There has certainly been some confusion about this, so we will try and clear things up.
Pokemon (they don't necessarily need to be psychic, the two pokemon involved in the breeding themselves would also be able to tell) can roughly tell what species a certain egg will hatch into and can make a good guess as to gender. Mind you, this will never be 100% and mistakes may happen, but those are things you can pretty safely determine about the eggs you are hatching.
Everything else remains up to chance and cannot be told before the egg actually hatches.
Of course, an experienced breeder can certainly calculate the odds of an egg in a particular clutch being shiny or having its Hidden Ability. And move-sets/egg-moves are, of course, simply a matter of looking at what the parents are capable of. However, it is not possible, by using pokemon or otherwise, to definitively say an egg is going to hatch into a shiny pokemon before it, well, hatches.
How do event egg providers do it? Dark magic rituals passed down from generation upon generation. We can neither confirm nor deny the need for blood sacrifices for these very arcane rituals.
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Pokemon (they don't necessarily need to be psychic, the two pokemon involved in the breeding themselves would also be able to tell) can roughly tell what species a certain egg will hatch into and can make a good guess as to gender. Mind you, this will never be 100% and mistakes may happen, but those are things you can pretty safely determine about the eggs you are hatching.
Everything else remains up to chance and cannot be told before the egg actually hatches.
Of course, an experienced breeder can certainly calculate the odds of an egg in a particular clutch being shiny or having its Hidden Ability. And move-sets/egg-moves are, of course, simply a matter of looking at what the parents are capable of. However, it is not possible, by using pokemon or otherwise, to definitively say an egg is going to hatch into a shiny pokemon before it, well, hatches.
How do event egg providers do it? Dark magic rituals passed down from generation upon generation. We can neither confirm nor deny the need for blood sacrifices for these very arcane rituals.