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Flip a coin. OK, since you have other AWs unlocked you may have to flip a 4,6,8,10 or 12 sided coin. Regardless it is statistically possible for you to come up with flips of 1 or 2 even 20 times in a row. Statistically possible means it is not a bug. You will not be able to explore enough Provinces to arrive at a valid sample. Time to look at what you can do instead of moaning about what the game doesn't do for you.
We did it! Then they made all AWs mandatory.This is not a problem for the devs to solve, it is a complication for us, the players, to work around. If the game were made as easy as some people want it to be, I would not only not spend money on it, I wouldn't play it at all.
Look upon the broken shards as being a "common pot", any breakages from any of the AW go into the pot but as soon as there are 10 broken shards any of your AW can use it as a guaranteed whole shard.Regarding "Needles and Excavation" Both weren't researched. After I did I already had 3x broken shrads for each.