arcpy.SelectLayerByAttribute_management("PointsFC","NEW_SELECTION","""MOD( "pointid",10) = 0""")
Are your original points evenly spatially distributed?
You could randomly take a subset of points, but that wouldn't be evenly distributed.
Alternatively, you could convert your points to a grid (something like point to raster) and then convert the raster back to points (raster to point). You would have to play with the cell size to make sure you got the right number of raster cells (which would be converted back to points). This method would mean you have a new set of points.
Let me know if that is at all sufficient.
CentX = int(X / NewCellSize) * NewCellSize + NewCellSize / 2