If you're on a high floor, most elevators that arrive first will be going down. On a low floor, most go up.
Why? An elevator moving randomly spends more time on the floors below you than above (when you're high up). So at any random moment, elevators are more likely to be below you, meaning they'll arrive going up? No -- they arrive going down because they must first pass your floor going up, then return going down!
On floor F of N: P(down) = (F-1)/(N-1)