# Does anyone know of a game that was drawn under the mandatory 75 move rule?

Numquam wrote:

Edit: We can even deduce from the rule itself that the series has to be finite, because an infinite series of moves can't end in checkmate, because checkmate terminates the series.

Prelim note: I don't think that is a valid argument because between the finite and the infinite is the undecidable - not being able to determine whether or not the answer is finite or infinite by proper algorithm. There is no number of moves N such that you can be sure that - when no checkmate is found - you will not find a checkmate at a move number >N. So you must go on looking forever. Unless of course you introduce one of a million meta-observations to reflect your (non-axiomatic) understanding of the game.

Since it is relevant, I chose to interpret your question freely as raising the issue of the finity of the chess game.

I started a reply and it grew and it grew and it will end up quoting system theory A-Z. So I aborted and decided on a short synopsis: This is the decidability question which depends on the finiteness of positions, not of move series. They are indeed finite - by our understanding of the game semantics - but not necessarily for different chess rules or different stipulations as in the examples of my forelast post. If you succeed in entering our understanding of the finiteness of positions in the definition of the axioms (plus language, alphabet ...), then you can indeed theoretically determine the scoring status of every position. If you can not or do not, you can enter it in the form of a repetition axiom - which has already been done in standard chess. Algorithmically, the use of a repeat axiom is highly preferred, since it is funny to base the diagnosis that a position will end in a draw, on the complementary elimination of all positions which might end in checkmate.

Arisktotle schreef:
Numquam wrote:

Edit: We can even deduce from the rule itself that the series has to be finite, because an infinite series of moves can't end in checkmate, because checkmate terminates the series.

Prelim note: I don't think that is a valid argument because between the finite and the infinite is the undecidable - not being able to determine whether or not the answer is finite or infinite by proper algorithm. There is no number of moves N such that you can be sure that - when no checkmate is found - you will not find a checkmate at a move number >N. So you must go on looking forever. Unless of course you introduce one of a million meta-observations to reflect your (non-axiomatic) understanding of the game.

I don't see how that would make the argument invalid. If a series of moves ends in checkmate, then it is always a finite series of moves. So you don't have to know if a series is finite or infinite. Only the series which turn out to be finite can potentially end in checkmate.

That is the complexity of infinities. Suppose you start with a dead position - which of course you won't know beforehand - at which point do you decide that no checkmate will be found and the position is therefore dead?

Whatever approach you chose you must guarantee that what you look for will be found or disproved in a finite number of steps. It is insufficient to state that you will find it in a finite number of steps only if it is there. If you were sure a checkmate was there in the first place, you didn't need to run an algorithm at all. Apparently you had the answer you are looking for all along.

edit: I think the issue you are addressing is different from mine. You are evaluating all the branches of the move tree - some of which are infinite - in order to find the one which leads to checkmate. I ignore that exercise and concentrate on the possibility that none get there, making your parallel algorithm disappear in infinity.

Arisktotle schreef:

That is the complexity of infinities. Suppose you start with a dead position - which of course you won't know beforehand - at which point do you decide that no checkmate will be found and the position is therefore dead?

Whatever approach you chose you must guarantee that what you look for will be found or disproved in a finite number of steps. It is insufficient to state that you will find it in a finite number of steps only if it is there. If you were sure a checkmate was there in the first place, you didn't need to run an algorithm at all. Apparently you had the answer you are looking for all along.

edit: I think the issue you are addressing is different from mine. You are evaluating all the branches of the move tree - some of which are infinite - in order to find the one which leads to checkmate. I ignore that exercise and concentrate on the possibility that none get there, making your parallel algorithm disappear in infinity.

Do you disagree with the following statement: 'If a series ends in checkmate, then the series is finite.'

It follows directly from that statement that series has to be finite. You know before you use some algorithm to find if it a dead draw that the series has be finite. So you don't even look at infinite series.

I think you lost me. Of course I agree with your first statement and it is part of my argument. I do not suggest trying to look for infinite series. Infinity is something you always run into unintentionally. The problem of an algorithm going to infinity is that it cannot interrupt itself and say "what I'm doing is silly, I stop" like a human would. And while it's going to infinity it is shouting at every move: "where is the checkmate, where is the checkmate" hoping to find it. Only we know it never will but the algorithm knows not. It can however continue playing "next moves" forever without a repeat rule to stop it.

Hello, on chess.com in normal dailies, is it a 30 move rule or a 50 move rule? I better find out before I have a turn.

50 move dumb dumb!!!

well I'm not going to believe anyone that answers in that nasty way i hope you don't teach your kids to play chess like that!

Arisktotle schreef:

I think you lost me. Of course I agree with your first statement and it is part of my argument. I do not suggest trying to look for infinite series. Infinity is something you always run into unintentionally. The problem of an algorithm going to infinity is that it cannot interrupt itself and say "what I'm doing is silly, I stop" like a human would. And while it's going to infinity it is shouting at every move: "where is the checkmate, where is the checkmate" hoping to find it. Only we know it never will but the algorithm knows not. It can however continue playing "next moves" forever without a repeat rule to stop it.

The algorithm doesn't go to infinity. It stops when a position has been reached twice in the series of moves. Then we can note that the problem of finding a checkmate from that position is already being solved. The number of positions is finite, so eventually the algorithm terminates. Next we can prove that any possible checkmate is found by this algorithm. We know that each series of moves which leads to checkmate has a finite number of moves. So we just take a series with length N and prove that if it leads to checkmate, then that checkmate is found by the algorithm. If that is true for this series, then it is true for all finite series of moves.

Numquam wrote:

The algorithm doesn't go to infinity. It stops when a position has been reached twice in the series of moves. Then we can note that the problem of finding a checkmate from that position is already being solved. The number of positions is finite, so eventually the algorithm terminates.

Yes! That is precisely what I have attempted to communicate in the past posts. You can stop when the same position is reached twice - in all possible variations not just one. But the algorithm must know this and therefore we must tell it that in the form of some automatically terminating repetition rule!

We know that the number of positions is finite but the system cannot find that out from the inference rules. Technically, the state of the system is determined by the whole game and the system cannot know how the ever changing game history affects the actual move options at some point in the game. We know it's only e.p. and castling right and choose to ignore 3REP and 50M claim options as state deciders (old rules). By this knowledge we can reduce potentially infinite games to finite relevant positions.

I guess we are in line again!

Note that you can always write computer programs to do all kinds of things for you (like detecting repetitions) and not include them in the axioms. At that point you effectively introduce you own intelligence to decide issues in the rules - with the consequence that you must do the same to the chess rules you publish. You must explain in some addendum which intelligent thoughts you had to answer certain questions of chessplayers. That does however make little sense when it is much simpler to include an automatic repetition draw in the chess rules.

this could be compiled into a chess phd thesis

Tooezforme wrote:

this could be compiled into a chess phd thesis

Oops! Isn't this the chess phd site?

Tooezforme escribió:

this could be compiled into a chess phd thesis

I have a Phd thesis on Soviet Chess on my computer