So for the Gengar, Psychic is pretty much a clearly better move than Hypnosis. There was an old thread that went into this, but I cant be bothered finding it now. From memory the odds if neither switches (or explodes) are something like, with LK you have a 25% chance of sleeping the Gengar, and with Psychic you have a 20% chance of KOing the Gengar. Furthermore, with LK its all or nothing, whereas with Psychic you have a bit over 40% chance of doing 50%. That extra 5% chance of having a positive outcome just isnt worth the additional value of the chance of the KO, let alone the benefit of the extra damage.
[edit] -
https://www.smogon.com/forums/threads/what-are-the-odds-gengar-vs-jynx.3540380/
My memory was poor!
But still, even with 37% vs 22%, that 15% isnt really worth it in light of the significantly better outcome when KOing.
Basically the potential outcomes are like:
- 56% of the time Jynx is slept without attacking so it doesnt matter what move you used.
- 22% of the time Psychic KOs before hypnosis hits, so whatever LK did, Psychic is altogether better.
- Of the remaining 22% of the time, you have something like 3% of the time where both Jynxes gets put to sleep anyway but the Psychic line has done 50% and the LK line has done nothing.
- Leaving about 19% of the time where LK is better than Psychic, although, the Psychic does have the compensation of damage on that Gengar.
For Eggy, think about it this way. If you were the Eggy user, and you knew 100% what move your opponent was going to do, what would you do? Like, if you knew for certain that Jynx is Blizzarding, are you really gonna stay in with Eggy to Sleep Powder? I'm only ever doing that if I am really fucking scared of that Jynx. But taking a Lovely Kiss? If I have a backup sleeper, then for sure. I am happy to sleep absorb with Eggy, especially with that chance of getting my sleep off first. By having Blizzard in your repertoire, you force the Eggy to switch, which is what you want.
Note: usual caveats around relative skill of your opponents apply.