Hello,
Keeping only 500 random points per horizontal area (aka per two dimensional area) would given higher point numbers on the ground on an open field or parking lot and lower point numbers on the ground if the horizontal area also has a vertical component with many samples. What you want is to reduce volumes (not areas) with higher density when considering all three dimensions. I think what you are after is lasduplicate with the '-nearby 0.02' option.
http://rapidlasso.com/lasduplicatehttp://lastools.org/download/lasduplicate_README.txt
Fortunately the 64 bit version has just come out in case your point clouds are very very big.
running the 32 bit module
>> lasduplicate -i tile.laz -nearby 0.02 -o tile_thinned.laz
making the 32 bit module run the 64 bit module
>> lasduplicate -i tile.laz -nearby 0.02 -o tile_thinned.laz -cpu64
directly running the 64 bit module
>> lasduplicate64 -i tile.laz -nearby 0.02 -o tile_thinned.laz
Regards,
Martin @rapidlasso