its root node being the starting state of the game.
If you go to the deepest node (the longest possible game under the modern rules) you will find several leaf nodes with one parent. The leaf nodes each represent one of three scenarios: white wins, black wins or draw. Now take the parent node and look whose move it is, if it's white's move and one of the leafs is a win for white then parent is reduced to a white wins node and the leafs discarded since we assume both players are playing optimally. The same logic applies for black wins and a draw. If you reduce the tree all the way back to the root node you get a solution for chess where both players play optimally.
Either white can force a win or a draw or black can force a win. The other player isn't able to do anything about it assuming optimal play.
The 3-fold repitition counts only the position. It doesn't matter if it's in sequence, if the same position repeats 3 times, it's a draw. Which is sufficient to prevent an infinite game, because there's finitely many positions on a chess board and you'd eventually exhaust them and have to repeat positions if the game is not to conclude in mate or draw by insufficient material. HOWEVER, the 50 move rule was created to prevent drawn endgames to drag out "forever", because even with 3-fold repitition can lead to quite long sequences of moves being prepeated. For instance, a rook and king vs a rook and knight endgame is in most cases theoretically a drawn endgame, but it can still drag out for quite long without a mate. To prevent such cases, the 50 move rule was invented to put a hard limit on how long a chess game can go on without anything happening.
this is the first time I heard the name bu I discovered this sequence quite a while ago in an unexpected place. I was playing around with infinite nested fraction. The fraktion starts with a 1 at the top of the numerator then you put division line and put the next number below, which is 2. Then the way to grow the fraction is by putting a "bigger" division line below and do the same below as you did above but with increasing numbers as you go down. Where thue-morse sequence comes in is if you instead structure it a product of all the integers but to the power of either 1 or -1, the sequence of -1 and 1 would be the thue-morse sequence.
Was waiiting for this for ages ! : )
There is also the 5 fold repetition rule and the 75 move rule, witch take affect whether or not the players notice
That's kinda a weird way of putting it. Rather, it takes affect whether or not the players want it. If no one notices something, how can it be enforced?
@@hamsterfromabove8905 The game is officially over at that point, whether the players notice or not. So even if someone "wins" after that, it doesn't count. They can play on, but the game is over.
The repetition of moves rule does not require that the moves be consecutive, only that the position be repeated three times with the same player to move.
please watch the whole video before commenting, it's starting to getting annoying
Photographic position rule prevents thus because if a position comes on a board 3 times (doesn't matter if its in a row or not), a player can claim a draw
Three-fold repetition refers to the position, not the sequence of moves. If a position occurs three times at any three points in a game, the game is drawn.
Occasionally the 50 moves rule is rescinded to (say) 75 or even lifted entirely, consider the "white to move and mate in 500+" puzzle where eight pieces are onboard including the two kings and white's first move is queen takes black queen.
That's... Totally not how 3-fold-repetition works
You didn't watch long enough
@@klieu90210
I did. But why would they even mention an imaginary rule in the first place?
It wasn't imaginary. That's how the rule used to be before the 1890s. Same deal with sequential repetition in shogi, until that too was changed, but much later (in 1983).
Good to know you're still alive!
You don’t have to claim a draw in these positions as arbiters can decide when they see it.
Assuming we're in a tournament, the game organizers can declare a draw, regardless of any repetitions, if it's clearly obvious each player is beyond the 50 move rule, as score must be kept. This happens in kid's tournaments sometimes especially if the time for the next round is approaching. No master-level players would do this, as one player almost always claims a draw as soon as the 3rd position arises, or the 50-move rule applies.
Keep in mind the 50-move rule is cumulative; that is, if not claimed on the 50th move, it can be claimed on 51st, or 52nd, etc, (so long as no pawns move or no captures take place. Either of those would restart the count. The same goes for repetitions.) Also, games are timed, so that tends to make infinite games unlikely.
I knew you guys were somewhere special at the outset by the lighting and the background. But wow, I was really surprised. So cool that it’s Alan Turing’s old haunt. I think he put ads in the Times seeking crossword geeks and chess players. Everyone must read Simon Singh’s The Code Book. The section on Bletchley Park is phenomenal.
The channel lives!
The construction of the sequence is amazingly similar to one way of making the dragon curve. If we say a 0 is a left turn and a 1 is a right turn, starting with a left turn the sequence can be built by adding a left turn and then going backwards along the previous step inverting each position. So the first step is a 0, then you add a 0 to the end and run backwards inverting it so 001, then again 001 0 011, etc, 0010011 0 0011011. So one very long curve would be 001001100011011000100111001100011001100011011100100111001101100010011000110110001001110011001110011000110111001001110011011
POintless discussion. First read, the rules: Article 9.2:
The game is drawn upon a correct claim by the player having the move, when the same position, for at least the third time (not necessarily by a repetition of moves):
a. is about to appear, if he first writes his move on his scoresheet and declares to the arbiter his intention to make this move, or
b. has just appeared, and the player claiming the draw has the move.
3 fold repetition has to do with the position appearing on the board, not the sequence of the moves
If the exact position repeats 3 times with the same person to play the game is declared a draw
Great clip. Thanks for sharing!
Actually there is also the five-fold repetition rule. after 5 repeated positions the game is drawn also if no player claimed it.
They talk about the 50 move rule in the video, but people still comment it.
It interesting, that according to endgame tables some positions are winnable, but require much more moves than 50. For example there is a position Queen and Knight against Rook, Bishop and Knight that requires 517 moves to win. Also if I recall correctly there is Queen and Knight against Queen endgame with 529 moves to win. Obviously no human player can make such an analysis behind the board.
Cool video. But I think there's a mistake at the end. Both added rules are sufficient on their own to prevent an infinite game from happening.
But the draw is essentially advantage to the player that is on the defensive .. cause he succeeded in defending himself ...
yes it is an advantage one party can claim if they think they can't win.
Yes, that's the entire point. If your opponent can't figure out or isn't able to checkmate, then they don't get to have a win. But you also can't win. So its a draw.
@@hamsterfromabove8905 but what would happen in say a final match of a tournament ....
It depends of the specific rules of a tournament. You could either have a tie for first place, or a rematch.
Nice to see another video from singingbanana, thanks!
I have been:
Missing you.
It was great to see you with Brian on the "illegal game"
This is similar to superko rules in go. There is positional superko, where the board state cannot repeat, and situational superko, where the board state cannot repeat with the same player to move, which have subtle differences in various pathological game states.
You cannot play forever, because the arbiter (eventually) will notice the repetition and will terminate the game, it's in his power and also his duty.
He says that the 50 move rule isn't sufficient, but I think it is.
The boardstates rule is also sufficient.
Could he have meant that they are individually sufficient, but they have both just to have more potential options so that the game doesn't drag on for days?
It's not the sequence of moves that has to be repeated 3 times, it's the specific board position that has to be repeated 3 times.
You didn't watch long enough
1:31 The repetition must not be in sequence. Any 3 repetition during the game gives the right to draw. Even more, the figures must not be the same figures, rooks or knights may have swapped their places, still validating for repetition.
Yeah, I was thining the same thing.. This rule alone would make an infinite game inpossible but they could become insanelly long so that is the reason for the 50 move rule..
No, you are quoting a different rule, that's the point of this video. The previous rule was a sequence of moves which is repeated 3 times in a row is a draw. The NEW rule is a repetition of position 3 times is a draw, with no rules regarding whether they are in a row at all.
@@philipmorse-fortier5499 Yes, exactly! They actually discussed this later. Still I left my hasty comment there, for those who don't dear to watch to the end.
Collab with Stand up maths?
If you want to dip into crazy chess rules, as far as the rules limit you, you can promote the king's pawn into a rook and provided that rook and the king haven't moved yet, don't castle out of, through, or into check, you can castle across the board toward the enemy. The king would still move his standard 2 moves. I've only seen it once and it didn't help the player, more just showboating.
I did some research into this and it appears that a couple of people wrote about the possibility of castling that way because it technically satisfied the wording of the requirements for castling in the FIDE rulebook. It was a loophole, one that was fixed in 1970 and has been an illegal move ever since. It has never been played in a tournament.
Bro your content is always brilliant and it'd be great if you made more vids :D
At 1:11, Black Queen check, White King moves, check-mate.
But only kings and knights would be classified as insufficient pieces, right?
It's more than just the position. You can have the same position three times with the king on e1 and a rook on h1, but it's not a threefold repition i.e. if castleing was a legal move the first 2 times, but due to some Kf1 Ke1 manouver the right to castle is lost (same goes for en passant, obviously)
At 6:50 Just to throw a spanner in the works I believe that the three fold rep has to be claimed by one of the players.. I'm not 100% sure but I reckon if both players so choose they can legally ignore the rule. Similarly the same thing may well be true of the 50 move rule.
Long time no see, James!
It's very easy to set up a an infinite game of chess. It's possible for the game to wind down to just the two kings. At that point, unless one of them messes up big-time, they will usually end up chasing each other around the board indefinitely, and they can do so with many moves before repeating one.
1) In fact, with just the two kings, it's _impossible_ to mess up unless you violate the rules :P
2) Many moves, but not _infinite_ moves. There's a finite number of board states, so eventually one will reappear.
Also, officially there is a 75 move limit. If no piece was taken and no pawn moved in 75 moves then the game is a draw, irregardless of what the players want.
When checkmate is no longer possible it is an automatic draw. But even disregarding that, before Euwe it would have been thought that eventually you would have a repeating sequence of moves in this case, and thus a draw. Clearly positions will repeat, but as Euwe showed, not necessarily sequences of moves.
As a chess arbiter i have to disagree. If the same position repeats 5 times, the game IS drawn by the ref, same for 75 moves without pawnmove/take.
Matt Parker did an excellent video about the Thue-Morse sequence on Standupmaths
Actually, the players can't play forever, even if they wanted to:
From the FIDE Handbook: www.fide.com/fide/handbook.html?id=171&view=article
"9.6
If one or both of the following occur(s) then the game is drawn:
the same position has appeared, as in 9.2b, for at least five consecutive alternate moves by each player.
any consecutive series of 75 moves have been completed by each player without the movement of any pawn and without any capture. If the last move resulted in checkmate, that shall take precedence."
while the 3-fold repetition and 50 move rule are "upon a correct claim by a player having the move".
"The game is drawn, upon a correct claim by the player having the move, when the same position, for at least the third time (not necessarily by sequential repetition of moves)" 3 fold repetition wiki
You didn't watch long enough
Wait, how does the 50 move rule not prevent an infinite game? Pawns can only move so many spaces before getting promoted, and there’s only a finite number of pieces that can be captured.
No, we still can't have a infinite game even if we don't claim a draw because for that reason we have 5 fold repetition and 75 move rule which forcibly terminates the game
Glad to see you back! Where have you been?
Some day I will know Bletchley park...!
"MATH ... CHESS" in case anyone's wondering. :) Great video!
3:25
I would say the sequence consists of the two building blocks "01" and "10".
That's also correct. Any length that is a power of 2 will give two different sequences of that length, which when replaced by 0 and 1, will give the original sequence.
Jivan Scarano
Exactly thats why I would use the shortest sequence.
@@maxmustermann3876 I would say the sequence consists of the 2 building blocks "0" and "1"
Just a little precision about the "threefold repetition" rules. You sais @ 1:30 that it has to repeat 3 times in a row. And it is not exactly correct. The players can claim a draw if : the same position occurs three times, or will occur after their next move, with the same player to move. It doesn't have to be in a row.
Watch the rest of the video. Repetition of the same move three times in a row was the original rule. They talk about the new rules later on.
Doesn't apply to chess since the 3 fold rules refers to the the position, however this is possible in shogi, since the rule works like you mentioned.
8min into 1 sentence
There is a limited number of configurations of pieces, thus at one point it must repeat and leads to an end.
If someone askes "but why showed it is not" then sorry they corrected it later on to waste time. The 3 move repetition rule does not exist anymore.
50 move rule is also automatically a none inifite rule
You have to capture or move a pawn within 50 moves, thus at one point you ran out of pawn/moves and things to capture and game ends.
What happens if you let you opponent move twice for every move you make
The threefold repetition rule just states that the same position (not sequence of moves) can not happen on 3 different occasions, so this is wrong
This video is about the old rule. We say "The rule was..." and explain the old rule and the problem with the old rule. We then describe the new rule at the end of the video.
even though that with the 3 move repetition must be claimed to make the game a draw, if the same move is repeated 5 times, the arbiter must stop the payers and make the game a draw. Likewise, if the same position is repeated 5 times or no player have moved a pawn or captured a piece in 75 moves, the game must end in a draw
Yay, new video!
I feel like this sequence is somehow connected to the dragon curve. I wonder if there is a nice mathematical relationship between them. I would also appreciate a longer video explaining the proof. Not every step was explained, and I'm somewhat struggling to fill in the gaps
Did you accidentally go to close to a black hole? Because it’s been a year m8
Maths Fest AND a new upload in the same week?! Close that prime gap people
The Threefold rule is not a sequence of moves, it's the same position being repeated three times...so it doesn't matter how you get to that position. Nice to see a video though!
please watch the whole video before commenting
No. That information needs to be forefronted since the video is called "The Infinite Game of Chess" and implies an error in chess as constituted now instead of previous flawed rules.
IIRC, someone found a position, where one player can force a win, doesn't capture any piece in between, and needs more than the alotted 50 moves.
Many such positions have been found using computers to construct "endgame tablebases" (Google'able term). The longest known sequence that leads to a win (with perfect play from both sides) is over 500 moves long.
Since several such positions have been discovered, and more will be in the future, but all are pretty much impossible to calculate by unassisted humans, it has been decided to keep the practical 50-move rule. (However, correspondence chess, which is often computer-assisted, apparently allows to claim such victories.)
@@jasondoe2596 Thank you, this is helpful.
You're welcome :)
the problem is that to get an infinite game neither play can be trying to win and have to only be playing move they know wont get them anywhere. also most ppl who are playing with these kind of rules (the little known ones) are always playing with a timer anyway... so yea its not really and issue.
wtf? its just longer sequence then 4 moves, thats it. There will not be infinite long sequence on finite chess board hence you cant infinitly play chess just by having rule of draw when 3 times same sequence. Also there are rules that forces you to take piece or move pawn with 50 moves so it makes those sequences smaller. (Sometimes it even makes diferent outcome on games coz someone forgot how to win in 50 moves and so on exapmple ending with knight bishup in 50 forced draw + some exceptions of needing more then 50 moves exist but rule is stil 50 coz theres very small chance of having those boards and coming up with solutions on the spot while defending position corectly). (and theres 75 move for referee)
Why not a 1-fold repetition, like in go? Of course referring to the position and not the move.
This is close to being the most unimportant and trivial video on youtube. It is almost 9 minutes long but could have been explained in under a minute. In any game or sport, of course, there is made a limit to how long a game can last, or else it wouldn't work at a high level. So to the question "Can there be an infinite game of chess?" - "No, because there are rules." That is the answer and it is very simple.
I don’t understand what is meant by odd position. There are to ones in position 1 and 2. Taking the first digit to be zero. So the double digits are on an even number and an odd number? Eg position number 1 and 2