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What gives a piece the ability to pin? (Improved Edition)

Sorry for double posts but this since there is no edit i have no option, i missed post #7 which i will reply too now.

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Your fundamental understanding of how a pin works is flawed. A pin occurs IF and ONLY IF a greater piece can be captured if the lesser piece moves. Since a pawn can only threaten the next piece if it captures, since if there is no capture available it may only advance in a direction it can't capture, there is no way for it to threaten 2 pieces in succession, regardless of how many tempos you give it. It can only fork. It's the same for a knight. Thus, the ability to pin does, in fact, require threat linearity."

Making a pawn "super" means that it can capture a piece if its two step away diagonally, this was the cause of deleting the last thread since the pawn kept violating the rule, but increases its scope to double tempo also means it can capture in double tempo.

this problem happens when a piece capture differently than the way it moves.

I really am enjoying this discussion so don't think of it as stubbornness of anything like that.
If you're increasing the scope of the piece, then the king in the first example is in check, because by adding the scope, since the knight can jump pieces, the king is in check, so it isn't a pin. Swapping out the pawn for a knight in the second example would indeed be a pin. But by increasing the attacking scope for the pawn you're giving it linearity in attack. Your whole pretense that somehow the ability to pin is not due to attack linearity is therefore flawed. /discussion
You make very good arguments, but i did mention this issue in my first post,
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Definition : a "double tempo'd" piece is a normal piece that can move twice in one turn, while still following the capture rule( a piece has to stop when capturing )*

Essentially, it has to stop when making capture, thinking of it as having to move to nearest square before going to the other.( like the bishop)
but i haven't expressed my thought correctly .

What i'm trying to say is direct linearity is not needed for a pin to happen, but a "path " is enough.
I just don't see the point of this.

I can't figure out what you are trying to prove.

In any field, theory is not meant to replace reality but explain it. By changing the rules to offer a hypotheses, you have provided a test that is incapable of explaining the game within its own natural bounds
It's truly absurd #15. He's making up pieces that have rules that don't fit the model of how chess is played in any part of the world.

This absurd "super knight" is basically given the scope of being able to threaten a piece as if it can move twice, but then can only move once if the first move would be a capture, which either ignores its ability to jump pieces, or means that the second piece is not actually threatened. The so-called "super pawn" is given the ability to threaten a square as if it could capture twice in a row, even if the piece moves and therefore renders its ability to capture twice void, meaning once the first piece moves the second piece is no longer under threat!

At best it's an attempt to bend all the rules to fit the model, or at worst it's a horribly warped understanding of how chess works, wrapped up in a pretentious attempt at writing some sort of academia on the subject of game theory. A paper written on this absurd pretense would receive an F by any professor in the field. It is horribly logicked.
Also, I just wanted to say, that while your knight example DOES in fact work to represent your proposed idea under the very specific terms you have proposed (the very same ones that then break your pawn example), if you have to violate the fundamental principles of the rules of the game regarding piece movement in order to make your hypothesis about movement work, then you fail. The rules say no piece can move twice. I don't think any chess variant in the entire world allows multiple movements.
alright, i surrender.

the purpose of this was to point an interesting? observation that pin can be performed even if a piece is non linear, i guess this however fails?

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