A discrete way of saying Dildo, often used with your friends around your parents.
Monica: Did you buy that 12" Dildo?
Eaven: Yes, I'm definitely gonna use it tonight.
Mom: What are you talking about?
Eaven: Just the Polished Stick I bought today.
While having intercourse, you wrap around, trap your partner, and perform a "death roll" customary to alligators. This action is not complete without yelling "Choot 'em!" right before orgasm.
The man grabbed his partner and performed the Gator Stick, rolling his partner around the bedroom.