This is SUPER helpful!
So...in other words...I need to:
Get a female with the hidden ability that I want from the Safari.
Get a male with the nature that I want from the safari.
Make sure both the male and female share one of the same IV's.
Slap a power bracelet of the desired IV to be pushed and everstone on the boy.
Ask the female politely to hold the Destiny Knot.
Breed until I get female pokemon with 3 IV's, the nature, and the ability that I want.
Replace the female as the mother.
Rinse, Lather, and repeat with different dudes until I get a chick with 4 IV's.
Then the same thing until I have 5 IV's.
Am I understanding correctly?
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Follow up questions:
1. How can the pokemon hold a power bracelet AND the Everstone?
2. Once I have the female with the correct ability do I even need the everstone?
3. Do I need to know what final attacks I want to use BEFORE I decide on what nature I want? (How would someone even know this starting out?!?!)
4. Wouldn't this be a lot easier to just use different dittos with power bracelets?
Thanks for the help! I really appreciate it! It is so hard to find these specific answers among ALL the different articles all over these interwebs!
ken
Longish post incoming...
If you're trying to get a hidden ability, then yes you'll want a female. UNLESS you're using Ditto, in that case you can grab a male since males will pass hidden abilities when breeding with Ditto (just not if they're trying to breed with a female of their species).
So for example, assuming you're starting out with nothing but 2 IV safari parents (though you can catch a lot and some will probably come out with 3 IVs) and you want a physical sweeper and the hidden ability for it. I would grab 2 with different IVs (say male with HP/Atk and female with SpD/Spe) and breed them, have one hold the destiny knot and the other hold a power item (optionally if you have a parent with the right nature you can start everstone now to save it unless you can re-introduce it later, which is what ditto is good for). Your goal is to get 3 IV parents from there, say a male with HP/Atk/Spe and a female with Hp/SpD/Spe. You'll then want to switch it up and swap out one of the parents for one with Def, have it hold the power item for def (belt I think), the other hold destiny knot, and breed them until you can get a 3-4 IV parent; for this example, you leave in the male and introduced a different female with HP/Def, your goal now is to get a male with HP/Atk/Def and ideally Spe if you can.
But regardless, you will now want to take that new male parent once you get it (HP/Atk/Def) and have it hold destiny knot, then breed it with the original female you had (HP/SpD/Spe) with everstone and what you're aiming for now (since your 5 IVs are accounted for) is a progressing chain until you end up with 4 or 5 IV parents; say your next batch of eggs gives you a new male with HP/Atk/SpD/Spe, you don't want to replace your current male as you'll lose Def. However if you get a male with HP/Atk/Def/Spe, then you swap it in over your current male as it now has 1 additional IV Destiny Knot will check against. Same for the female, you'd reject say a HP/Atk/Def/Spe one since the male has no SpD, but you would keep a HP/Def/SpD/Spe (you would also reject any without the hidden ability as you MUST have it, otherwise it you swap it for a female without it, then you'll be stuck with just whatever normal ones it has). But really from here, it's just breeding enough so you'll replace your 3 IV parents with 4 IV parents, and from there should be pretty quick to get that 5 IV egg with the IVs you want passed down. Of course, you could get really lucky at the 3 IV stage and end up with the egg you want, but your odds increase as you replace your 3 IV parents with 4 IV parents.
This is probably why it helps to trade or otherwise get a "spitback" parent if you can, ie a rejected one from someone because it doesn't have the right IVs they want. But since these are 3-5 IV parents (ideally male in the egg group you want), it cuts down on the time you need to expend breeding quite a bit. Male parents (unless you're going for egg moves) in this sense are more valuable since species is determined by the female, so if you have a 4-5 IV male parent, you can breed with anything in its egg group while only needing to get the right female and ability (nature also I suppose if the male one isn't one you want).
For your other questions:
1. You can only hold a power item and everstone if you give up destiny knot, which isn't ideal since you're then only down to passing 3 IVs from either parent, only 1 guaranteed. Generally, use destiny knot/power item to try getting a good male parent (assuming you're not using ditto), then use the resulting male parent with destiny knot and the appropriate female with everstone (or vice versa if the male has the right nature).
2. Again everstone doesn't affect abilities, so no. Everstone is only held by the parent with the right nature.
3. If you're trying to get a specific egg move (say aqua jet on azumarill), then you'll need one of the parents to have that move since Pokemon can now inherit moves from either parent (before it was male only). Otherwise if it's an attack they'd otherwise learn via level up or TM, then no you don't need to decide on any final attacks.
4. Power items are only useful to guarantee 1 IV will pass off the parent it's held on. So regardless, you'll eventually be dropping it for Destiny Knot once you have 3-4 IV parents since the power item hogs up the everstone slot, unless you want to try randomly getting the nature you want (no you don't btw, worse odds than getting a perfect IV in a given stat).