I think Psionics can be any one of the three mental stats. In the 3e Psionics handbook I think that different contests would test different attributes too. Personally I've always associated will and willpower with Wisdom, Charisma in certain circumstances.
The question really should be why we're making a roll in the first place, unless it's a wisdom save against something else, otherwise it should be our target that makes the save.
I feel like we're making a 'to hit' roll of sorts, I suppose?
Or maybe a lockpick roll is a better comparison? I don't know.
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I tried to look up the 5e mind flayer, and it appears to use Int. for its innate spellcasting (psionic) abilities.
