Here's a brief table explaining how different systems say to handle Specialty rerolls.

"Recursive" means that if you get a 10 on the result of a Specialty reroll, you roll it again; if you get another 10, then you reroll that as well, and so forth. If this is "no", then you only get to reroll once, regardless of whether you get a 10 on the reroll or not.

"1s count" means that 1s on a Specialty reroll subtract successes as normal. If this is "no", then 1s on a Specialty reroll do not subtract from your total successes.

System Recursive? 1s Count?
Vampire yes yes
Mage, Demon, other yes yes
Werewolf no no
Hunter yes no