@399
The final position of this game is a draw by stalemate, is legal,
and is not reachable from the initial position by optimal play.
https://www.chessgames.com/perl/chessgame?gid=1424841
So now all you have to do is prove it.
Yes, with his convention a "position" corresponds to one or two positions by a normal definition (where a specific side is to move). The reason for this is the starting point as a simple configuration of pieces.
Of course, in addition to player to move, basic chess positions would also be distinguished by the existence of potential e.p. captures, and the state of castling rights.
There are motivations to dealing with several positions in one go - there is a close relationship between the legal moves in each, and retrograde analysis is also closely related. I am not sure whether these are relevant to efficiency of tablebase construction or other rigorous analysis like constructing a proof tree.
The Syzygy tablebase construction deals with huge numbers of competition rules positions at one go if you identify nodes and positions. (There seems to be no meaning of "position" generally accepted throughout the chess community but the chess community almost universally behaves as if there is.)
The general notion is that of a "state" in a combinatorial game, which has to determine the possible future moves. In chess it is the arrangement of pieces plus some other information according to the rules being used.
For basic chess it includes person to move, castling rights, e.p. square, everything in a FEN except the half move clock and the (unimportant) full movie count. (This version of chess is theoretically very relevant to those with additional drawing rules, but has the theoretical oddity that it permits infinite games).
And as I said there's no general agreement in the chess community. That's one (sensible) definition of "position", but @tygxc has disagreed strongly with it and many people post diagrams and refer to them as positions. The Syzygy site refers to positions as (apparently) entries in it's tablebase, basically as defined here (I think), but to convert the numbers to @tygxc positions you have to not only multiply by 8 when there are no pawns or 2 when there are but also divide by the factorials of the numbers of pieces of the same type and I think there's some complication with bishops. Tromp talks about positions independently of the chess game in question, though the game states are different in different versions.
Not sure if anyone noticed my challenge. It may or may not have an easy solution. Here it is again.
Exhibit a position that is:
or prove no such position exists.
This is actually a pretty interesting challenge on second thought. since you cant prove opimal play from the start, you would have to set up a known drawn position such that the only way to reach it wold be to have a "mate in X" position right before it.
@399
The final position of this game is a draw by stalemate, is legal,
and is not reachable from the initial position by optimal play.
https://www.chessgames.com/perl/chessgame?gid=1424841
but that isnt a proof, which is the point of the question.
Even though this is probably an extremely good candidate to work off of, until you can prove that any point that could end in that position is a Mate in ____ the question remains unanswered.
Yes, it helps to avoid analysis problems to be in a tablebase.
Yes, with his convention a "position" corresponds to one or two positions by a normal definition (where a specific side is to move). The reason for this is the starting point as a simple configuration of pieces.
Of course, in addition to player to move, basic chess positions would also be distinguished by the existence of potential e.p. captures, and the state of castling rights.
There are motivations to dealing with several positions in one go - there is a close relationship between the legal moves in each, and retrograde analysis is also closely related. I am not sure whether these are relevant to efficiency of tablebase construction or other rigorous analysis like constructing a proof tree.
The Syzygy tablebase construction deals with huge numbers of competition rules positions at one go if you identify nodes and positions. (There seems to be no meaning of "position" generally accepted throughout the chess community but the chess community almost universally behaves as if there is.)
The general notion is that of a "state" in a combinatorial game, which has to determine the possible future moves. In chess it is the arrangement of pieces plus some other information according to the rules being used.
For basic chess it includes person to move, castling rights, e.p. square, everything in a FEN except the half move clock and the (unimportant) full movie count. (This version of chess is theoretically very relevant to those with additional drawing rules, but has the theoretical oddity that it permits infinite games).
And as I said there's no general agreement in the chess community. That's one (sensible) definition of "position", but @tygxc has disagreed strongly with it and many people post diagrams and refer to them as positions. The Syzygy site refers to positions as (apparently) entries in it's tablebase, basically as defined here (I think), but to convert the numbers to @tygxc positions you have to not only multiply by 8 when there are no pawns or 2 when there are but also divide by the factorials of the numbers of pieces of the same type and I think there's some complication with bishops. Tromp talks about positions independently of the chess game in question, though the game states are different in different versions.
It is much better to think of "states". "Positions" have a naive intuitive association with just the arrangement of positions, whereas the definition of a state include it determining all legal continuations.
Of all legal positions only the drawn positions are relevant to weakly solve Chess.
Of all legal drawn positions only those that can be reached by optimal play are relevant to weakly solve chess.
@399
There are many more draws that are legal and no optimal play.
I meant drawing basic chess positions. These are positions where neither player can force a win.
@417
Well neither player can force a win
Nah chess is unsolveable
@417
Well neither player can force a win
Not sure if you have forgotten the question, but it was to find positions which were drawn but could only be reached in a game that was winning for one side at some point.
tygxc just claimed (elsewhere) that a set of games was perfect but also that the games may have had errors. simultaneously. and then wonders why we are pointing out a contradiction.
btw @Ethan_Brollier, since you will be returning from my message, you have literally several PAGES of unaddressed tygxc delusion including the testimony of several others against tygxc while nobody else has defended tygxc.(i recommend you read from the start as I posed a game theory quiz question to explain how an invariant works, but the conversation devolved as a REAL troll misinterpreted the question)
in addition, you didnt even try to address most of my initial examples of tygxc's fantasy. there were still whole posts of many examples that you didnt even acknowledge, as well as the rebukes of your attempted defense by myself and others.
@399
The final position of this game is a draw by stalemate, is legal,
and is not reachable from the initial position by optimal play.
https://www.chessgames.com/perl/chessgame?gid=1424841
I was thinking of positions where there was still play, or any 1 move blunders of stalemate from winning positions would do!
But you have to be careful. In your example, I presume you checked the position where black has an extra queen on e6 the move before (so the capture gives the same stalemate). Fortunately, black is (probably) still losing despite having 2 queens (it evaluates +12).
There is an easy class of positions meeting my requirement - those where perpetual check saves someone who was losing. These can be relevant to real play. Stalemate saves tend to be more the preserve of problemists.