You know, the one really interesting dynamic domain is chaotic, which is a subdomain of the deterministic! I figure free will is a chaotic phenomenon.

Groundhog day is your intuition pump here. Go back in time and most assume that the day will go mostly the same, except for the butterfly effect if you change something. Given exactly the same conditions (we went back in time, so that's pretty exact), people will make the same decisions.

Most people don't assume that the day will be completely different the next time loop. The town won't suddenly spontaneously all start breakdancing or standing on their heads.

(Edit: The murderer is the one who -given the same/similar conditions- will murder again. I'd politely suggest maybe we put them behind bars as a precaution against that; until/unless they learn to act differently. )

(Edit 2: Throw in stochasticity and this actually tends to smooth out chaotic systems. This is counter-intuitive! People's brains break on Evolution in the same way. Meanwhile somehow folks intuit birdshot without difficulty; which is weird!)