### Post by curmudgeon on May 10, 2006 19:30:16 GMT -5

Something to play around with, even if the person originating this seems to have lost interest. This arose on a thread entitled "Motorized Chess", back on the forbidden board.

Somebody calling himself "Rusted Iron" wrote

going on to add, after a few other people had written in, that

to which I responded with another possibility:

Two modifications I'd like to toss in ...

Were this game to be run on a computer, the moves suggested by the originator of the chess variant I'm referring to would be easily done. (Picture the board aligned in a standard Cartesian Coordinate system, with the edges running parallel to the axes. The bishop moves as far as the player wishes along lines of slope +1 or -1, the rook moves parallel to one axis or another during a move (as far as the player wishes), queen moves as a rook or bishop, Knight "leaps with a bearing of arctan(0.5), arctan(2), arctan(-0.5) or arctan(-2) up to a distance of sqrt(5)" , "1" meaning 1", or 1/8 of a board length. The King moves orthogonally up a 1/8 of a board lngth or diagonally (along a line of slope +1 or -1) up to sqrt(2)/8 or the board length. The pawn moves parallel to the y-axis, away from the x-axis, up to 1/8 of a board length, capturing other pieces along lines of slope plus or minus one, up to a distance of squrt(2)/8 of a board length, where squrt(2) is the square root of two. Captures are as you'd expect them to be: carried out by moving one's pieces so the enemy piece is within a radius of 1/8 of a board length.

On a computer screen, this is easy, because we're just adding numbers together and keeping track of them. Out on the dirt, this is not as simple because even on the Playa, the ground is not completely level. Irregularities will throw off the direction of travel.

Suggestion: Make a virtue of inescapable necessity. Instead of demanding that pieces travel in precisely the right direction, allow them to deviate from their course by some fixed number of degrees. Then, on arrival, before captures are taken, "scatter the piece" by displacing the piece along a vector determined by some probability distribution, trying this into the "Kismet" theme camp concept that I can't get anybody interested in. Yet.

Having our displacement random vector be a bivariate Gaussian would be a little mean. I'm thinking maybe something of the form [U1,U2], where U1 and U2 are independent, uniformly distributed random variables on the interval (0,L/16), where L is the length of the field. The referee pulls a pair of numbers of a printout of random numbers, scales, tells the player how much to move the piece by along each axis, and then captures are taken. The piece might be thought of as being randomly adjusted in the square that materializes beneath its feet, in a manner of speaking.

Any thoughts?

Somebody calling himself "Rusted Iron" wrote

Here's the concept:

Electric motor scooters, (the kind you ride standing up), turned into chess pieces, with the playa as our board.

Anyone want to join in?

Electric motor scooters, (the kind you ride standing up), turned into chess pieces, with the playa as our board.

Anyone want to join in?

going on to add, after a few other people had written in, that

Wish I could provide scooters, but I can't do that.

I've considered doing it with bikes, but it doesn't seem right to have the pieces sitting down.

How to make the board? Two ideas:

1) sketch it in the playa... it's temporary anyway.

2) turn the city into a giant board... a bit anarchistic, you have to trust pieces who've been killed to stay dead. Okay, that probably won't work.

I've considered doing it with bikes, but it doesn't seem right to have the pieces sitting down.

How to make the board? Two ideas:

1) sketch it in the playa... it's temporary anyway.

2) turn the city into a giant board... a bit anarchistic, you have to trust pieces who've been killed to stay dead. Okay, that probably won't work.

to which I responded with another possibility:

3. Revise the rules of the game so that you don't need squares, any more. All you would need would be four posts marking the field of play, for pieces whose positions would be defined as coordinates on a grid aligned with the posts, the coordinates taking on continuous instead of discrete values. One piece of dust is as valid a center for a square as any other, so no need to mark out squares and no colored moop in the dust to deal with after BM2006.

Guessing that somebody probably would have played around with this idea, I did a search under the words "continuous chess" and came across this page on the chessvariants dot com site, which you can find archived in the Internet Archive should the original copy go down.

The rules are set up for an 8" by 8" board, but scaling them up to a larger playing field should be easy. Maybe the biggest change in the rules is that these is no en passant capture. The rule limiting the nearness with which one pieces may approach another without stopping could be enforced by placing circular bumpers around the motorized pieces, with appropriate radii and trip switches temporarily cutting power to a piece on impact.

Guessing that somebody probably would have played around with this idea, I did a search under the words "continuous chess" and came across this page on the chessvariants dot com site, which you can find archived in the Internet Archive should the original copy go down.

The rules are set up for an 8" by 8" board, but scaling them up to a larger playing field should be easy. Maybe the biggest change in the rules is that these is no en passant capture. The rule limiting the nearness with which one pieces may approach another without stopping could be enforced by placing circular bumpers around the motorized pieces, with appropriate radii and trip switches temporarily cutting power to a piece on impact.

Two modifications I'd like to toss in ...

Were this game to be run on a computer, the moves suggested by the originator of the chess variant I'm referring to would be easily done. (Picture the board aligned in a standard Cartesian Coordinate system, with the edges running parallel to the axes. The bishop moves as far as the player wishes along lines of slope +1 or -1, the rook moves parallel to one axis or another during a move (as far as the player wishes), queen moves as a rook or bishop, Knight "leaps with a bearing of arctan(0.5), arctan(2), arctan(-0.5) or arctan(-2) up to a distance of sqrt(5)" , "1" meaning 1", or 1/8 of a board length. The King moves orthogonally up a 1/8 of a board lngth or diagonally (along a line of slope +1 or -1) up to sqrt(2)/8 or the board length. The pawn moves parallel to the y-axis, away from the x-axis, up to 1/8 of a board length, capturing other pieces along lines of slope plus or minus one, up to a distance of squrt(2)/8 of a board length, where squrt(2) is the square root of two. Captures are as you'd expect them to be: carried out by moving one's pieces so the enemy piece is within a radius of 1/8 of a board length.

On a computer screen, this is easy, because we're just adding numbers together and keeping track of them. Out on the dirt, this is not as simple because even on the Playa, the ground is not completely level. Irregularities will throw off the direction of travel.

Suggestion: Make a virtue of inescapable necessity. Instead of demanding that pieces travel in precisely the right direction, allow them to deviate from their course by some fixed number of degrees. Then, on arrival, before captures are taken, "scatter the piece" by displacing the piece along a vector determined by some probability distribution, trying this into the "Kismet" theme camp concept that I can't get anybody interested in. Yet.

Having our displacement random vector be a bivariate Gaussian would be a little mean. I'm thinking maybe something of the form [U1,U2], where U1 and U2 are independent, uniformly distributed random variables on the interval (0,L/16), where L is the length of the field. The referee pulls a pair of numbers of a printout of random numbers, scales, tells the player how much to move the piece by along each axis, and then captures are taken. The piece might be thought of as being randomly adjusted in the square that materializes beneath its feet, in a manner of speaking.

Any thoughts?