So I worked this out. Yes I'm a nerd. Assuming there's 1 diamond in each board, and the board is 20 blocks, and Discovery isn't rigging the thing, you have a 2% chance (i.e. 1 in 50) of getting 3 or more diamonds in a 12-week period.
You have roughly a 10% chance of getting exactly 2.
~34% chance of getting one.
~54% chance of getting zero.
So that's actually not too shabby, if 1 in every 50 Vitality customers gets a fairly decent reward then they might actually be shelling out quite a bit to reward those who stay active. It's certainly motivation enough for me.
The maths of how to work this out are on this page:
http://www.statisticshowto.com/prob...nomial-theorem/binomial-distribution-formula/