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I was reading up on Bulbapedia about the Egg cycle earlier because I couldn't figure out why sometimes it look up to an hour for the daycare man to give me an egg when I was taking the exact same route and reloading the area so he could be seen from outside. It said the following.

Generation II
Every time an Egg cycle is completed, the game goes through the Eggs in the player's party in order and performs the following:
Subtract 1 from the Egg's cycle count. If its Egg cycle count is now 0, the Egg hatches and no other Eggs are processed.

Does this mean for an egg to spawn I need to not have a full party of eggs and my Pokemon? Or am I just interpreting this wrong? (I'm shiny hunting for Sentret so I can have a pink baby Furret :D)

Any help would be much appreciated I just want to speed up the hatching process as much as I can in vanilla Pokemon Crystal.

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The quote you have refers only to hatching eggs, not to generating them. The issue is that in Gen 2, the chances of generating an egg per egg cycle are significantly lower than in later generations, ranging from 4-31% vs 20-88% in later Gens.
In particular, if you’re breeding different species from the same trainer, you’ll get the low-bound of only 3.91% chance of an egg per cycle, meaning it’ll take 6,547 steps on average to get an egg, which for reference is nearly 1,500 steps more than hatching an average (20 cycle) egg. And that’s just the average; it could absolutely go way over that if you’re unlucky.

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