So the game alleges that it's mostly deterministic, but I can't figure out how to force a girl to Fantasize/Stiptease. Slaughter at least seems consistent on being triggered if another girl is surrounded and it wouldn't drop the surround turns to less than 1. Do these action also have some sort of cap per battle?
Generally it's very hard to make Chosen do Fantasize more than 4 times per Combat, and they won't use it unless they have at least some Trauma damage on them. Are you trying to get them to use it for the first time or after they've already suffered the Tier 3 Break? The logic is different, just like Tier 1 Breaks--once they've used it once, they'll use it in most situations that it makes sense to do so.
If you're trying to get them to use it for the first time:
Fantasize: Ambush the Chosen you want to use it and make sure you're dealing some PLEA damage during the surround, get it above 1000 and they'll use it the first time they can't use a different T3 move, generally. They use it to avoid taking damage in whatever Trauma is lowest in level.
Striptease: Deal EXPO damage to a *different* Chosen from the one you want to use Striptease, and get that one to Level 2 (1000) EXPO damage. The Chosen that you want to Striptease should use it around then.
If you're trying to get them to use it repeatedly after it's originally broken:
Fantasize and Striptease: They're best raised the same way, along with Slaughter. Send a standard Commander, max Captures and Duration up to 6, Flight if you have it (if not you only need 3 Captures). Start an Orgy as soon as you can, before Extermination finishes. Once Extermination finishes (when the Orgy ends), Surround only one Chosen at a time, starting with the one with the highest #Surround turns. During the last turn of the Surround, Surround another Chosen. The free ones will alternate between Slaughter, Fantasize, and Striptease.
Notes on Tier 3 Selfish Tactics: They'll never use them two turns in a row (exception: Self-Destruct can be).
They'll never use Striptease unless either 1) At least one Chosen is surrounded and not affected by the considering Chosen's previous Striptease, or 2) Their EXPO level will result in a more powerful Striptease than the one that currently affects the Surrounded Chosen.
They will generally only use Fantasize 4 times in a fight, so raising their Circumstances before they start doing that is critical for gaining Punisher Effectiveness. Set up your initial Surrounds so that there's no point where two Chosen are freed at exactly the same time, so that you can re-surround each the exact turn that they're free. If you can't do that, Retry and change up your moves.
