Vampires in Chess

https://lichess.org/study/cxSbcRkN/oqHyxGjD

it should NOT have taken me this long to realise that axb6 was FINE because it didn't allow the rook to roam on the a-file to lose tempo, because that loses castling rights.

if you want to follow my descent into madness i have notes lol. they are not in order.

https://lichess.org/study/cxSbcRkN/oqHyxGjD it should NOT have taken me this long to realise that axb6 was FINE because it didn't allow the rook to roam on the a-file to lose tempo, because that loses castling rights. if you want to follow my descent into madness i have notes lol. they are not in order.

ambrona

@Whyareall

Well done! And welcome to madness :)
I would love to see those notes you mention.

@Whyareall Well done! And welcome to madness :) I would love to see those notes you mention.

Rob_AOE edited

Either I'm not smart enough or its because of the language barrier, but I didn't quite get the logic of illegal mirrors / knights circling thing

Whyareall

@ambrona said in #52:

@Whyareall

Well done! And welcome to madness :)
I would love to see those notes you mention.

they're in the study i linked

@ambrona said in #52: > @Whyareall > > Well done! And welcome to madness :) > I would love to see those notes you mention. they're in the study i linked

ambrona

@Rob_AOE said in #53:

Either I'm not smart enough or its because of the language barrier, but I didn't quite get the logic of illegal mirrors / knights circling thing

What do you think is hard to follow?

The mirror image of the starting position is the same position with Black to move.
We claim this position is not legal, i.e. it cannot be reached in a game of chess.

The only attempt to achieve it is to move knights around and hopefully "lose a tempo" so that it becomes Black to move after you reach the starting array again.
This turns out to be impossible because of a parity problem.

In a nutshell, count +1 for every knight (either white or black) that lies on a dark square. Ignore knights on light squares. The starting position has a count of +2. If you move, 1. Nc3 the count goes up to +3 and if you then answer with 1... Nf6 the counts increases again to +4. The thing is that when it is White to move, the counter is even and when it is Black to move, the counter is odd. This means that it will always be White to move when you reach the starting array.

@Rob_AOE said in #53: > Either I'm not smart enough or its because of the language barrier, but I didn't quite get the logic of illegal mirrors / knights circling thing What do you think is hard to follow? The mirror image of the starting position is the same position with Black to move. We claim this position is not legal, i.e. it cannot be reached in a game of chess. The only attempt to achieve it is to move knights around and hopefully "lose a tempo" so that it becomes Black to move after you reach the starting array again. This turns out to be impossible because of a parity problem. In a nutshell, count +1 for every knight (either white or black) that lies on a dark square. Ignore knights on light squares. The starting position has a count of +2. If you move, 1. Nc3 the count goes up to +3 and if you then answer with 1... Nf6 the counts increases again to +4. The thing is that when it is White to move, the counter is even and when it is Black to move, the counter is odd. This means that it will always be White to move when you reach the starting array.

dboing

Is it always about knight cycling and pawn moves? for all of them. Or was this question only about the standard chess starting position. Not deeper vampires? sure one could cycle knights for long before hitting one of those impatient rules of termination.

ambrona

I assumed the question was only about the starting position.

We will see that there are much richer vampires, relying on more complex motifs.

Part II is finished and coming soon!

I assumed the question was only about the starting position. We will see that there are much richer vampires, relying on more complex motifs. Part II is finished and coming soon!

brianch

I had seen many types of problems/puzzles involving chess, but this is totally new to me!

Thanks a lot for writing it! Best blog post I ever saw on lichess :)

I had seen many types of problems/puzzles involving chess, but this is totally new to me! Thanks a lot for writing it! Best blog post I ever saw on lichess :)

anselan edited

To make things more manageable, we can partition the vampires into 16 clans. The chief (root position) for each clan is the game array, with some specific combination of castling rights enabled. Clearly, the 16 clan chiefs are legal: the game can begin with a little dance of knights and rooks to disable any particular castling right.

Then when considering the descendants of each clan chief, we can assume that castling rights are never subsequently lost. I.e. the relevant rooks and kings are frozen in place. This is because after a first move of rook or king, the position is indistinguishable from the one in a different clan where the right was already lost. Since we don't want to count a position twice, we assume that those clans with castling rights preserve them.

Similarly, I suppose that no rook can be captured unless it has already moved. (Although I think that a rook capture is likely to be a cure for vampirism anyway.)

The other corner case is castling itself. Does any vampire end with a castling move? I think not, but I don't have a proof.

To make things more manageable, we can partition the vampires into 16 clans. The chief (root position) for each clan is the game array, with some specific combination of castling rights enabled. Clearly, the 16 clan chiefs are legal: the game can begin with a little dance of knights and rooks to disable any particular castling right. Then when considering the descendants of each clan chief, we can assume that castling rights are never subsequently lost. I.e. the relevant rooks and kings are frozen in place. This is because after a first move of rook or king, the position is indistinguishable from the one in a different clan where the right was already lost. Since we don't want to count a position twice, we assume that those clans with castling rights preserve them. Similarly, I suppose that no rook can be captured unless it has already moved. (Although I think that a rook capture is likely to be a cure for vampirism anyway.) The other corner case is castling itself. Does any vampire end with a castling move? I think not, but I don't have a proof.

dboing

edited

I was wandering whether non-vampires did not have their own vampires based on their timing of turn, but the transitivity of non-vampirism from initial standard would keep going. so it might not be about legality anymore, or I am missing something.

what makes the standard initial position timing base preservation so different than any other position, so that one could not have the definition extended to all position. I think non-vampirism are the interesting positions (those giving me trouble). as my own dissonant statement provider. I missed something.

That last question of previous post is also something that puzzles me. I could not put finger on or ask yet.

a) Castling move or Castling-rights changing moves more generally (if that was not already the same, I do trip over words as learner), are like pawn moves, irreversible.
b) pawn move of the 2 step kind are also unique happenstance in that they are also irreversible as any pawn move, but in an another "angle" of position information definition, the en-passant vector (or whatever keep memory of that status for each file).

what of irreversible moves and my notion of timing imbalance (or color sidedness) have to do with vampirism or not?

We should collate all examples seen so far for their moves.
I did not get the 16 clans. point.
And in a sequence ending with vampire, all interior nodes should have been vampires per the result of invariance stated previously. They did not have the irreversible moves them selves. I am trying to verify my understanding of the definition via juggling with the results. looking for dissonance in my own understanding, leading me to need to reread... or ask you.

I was wandering whether non-vampires did not have their own vampires based on their timing of turn, but the transitivity of non-vampirism from initial standard would keep going. so it might not be about legality anymore, or I am missing something. what makes the standard initial position timing base preservation so different than any other position, so that one could not have the definition extended to all position. I think non-vampirism are the interesting positions (those giving me trouble). as my own dissonant statement provider. I missed something. That last question of previous post is also something that puzzles me. I could not put finger on or ask yet. a) Castling move or Castling-rights changing moves more generally (if that was not already the same, I do trip over words as learner), are like pawn moves, irreversible. b) pawn move of the 2 step kind are also unique happenstance in that they are also irreversible as any pawn move, but in an another "angle" of position information definition, the en-passant vector (or whatever keep memory of that status for each file). what of irreversible moves and my notion of timing imbalance (or color sidedness) have to do with vampirism or not? We should collate all examples seen so far for their moves. I did not get the 16 clans. point. And in a sequence ending with vampire, all interior nodes should have been vampires per the result of invariance stated previously. They did not have the irreversible moves them selves. I am trying to verify my understanding of the definition via juggling with the results. looking for dissonance in my own understanding, leading me to need to reread... or ask you.

Your network blocks the Lichess assets!