The check for balanced tablets in the randomwalk Concurrent test too easily fails.
Here is a real-life example from the test for the number of tablets across five tablet servers: 2, 5, 2, 2, 3. (An old unrelated table plays into these totals.) This produces a mean of 2.8. The cluster is considered unbalanced by the test when any server's count differs from the mean by the larger of 1 or the mean divided by 5. In this case, 2.8/5 is less than 1, so the second tablet server fails since it has more than 3.8 tablets. Even a 4 would fail.
Part of the problem in this particular case is that there are so few tablets, and so few tablet servers. The cluster also seems happy to leave these counts as is, as I continue to check it, so the test's definition of unbalanced is too narrow.
The test needs to be refined to detect unbalanced conditions with a statistically decent calculation.