Help me run the numbers on a perfect IV ditto

So I am currently playing Pokémon Sun version and am attempting to collect a ditto with perfect IVs. I’m using the SOS battle method with an Alola raticate that knows hidden power. It has only one resistance which is dark type because I know a hidden power from a Pokémon with perfect IVs is a dark move. So I’m calling any ditto using a hidden power (dark) a pseudo perfect ditto. Only after I check it in the computer do I know if it’s truly perfect.

So my question is this. Given that every ditto caught is guaranteed to have at least 4 perfect IVs and guaranteed to have a dark type hidden power, what is the possibility space? How many pseudoperfect ditto can I expect on average to catch in order to find a true perfect ditto?

• The type of hidden power can be shortened to the odd or even-ness of the IV. Given that you have 4 perfect IVs, that indicates that 4/6 of these IVs are odd. Hidden power dark occurs when you have all odd IVs, so the last two IVs must be odd (1/16 chance). This suggests there is a 1/256 of a "pseudo-perfect" ditto being perfect. Nov 16, 2017 at 22:05
• @KevinL okay, that’s a higher number than I was hoping for but I’m glad to know what I’m up against. Nov 16, 2017 at 22:08
• @KevinL Why don't you post that as an answer? Nov 16, 2017 at 22:21
• @DanmakuGrazer I was on my phone and wasn't able to type up a complete answer Nov 16, 2017 at 22:53
• @KevinL That's no reason to post an answer in a comment. That was a fully-fledged answer, so it should've been posted as such. Nov 16, 2017 at 23:02

``````let a, b, c, d, e, f = HP, Atk, Def, SpA, SpD, Spd IV mod 2
where the resulting number `type` is an integer from 0-15, and the type number is mapped to a hidden power type. Since we are looking at hidden power dark, we want a `type` of 15, which is only possible when `a,b,c,d,e,f` are all odd, or the pokemon's HP, Attack, Defense, Special Attack, Special Defense, Speed IVs are all odd.