Laying Low
Premise
If you start as godfather for example, it's a pretty good strategy to try to have a low profile. Refrain yourself of talking too much during the day or start wildly accusing people, since that draws suspicious.
However, you must say something or else you draw suspicion again. You need to search a balance between stating something obvious in the chat and saying nothing.
Always follow the sheriff's or investigator's word unless they're accusing a fellow mafia. If the sherrif seems determined of the guilt of the fellow mafia member do not try to minimise the sheriff's or investigator's claims because that will once again make you suspicious.
Applicable Situations
Advantages
If you're lucky and the investi's or sheriffs don't think your suspicious, they won't be inspecting you till late game. This is very interesting, because the Town will be weeding out any contending Serial Killers or Arsonists.
If there's an investigator in play instead of a sheriff, false claims may be spread throughout the chat at day and innocent people could be lynched.
This strength of this strategy is that you let the town kill themselves.
When 2 dogs strive for a bone, the third one swipes it away
You let the town do the dirty work.