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decrease density of points

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If I have a point feature class with about 1 million points that are spread one meter apart each, how can I EVENLY reduce the density of these points by about an order of magnitude?

I tried selecting every 10th record, but this did not evenly select the points spatially. Some areas were denser with points than others despite the total number of points selected being correct.

This is how I selected every 10th point :

Code:

arcpy.SelectLayerByAttribute_management("PointsFC","NEW_SELECTION","""MOD( "pointid",10) = 0""")
Can sombody tell me a method to do this spatially rather than just using the sequential pointid field? Thanks.

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