There's also a counter-theory, suggesting that the absence of a second-night kill is because Sky is Mafia. In this case, Master's Mafia status is questionable – not definitively, but it is.
In this scenario, with Sky as Mafia, we have the execution of a Mafia member prevented, full protection for the Godfather, and all Mafia members are safe.
In the scenario where Sky is the Godfather, we have the execution of the Godfather prevented, all Mafia members are safe, and protection for the Mafia member.
In the scenario where Master is the Godfather, we have the execution of the Godfather prevented, all Mafia members are safe, and protection for the Mafia member.
In the scenario where Master is another Mafia member, we have a Mafia member executed and protection for both the Godfather and the Mafia member.
Even with this scheme, it's still mathematically more advantageous to execute Master than Sky. Of course, this is based on the assumption that he is Mafia, but at the moment, I personally need a strong argument to deny this. Not because of Freud's execution itself, but because of all the related factors.
I just want to point out this possible (not definitive) scenario so that it's immediately clear.