Some more thought (can't edit below due to noprocrast :). As he suggests at the end, the distance between points (cards) on the table seems to be important. If

Some more thought (can't edit below due to noprocrast :). As he suggests at the end, the distance between points (cards) on the table seems to be important. If we have some set with a given mean distance between point (or some better measure of clustering), and we choose a set at random, since there are more sets made of distant points, the remaining points will be on average closer together. This is our badness measure (closeness of points on the table) probabilistically getting worse. I'm sure he got that far. The hard part is choosing a distance measure that's amenable to analysis under random-set-removal, but you could probably get a weak result just on mean distance, no? Can't sleep, sorry for rambling.