Author: h.g.muller
Date: 13:41:03 02/14/06
Go up one level in this thread
I can see a way for the (0,1)+(0,2)+(1,1) that is indeed extremeley tedious: it can prevent the bare K from crossing a diagonal, thereby confining it in a (possibly very big) triangular corner. But to keep it there if the K starts to walk along the diagonal it would have to follow the K move for move. Only if it reverses, which it sooner or later has to do because of the edges, you gain 1 move, which you can use to approach your own K. After that, you have to run to the other edge with the Leaper to maintain confinement before you get the next move for your K. The number of moves diverges as the product of the initial distance of the bare K to the corner and the distance between the Kings (so as the square of the board size). The KqKp with P on 7th is speedy by comparison! Remarkable is that this strategy would even work on an quarter-infinite board (2 edges and one corner). That shows that it can be done on any size board. Conversely, a win on a board of any size does not mean that it also works on the (quarter-)infinite board. At least, I could not think of a way where the Squirrel could do it on such a board, because it only seems to be able to confine along a rank or file it really needs the fact that there is an end on both sides of this. In that respect the (0,1)+(0,2)+(1,1) is the stronger piece! (Perhaps the Squirrel can do it on an infinite strip of arbitrary width, but this Leaper can do that too, because also diagonals have two ends there...) The other pieces seem very clumsy, they lack manouevrability. I could not devise a way where the (0,4)+(1,4)+(2,4) Leaper would confine the bare K. To keep on hindring it it must slowly retreat, by one rank for every 2 moves of the bare K. That means that the winning K can just keep up with it, but not approach. I suspect that the only reason this is a win is that the board is finite in ALL directions. This makes it impossible for the bare K to outrun the winning K forever, at some point it has to turn a 90-degree corner to avoid approaching the nearest edge voluntarily (and finally running into it). The winning K can then take the inside corner to cut off some distance. In the end it will catch up. Did you watch the computer play a very deep mate against itself on a big board, and does it indeed use this strategy? I guess it would require a pretty big board (32x32?) to recognize the pattern, otherwise the edges are always so close that it starts to use the accidental advantages it can derive from this...
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.