This is a good example of why you need to be very precise.
Yes. Notice I was careful to use the term "diagrams"
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in the context of my previous post it is true for both diagrams and positions.
Not under competition or ICCF rules.
how do those rules matter? A single missed diagram doesnt change the fact of what the paper is estimating and calculating
why would they be multiplied by two? are you referring to symmetry or smth?
the short of it is that if the paper was allowing promotions to pieces previously captured, then they would have calculated based on allowing bishops of more than just the opposite colors to exist.
why would they be multiplied by two? are you referring to symmetry or smth?
Side to play (but it's not exact).
the short of it is that if the paper was allowing promotions to pieces previously captured, then they would have calculated based on allowing bishops of more than just the opposite colors to exist.
It falls between two stools. It rules out the bishop situation you mention, but rules in many positions that can only be arrived at by promotion to a previously captured piece. Estimating the size of the latter set is not addressed.
@388
"The paper's figures have to be multiplied by 2 in all sets of rules to arrive at positions.
++ Yes, except for diagrams where one king is in check.
"if by that term you refer to nodes in the game tree" ++ No, then you have to divide by 2.
Besides a node also includes the history and the provisional heuristic evaluation.
Nodes take care of 3-fold repetition and 50-moves rule, positions do not.
(1) Take this position:
(2) Is a perfect up/down mirror image of (1):
(3) This position is the same diagram as (1) but with black to move:
(4) The same diagram as (2) but with white to move is the up/down mirror image of (3):
So 2 diagrams = 4 positions = 2 nodes
@388
"The paper's figures have to be multiplied by 2 in all sets of rules to arrive at positions.
++ Yes, except for diagrams where one king is in check.
"if by that term you refer to nodes in the game tree" ++ No, then you have to divide by 2.
Besides a node also includes the history and the provisional heuristic evaluation.
Nodes take care of 3-fold repetition and 50-moves rule, positions do not.
(1) Take this position:
(2) Is a perfect up/down mirror image of (1):
(3) This position is the same diagram as (1) but with black to move:
(4) The same diagram as (2) but with white to move is the up/down mirror image of (3):
So 2 diagrams = 4 positions = 2 nodes
You get loopier.
(1) and (3) are the same diagram, so counted once in the paper. They occur in the reduced game tree under basic rules in different places because one is White to move and the other is Black to move. (By the reduced game tree I mean the tree generated by moves with nodes having identical forward plays overlaid until none remain.) So under basic rules that's two nodes, therefore you multiply by 2 to get from your diagram to nodes in that tree.
Under competition/ICCF rules you need to multiply by an awful lot more because the forward trees from each are different for each of up to 150 diagrams preceding the nodes. Different sets of 150 diagrams give different nodes. I'll leave you to determine how many nodes your diagram corresponds to in those games.
Similarly for (2) and (4).
You have shown 2 diagrams which correspond to 4 reduced game tree nodes under basic rules and I'll leave you to estimate how many under competition/ICCF rules.
By the way if you want to count games that include draw offers/acceptances and resignations as examples of the games you are proposing to solve, each of those may be blunders and should also count as moves between nodes in the tree. The diagrams you show have different possible forward play depending on whether any of those have occurred, e.g. if the diagrams are as shown and White has offered a draw.
@388
"The paper's figures have to be multiplied by 2 in all sets of rules to arrive at positions.
++ Yes, except for diagrams where one king is in check.
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Added after my previous post.
That's one of the reasons I said it's not exact. There are many other positions which can only be one side to move.
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.
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.
What's the difference between perfect play and optimal play in your lexicon?
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.)
My blitz bullet and rapid where all 2000 once it happens 🤷
Actually that's only cause he plays rapid and daily so it logs as 1200 elo since that's what he signed up as
@396
"(1) and (3) are the same diagram, so counted once in the paper."
++ Yes. 1 diagram is generally 2 positions, except when a king is in check.
"therefore you multiply by 2 to get from your diagram to nodes in that tree"
++ No. Positions (2) and (4) are exact up/down mirror images of (1) and (3),
so are the same nodes despite being different diagrams.
Therefore you divide by 2 to get from positions to nodes in that tree,
except for up/down symmetrical positions.
"Under competition/ICCF rules you need to multiply"
++ No. A diagram is the placement of the men on the board.
A position is a diagram plus side to move, castling rights and en passant flag.
A node is a position plus history plus provisional heuristic evaluation e.g. +0.33.
The history tracks the 3-fold repetition and the 50-moves rule.
The Laws of Chess clearly state what are and are not different positions:
'9.2.3 Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:
9.2.3.1 at the start of the sequence a pawn could have been captured en passant.
9.2.3.2 a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.'
In other words, a position is a FEN without the move number.
@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
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).
This is a good example of why you need to be very precise.
Yes. Notice I was careful to use the term "diagrams"
...
in the context of my previous post it is true for both diagrams and positions.
Not exactly. The paper's figures have to be multiplied by 2 in all sets of rules to arrive at "positions" if by that term you refer to nodes in the game tree. Something much larger in competition/ICCF rules. But there may be dependencies in some diagrams whether promotions such as the one I posted could occur within a 75 move rule.