Egg drop chance

Solution 1:

You are unlucky, like me.

It is completely random. A friend of mine got a 10 km egg right the day after starting, so it is not based on trainer level or km walked or similar.

It will probably help to hatch more eggs, but it won't increase the chance itself to get a 10 km egg. You just have more chances to get one.

Solution 2:

From my experience (I am level 11), the majority of eggs in my inventory are 5 km ones (I almost always have 9 eggs on me). I have received and hatched four 10 km eggs, and about the same goes for 2 km eggs. Although it is worth mentioning that I don't buy incubators and only use the infinite one and the ones I get from level-ups, and I priortize hatching 2 and 10 km, and that's why 5 km occupy my egg inventory.

Solution 3:

My second egg ever was a 10km. I think I was at Level 5 or thereabouts when I received it. It seems to be completely random. FWIW, it hatched a 221cp/40hp Jynx.