He can end up one against one with a Mafia member. And here, randomness will essentially determine the winner.
Or two against two Mafia members.
Since Oyun is "easily defeated" and so on, here are two options:
1. 100% doubling, but every 2 turns.
2. 100% doubling every turn (in case of a block or using an ultimate, the vote remains one).

I don't want to remove the percentages from Oyun because it's a characteristic of the character, not a particularly pleasant one, but still.
Until the third day (1st, 2nd, and 3rd night, 1st, 2nd, and 3rd day), he cannot be killed or hanged. From the 4th night, he has one protection against being killed.
Why so long? It will be awkward to have the ability to execute only Mafia members for three days in a row, while the main threat is unattainable. They can help against the Mana, especially if the trio dies. Although I agree about the invulnerability until the fourth night.
If one of them (Bachelor, Haruspex, Commander) kills someone personally, they receive a one-time protection against being killed in addition to their immunities. (the second protection will not accumulate until the first is used, the protection saves from one kill, but will not help in case of a double shot)
And yes, protection against execution for each world that leaves the trio, regardless of the reason for leaving.