Annoying? Yes.
“Statistically impossible”? (laughs in combinatorial probability spreadsheet)
Here’s how the overall probability of having Y unique dragons after X eggs actually maps out:
(Ask me how this is calculated. I dare you.)
15 eggs is the “expected value”, but as you can see there is a significant chance of NOT having a full set by then, and even a 3% chance of not even having 5 dragons yet!
Even by 30 eggs, there’s still a ~2.5% chance of NOT having the full set.
So it really is more likely than you think.
Alternative plots of the same data
Here’s a non-stacked version:
And here’s a Y-logarithmic plot:
Note how in a logarithmic plot, each series converges to a “straight line” aka. an exponential decay of * (# dragons / 6) per egg crafted, which is of course the basic probability of getting a duplicate.
(PS - if you are tracking your craft dates for individual eggs, or at least the sequential order, I’d love to add them to my spreadsheet data.)