TITLE: What is the resistance between two points a knights move away on a infinite grid of 1-ohm resistors
QUESTION [20 upvotes]: On an infinite grid of ideal one-ohm resistors, what's the equivalant resistance between two nodes a knights move away?

(please fix the tags, I didn't really know where to put it)

REPLY [4 votes]: The good answer is indeed $\frac{4}{\pi}-\frac{1}{2}$. You can find a complete solution in the book of R. Lyons and Y. Peres "Probability on trees and networks", section 4.3, p. 124-127. This mainly uses Fourier analysis and the symmetry of the grid.