Cue the masochism. I'm taking a crack at Eevees today.
I was rewarded with a Shiny on Egg #15 (the first one hatched). I wasn't looking as it hatched, reading something on here, then I looked at the screen as I went to tap the B button to cancel nicknaming. Before I hit the button, I did a double-take. "Is Eevee usually this white?" I thought. I hatched the next one and heypresto, it was a normal one.
Talk about lucky.
I didn't have a single female in the batch, however. I am attempting a Calm Eevee with Anticipation and an Egg Move, so I need at least two females, preferably 5IV. Going 0/18 on the first crack wasn't good, but I found that Anticipation was being passed on very well for a male Eevee (10/17 through the Ditto, not including the Shiny - which also has it, but was also the only 1IV in the batch - go figure). Three 5IV Eevee came out of the batch, which I accepted as a good starting point. If I can now get just one female Eevee, with at least 4IVs, I can proceed with breeding nature from the Tauros I have on standby (now that's a load of bull).
UPDATE: I now have 42 male Eevees. I have 0 females. 12.5% female my Ash. And not even a single Calm one in the batch. I mean, at least that would SAVE me a step.
UPDATE: No replies since, so I'll edit. The 49th Egg turned out to be my first female. The 54th Egg turned out to be the exact female I was trying to end up with (nature as well), so the Bouffalant I pulled aside basically got some exploration time and not much else. I immediately fetched some Munna and chose an HP one to cover the female's weakness (00/31/31/31/31/31). The breeding didn't go so well; unlike the first round where I got three 5IV males instead of a female, and swapped one in, I got only one 5IV and six 4IVs in this batch of 24 (and I had eight 1s to choose from; last time, I had six). Ironically, no females, but this doesn't surprise me any longer. The good news is I shared two Egg Moves, so these are store quality Eevee that I'm producing. I'm happy about that!
I've made the executive decision to run another batch using this male since the Egg Moves still ought to pass down. After this run, I should be successful and ready to trade. This will also provide good store material one day too, but that's for another discussion.