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#Post#: 613--------------------------------------------------
Perpetual check in Infinite Chess (new proposed rule)
By: chilipepper Date: March 18, 2018, 1:58 pm
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This topic is concerning the game "Chess on an Infinite Plane"
which is one type of infinite chess. For reference the
game-rules can be found here:
HTML https://chessvariantforum.createaforum.com/variant-reviews/variant-description-chess-on-an-infinite-plane/
Some game players have noted that there are theoretical
end-positions in infinite chess which result in a "perpetual
check". In such a position, the king is placed in serial check
(checked on every move), with no prospect for conversion to
another game-state. In one example, the king is forced to move
in the same direction perpetually and without the involved
pieces being prevented from changing their move pattern. The
pieces move without repetition of absolute position, but there
is "pattern" or "translational" repetition.
To my knowledge, this game state has not been seen in any actual
games, but is theoretically possible. One example is shown in
this example (simplified on an 8x8 board):
[FEN "8/8/K7/8/8/6k1/8/5Q1R w - - 0 1"][SetUp
"1"][CurrentPosition "8/8/K7/8/8/6k1/8/5Q1R w - - 0 1"]1.Rh3+
Kg4 2.Qf3+ Kg5 3.Rh5+ Kg6 4.Qf5+ Kg7 5.Rh7+ Kg8 6.Qf7# *
To address this game-state, a new proposed rule is being
considered, stated as follows:
A player may claim a draw if the king is forced to move one
square in the same direction for six consecutive moves with the
involved pieces exhibiting translational repetition, and if the
involved pieces are moving in a way that the game-state will not
otherwise be changed (for example the checkmating pieces are
blocked by an occupied square, or to a square which is attacked
in a way that resolves the check).
The infinite chess committee is accepting public comment on this
proposed rule. If there is no objection, the rule will be
effective for all games starting May 2 of this year and after.
#Post#: 616--------------------------------------------------
Re: Perpetual check in Infinite Chess (new proposed rule)
By: chilipepper Date: March 20, 2018, 9:47 am
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Elaborating on the example above:
The perpetual check can be expressed as follows (standard board
notation with unbounded files and ranks):
Rh3+...Kg4
Qf3+...Kg5
Rh5+...Kg6
Qf5+...Kg7
Rh7+...Kg8
Qf7+...Kg9
Rh9+...Kg10
Qf9+...Kg11
...
(and so on)
With the proposed rule, the game could end as follows:
Rh3+...Kg4 (1st check)
Qf3+...Kg5 (2nd check - 1st instance of forced repetition)
Rh5+...Kg6 (3rd check - 2nd instance of forced repetition)
Qf5+...Kg7 (4th check - 3rd instance of forced repetition)
Rh7+...Kg8 (5th check - 4th instance of forced repetition)
Qf7+...Kg9 (6th check - 5th instance of forced repetition)
Rh9+...Kg10 (7th check - 6th instance of forced repetition,
Black claims a draw)
Note: if the king makes a repeated move, but the move is not
forced, then there is no forced repetition, and a draw cannot be
claimed.
#Post#: 617--------------------------------------------------
Re: Perpetual check in Infinite Chess (new proposed rule)
By: John_Lewis Date: March 20, 2018, 11:21 am
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May I suggest a more intuitive number of moves? Off the top of
my head I would say 8, because that would push you "off" a
normal sized Chess board.
#Post#: 618--------------------------------------------------
Re: Perpetual check in Infinite Chess (new proposed rule)
By: chilipepper Date: March 20, 2018, 2:21 pm
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Thanks for thinking about this situation. When I devised this
suggestion, I was first thinking three moves, but then realized
the pattern repeats itself every other move. So three cycles of
"two-moves" is 6 moves total. So it is basically "3 fold
repetition" of the same pattern.
On a normal 8x8 board, this situation resolves itself in five
moves or less. The king starts on the third rank or higher, and
becomes checkmated after he moves to the 8th rank (hits the edge
of the board). But other than that I didn't feel that this
number carries over to infinite chess in any way.
On the other hand, I wouldn't be surprised if someone can make a
similar pattern where the pattern repeats itself on every third
move. There might even be other strange theoretical endings in
infinite chess which haven't been thought of. I'm just trying to
keep the rule-book one step ahead of the actual games. :)
#Post#: 621--------------------------------------------------
Re: Perpetual check in Infinite Chess (new proposed rule)
By: John_Lewis Date: March 21, 2018, 10:58 am
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While this appears like a reasonable solution, if the player who
is being forced wants to, they can change the direction of the
forced move, from a straight line to a diagonal and back (for
example) because there are no board edges to be forced into. So
this rule is slightly exploitable by a troll who wanted to the
game to last longer. (For example if the opponent's clock is
running low.)
How about you stick to the simplest set of criteria:
"If one King is put into Check on eight consecutive turns,
either player may claim a draw."
#Post#: 623--------------------------------------------------
Re: Perpetual check in Infinite Chess (new proposed rule)
By: chilipepper Date: March 21, 2018, 3:03 pm
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[quote author=John_Lewis link=topic=95.msg621#msg621
date=1521647907]
While this appears like a reasonable solution, if the player who
is being forced wants to, they can change the direction of the
forced move, from a straight line to a diagonal and back (for
example) because there are no board edges to be forced into. ...
[/quote]
In the example I provided, Black's king is always forced to stay
in the same file, and move one square up on each move. There is
a White queen on file-f, and a White rook on file-h, so the
Black king is stuck on file-g.
fyi, unlike in normal chess, one of my goals is for this game to
be mathematically "perfect". It doesn't have rules based on
arbitrarily selected numbers (which is nearly the case of FIDE
chess, but not totally so).
FIDE chess has the 50-move rule. Some game theorists cite this
as being arbitrary, because some checkmates require more than 50
moves to perform. This means that a game with a winning position
may end in a draw due to an arbitrary number. In infinite chess,
I'm not using rules such as this. Games should only be called a
draw if it is mathematically provable to be a drawn position.
Draws can also happen if the players agree to a draw, but this
is related to a player's skill, and not the game rules. :)
#Post#: 624--------------------------------------------------
Re: Perpetual check in Infinite Chess (new proposed rule)
By: Martin0 Date: March 22, 2018, 3:50 am
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If the goal is to make a mathematical perfect game, then this
sounds like a terrible rule. If the exact same position is not
reached, then you can't really say that no progress has been
made or not. Let's say black has a pawn on g15 for example. Then
the sequence of
Rh3+...Kg4
Qf3+...Kg5
Rh5+...Kg6
Qf5+...Kg7
Rh7+...Kg8
Qf7+...Kg9
Rh9+...Kg10
Qf9+...Kg11
is really not just repeating the position. Each step the black
king takes is one step closer to his pawn on g15. So the game
should continue:
Rh11+...Kg12
Qf11+...Kg13
Rh13+...Kg14
Qf13#
The same argument could be made if instead of a pawn on g15,
black had a rook on g999999. Eventually the sequence would end
with:
Rh999997+...Kg999998
Qf999997#.
#Post#: 625--------------------------------------------------
Re: Perpetual check in Infinite Chess (new proposed rule)
By: chilipepper Date: March 22, 2018, 9:16 am
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[quote author=Martin0 link=topic=95.msg624#msg624
date=1521708618]
...Let's say black has a pawn on g15 for example. ...
[/quote]
Hi Martin0, good to see you here. :)
I believe the rule was written to address the situation you
describe. The rule has this statement:
...and if the involved pieces are moving in a way that the
game-state will not otherwise be changed (for example the
checkmating pieces are blocked by an occupied square, or to a
square which is attacked in a way that resolves the check).
I'm not sure if I phrased it in the best way, but I intended for
the rule to not apply if the moving pieces "run into" some other
pieces, or attacked squares which changes the situation.
#Post#: 626--------------------------------------------------
Re: Perpetual check in Infinite Chess (new proposed rule)
By: chilipepper Date: March 22, 2018, 9:21 am
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I should also point out that in the example provided (with only
the pieces shown), White actually has a forced mate. He could
simply move the king to the g-file (such as in your example),
and White can win.
So the example represents a situation where Black has other
pieces, and White believes he is inferior, but White plays for
the draw by performing the perpetual check.
Thanks for your analysis of this game ending. I'm pretty sure
there are situations that I haven't addressed. But I hope to get
them in the rule book before they are ever seen in actual play.
:)
#Post#: 627--------------------------------------------------
Re: Perpetual check in Infinite Chess (new proposed rule)
By: Martin0 Date: March 22, 2018, 11:43 am
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The easiest assumption is that white must keep checking or else
he is getting mated. Playing for a draw (perpetual) while your
opponent has only a king left does not sound like a good
strategy.
Anyway, "game-state will not otherwise be changed" is something
hard to define or understand exactly what it means. Pieces "run
into some other pieces, or attacked squares" is something that
does not need to change within the moves the draw is declared,
but much later. To me it sounded like you referred to moves made
when the draw was declared, not any number of moves in the same
direction.
But really "game-state will not otherwise be changed" is
something you can't really define properly since the relative
position between all pieces can matter in a position. If I just
do a lot of checks to make my opponents king inactive and then
wants to do something else (maybe my opponent having an inactive
king will decide the game!), then what is your definition of
"game-state will not otherwise be changed" in order to make my
strategy valid? If you include king activity in the equation,
then no position could be declared a draw this way.
So in my eyes the rule is flawed and should not exist. If a
player makes "no effort to win", then an arbiter could declare
the game a draw. It doesn't matter which of the players refused
the draw offer.
One side note is that a "fast forward" could help in some cases.
Requiring a player to answer if he will check indefinitely or do
something else x moves into the line, then the game could be
declared a draw if indefinitely is the answer. That rule can
include any repeated moves in the position, not just checks.
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