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| | Page: [Previous] [Next] 1 2 3 | | (21) Posted by Kevin Begley [Sunday, Jan 6, 2013 04:01]; edited by Kevin Begley [13-01-06] |
It now occurs to me that there are two types of rider units.
The first type is the standard rider -- rooks are well known to be {0,1}Riders (vizir-riders), for example.
The second type would be a rider which makes successive leaps (let's just call this a 'Stepper').
The first types of riders do not precisely do this.
What's the difference?
scheme:
 (= 4+3 )
#1
  = Grasshoppers.
a)   = {0,1} Rider.
b) = {0,1} Stepper.
a) 1.Re8# (1.Rh1? ...Rh7!)
b) 1.Rh1# (1...Rh7? illegal; 1.Re8?? illegal).
Why is 1...Rh7? illegal.
The stepper on e1 can take successive leaps Northward (to e2, e3, e4), but the line ends at e5 (which is an illegal self-check) -- and there is no continuing passed this (to e6, e7, or e8).
Same goes for black's stepper on b7 -- it can take successive leaps Eastward (to c7, d7, e7, f7), but the line ends at g7 (illegal self check) -- and there is no continuing passed this (no blocking check on h7).
The movement that I described in the possible Alice variant (see post #16 in this thread), were not standard riders -- they were, in fact, steppers (with an imaginary component).
But, the imaginary component is pointless -- this should be modeled instead as 2D movement patterns, plus a 3rd dimension, which can only be reached by an anticirce style rebirth!
This does a remarkable job describing Alice, and a vast array of Alice alternatives.
But, Steppers may have independent significance, even without the imaginary components.
For example, the orthodox King's component of the castling move can be modeled as a horizontal-only {0,1}[0,2]Stepper (where [0,2] is a rider limitation).
For variants where castling anywhere is possible, remove "horizontal-only."
And, for variants with long-castling, model the King's castling move as a {0,1}Stepper (without limitation).
If I want to build a standard model, based upon movement patterns:
What's the proper standard model for the rook's portion of the castling move?
A hop? A simultaneous ride (K+R tunnel through one another)? A leap?
What's the proper standard model for the pawn's double-step move?
A residual-step? A residual-ride? A residual-decomposed leap?
What's the proper standard model for promotion?
I'll have to think more about this one!
Are there any previous examples of successive leaping units ("Steppers", as described here)?
| | | (22) Posted by Sarah Hornecker [Sunday, Jan 6, 2013 04:53]; edited by Sarah Hornecker [13-01-06] |
It seems to me that with steppers 1...Rh7 is already illegal for the reason that on c7, d7, e7, f7 and g7 the Black king still is in check?
| | | (23) Posted by Kevin Begley [Sunday, Jan 6, 2013 05:01]; edited by Kevin Begley [13-01-06] |
Siegfried,
Not sure I understand...
If you removed the wGrasshopper, phase b) would have no solution.
After 1.Step-Rh1+, black could block with 1...Step-Rh7!
The stepper Rook on h1 can make a series of leaps, Northward (h2,h3, ... h6, and even capture h7), but it can not go beyond h7 (that's still the end of the succession).
In phase a) both w+b are {0,1}Riders -- standard rooks.
In phase b) both w+b are {0,1}Steppers.
| | | (24) Posted by Sarah Hornecker [Sunday, Jan 6, 2013 05:41] |
You say the black Stepper can not go to h7 because it puts the king into check when going over g7. But then why can it go over c7 etc if the king also remains in check there?
| | | (25) Posted by Kevin Begley [Sunday, Jan 6, 2013 06:15]; edited by Kevin Begley [13-01-06] |
I understand your question now.
I was describing a movement pattern, only; but, I see now that this needs significant clarification!
A rook (or any rider) may continue to the choice of any square along the line, ignoring squares which inflict a self-check along the way.
As such, the rider is not a successive leaper (it is a leaper with an extended set of options).
I was attempting to remedy this, but the matter is far more complicated than I first appreciated!
Ignore the checking move -- let's say black is on the move, in phase b).
Black's stepper can move in successive leaps, c7 d7 e7 f7, and the line ends.
But, if black is already in check, the movement pattern would require complex calculation.
Quite right!
It is not enough to calculate additional check (say from n-tuple checks, I cannot say that the stepper is can not incur n+1-tuple checks -- because remedies and incursions of check may prove a sorted affair).
And, it certainly makes no sense to say that the stepper idles on checks.
How to remedy this?
I can not remove all checking units, calculate the movement pattern, then return the checking units, and continue -- because the Stepper could start on e2, capture a black pawn on h2, and removal of h2 could reveal a second stepper on h1 (I don't get out of check).
Nope. I see no remedy.
Looks like a terrible idea.
| | | (26) Posted by Sarah Hornecker [Sunday, Jan 6, 2013 06:29]; edited by Sarah Hornecker [13-01-06] |
I actually think your idea is brillant, but needs a good description.
"The stepper might not cross any field that would, if his move would end there, lead to an additional check against his own king."
Something like that.
It gets interesting if you combine this with a condition that makes the stepper unable to give check to the enemy as well. Does it count as check if he oversteps such a field like f7 in your example?
| | | (27) Posted by Kevin Begley [Sunday, Jan 6, 2013 07:23]; edited by Kevin Begley [13-01-06] |
That's a good point -- check to the enemy king could also end the succession!
The problem is, a move defined, based upon a theory of no additional checks, resorts to n-tuple check counting.
Suppose the stepper's move incurs a new check, at the same time it prevents an old one.
It gets terribly confusing, fast.
It may be that the successive leaper must be confined by checks of the enemy king, and self-checks (in situations where there were none).
In situations where already in check, the steppers must revert to a single step (each way).
If the step is illegal (self-check, even by prior check), the rest of the ride (in that direction) is nullified.
That's how it has to be.
And, remarkably, it seems to preserve the integrity of the scheme offered.
Except that the stepper on b7 can forget about h7 -- it can try c7, fail, then forget about d7, e7, f7, g7, or h7.
Correction: err, the scheme above may or may not be busted, b) 1.Rh1 is not even check -- if the movement of the Stepper cannot go beyond check to the enemy King, it would seem the check can be ignored.
Thus, the stepper can not be limited by the opposing King!
| | | (28) Posted by Kevin Begley [Sunday, Jan 6, 2013 08:11]; edited by Kevin Begley [13-01-06] |
So, here's a better definition:
Stepper {x,y} : First makes a virtual move, as an {x,y}Leaper, and providing no self-check is incurred, may continue making a succession of such virtual steps ({x,y}Leaps, in the same direction, unto capture or self-obstruction, stopping at any point). Thus, it moves like a standard Rider, except it can not extend its lines beyond the first virtual encounter with self-check.
For clarification:
1) Checks are resolved after each virtual step, as if the step itself were a complete move (including any rebirths).
2) Checks incurred prior to the move would still count as self-check.
Thus, a stepper may be limited to only a single step to prevent any check; however, so long as the check is prevented on the first virtual step, a continued succession of virtual steps may be considered, along this same line.
How's that?
I think that does it.
I just need some good examples.
Correction: For now, I have removed the suggestion that checks to the enemy King would end the succession. This is an interesting option, but the absurdity of this (reflected in the above scheme) requires serious consideration!
After 1.Rh1, black laughs, "I'm not in check, because your checking unit is limited to one step -- so, it does not really threaten to capture my King!"
But, white may roar back, "then, you have no defense against 2.Rh7#, since there's no threat to capture your king, you're not in check, and if you're not in check, I can keep riding, clear up to h7!"
This is highly interesting (steppers would be unable to give mate, except at the distance of a single leap)... but, this crazy scenario requires considerable thinking.
Maybe "mutual steppers" (based upon both check and self-check) is an option -- but, I really have to think more about this!
| | | (29) Posted by Hauke Reddmann [Sunday, Jan 6, 2013 19:23] |
Come to think of it, in castling the King acts quite like a stepper!
(Nooo running through a self-check on f1!)
Hauke
| | | (30) Posted by Ian Shanahan [Monday, Jan 7, 2013 02:33] |
Isn't Kevin's stepper idea already covered under the "non passant" condition? i.e. (0,1}stepper = non-passant Rook.
| | | (31) Posted by Kevin Begley [Monday, Jan 7, 2013 22:23]; edited by Kevin Begley [13-01-07] |
Ian,
I find a bunch of different definitions for "non-passant."
Mayhematics gives:
"NON-PASSANT RULE: The rule that royal pieces may not pass through check.
This applies to the king's double step in castling in orthodox chess.
But in the case of royal riders it is usually assumed that they can ride through check unless the non-passant rule is specified (on the principle that anything not prohibited is allowed).
This is very different -- applying only to the royal units themselves.
ps: I think Strider (step-Rider -- borrowed from JRT) is a better term than Stepper.
| | | (32) Posted by Nikola Predrag [Tuesday, Jan 8, 2013 00:07] |
Exceptional rules like castling as a basis for general rules, this might be very amusing. A King becomes a "yet-unmoved-non-passing-through-check Strider" and Rook becomes a "yet-unmoved Rookhopper". Perhaps even a "yet-unmoved Strider-Rookhopper" in case of 0-0-0.
| | | (33) Posted by Ian Shanahan [Tuesday, Jan 8, 2013 04:56] |
@Kevin. The basic principle is the same - just with your strider, the concept is generalized: the unit doesn't have to be royal.
| | | (34) Posted by Kevin Begley [Wednesday, Jan 9, 2013 08:08] |
I agree, Ian -- since I did not invent the movement pattern, I will not claim to have invented Strider units.
All I did was generalize them -- for all units, rather than just royals (which was poor); and, offer a better name.
This had to happen eventually.
| | | (35) Posted by Kevin Begley [Wednesday, Jan 9, 2013 08:19]; edited by Kevin Begley [13-01-09] |
@Nikola,
>Exceptional rules like castling as a basis for general rules, this might be very amusing.
You have the general intent inside out -- the point is to build a standard model of movements, for all rules (including special cases), based upon well defined movement patterns.
Not the other way around!
This should have happened long ago.
>A King becomes a "yet-unmoved-non-passing-through-check Strider" and Rook becomes a "yet-unmoved Rookhopper". Perhaps even a "yet-unmoved Strider-Rookhopper" in case of 0-0-0.
You're starting to sense the general idea -- even the special case moves must be fundamentally defined, in terms of logical movement patterns (e.g., leapers, riders, striders, hoppers, etc).
But, don't get ahead of yourself...
Kings and Rooks are not the fundamental objects -- these are just attributes of a square (and square is the wrong word, because they need not be square -- I prefer node, as in 'storage node').
Unit objects are all made up of images, abbreviations (even with figurine-notation, abbreviations do not become obsolete), and movement patterns.
Don't assign "yet unmoved" attributes to the units.
The point is, we want a standard model, which fully describes all rules -- in a manner that is both elegant, and concise.
The position may hold information -- not all will reside in the unit objects, which are attributes of the squares.
| | | (36) Posted by Hauke Reddmann [Wednesday, Jan 9, 2013 12:58] |
Kevin wrote: "The position may hold information -- not all will reside in the unit objects, which are attributes of the squares."
True, true. You can code the movements as an S-matrix like in quantum theory,
but unlike in quantum theory, you must even consider "hidden variables"
(e.g. castling right, to name an orthodox).
Just for the record...Kevin, is your ultimate dream to code fairy rules
exactly like a (good :-) programmer would code them?
Hauke
| | | (37) Posted by Kevin Begley [Thursday, Jan 10, 2013 00:55]; edited by Kevin Begley [13-01-10] |
It is not necessarily my goal to code a program to express legality for all fairy chess elements -- no!
My goal is to describe fairy chess, as much as possible in fundamental algorithmic terms, such that no two programs would ever disagree (or we'd all know, immediately, which was in error).
What can not be described in simple terms, quite simply, should not be sanctioned (by the governing body).
This requires sanctioning elements, as we go.
The fundamental elements, in my view, are the algorithmic descriptions of movement patterns (leapers, riders, striders, hoppers, locusts, decomposed-leapers, etc) -- everything else is a storage element: the position, the board, the squares, the attributes of various squares (e.g., promotion square? double-step square? rebirth square? etc).
Eventually, we will come to the issue of stipulation -- for which I have several good strategy suggestions (which may greatly simplify the description of all formal themes).
Until we can, at least, fully describe orthodox movement, this has to wait.
But, I can not decree a concise description which spans all of fairy chess movement, by myself.
Even orthodox chess requires some consideration, and feathers are sure to be ruffled.
Thus, some higher authority has a duty to arbitrate such matters.
The best I can do is suggest where the descriptions are poor.
Defining a more generalized form of the Strider's movement pattern might help to describe the King's component in castling movement; but, this is relatively easy in comparison to the "residual" pattern of en passant capture.
As each debatable element arises, I believe the best solution is to accept the most fundamental description possible -- this helps preserve opportunities to disambiguate special case rules.
So, considering the Rook's component of castling, one has to admit there is a possibility of ultra-long castling on a vertical cylinder.
Regardless whether we want to accept this as the standard rule (some do not), we must all concede that the most fundamental description must do three things:
1) allow for the broadest range of possibilities,
2) allow some filtering mechanism to select among the options, and
3) prefer the simplest possible set of default rules.
Most of us will manage to find easy agreements on castling, and promotion.
But, en passant capture is a far more complex issue.
| | | (38) Posted by Ian Shanahan [Thursday, Jan 10, 2013 05:31] |
@Kevin "All I did was generalize them -- for all units, rather than just royals (which was poor); and, offer a better name.
This had to happen eventually."
Absolutely! But for the sake of semantic economy, would it not be better to call them "non-passant riders"?
| | | (39) Posted by Kevin Begley [Thursday, Jan 10, 2013 18:28] |
@Ian
No, I don't think so -- "non-passant riders" is a very, very poor name.
I don't know who came up with this turkey, but I'm actually glad that they completely failed to state the general expression for non-royal step-rider units.
It's not just that "Striders" is a better name -- the alternative represents a failure of convention (or worse, it may be perceived as an attempt to extend influence upon other conventions).
There are many residual issues (pun intended) with the general case of en passant (yes, there is a general case of en passant capture, which extends to units beyond pawns)!
Such a profoundly misguided naming convention would likely cloud these issues.
The name "striders" is neutral (free of all such baggage), and fits the form (ala leapers, hoppers, riders, etc).
It's difficult enough to undo poor naming conventions, when the inventor has expressed the general case.
Here's a case where the inventor's failure makes our life easier (one fewer bad idea to overturn).
We should take advantage of this.
| | | (40) Posted by Ian Shanahan [Friday, Jan 11, 2013 00:40] |
OK, your argument is convincing (even though non-passant is here to stay).
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