I'm gonna admit it, I've been playing mafia solely luck-based for the past month. I've come to learn that it is actually a pretty legitimate way to play the game, given that you're using intuitive reasoning and common sense at some level, and making educated guesses. I'd actually started out with keeping a record of almost all things but I lost the file 3 weeks ago and was too lazy to redo it; but from what I had gathered, statistics are largely unreliable when using this approach. I would totally recommend this method because it has made mafia fun for me again. You can not expect this to be 100% reliable, but it's a pretty solid approach if you apply it properly and the best thing is you put in minimal effort, and I really mean it when I say minimal.
I'm listing down some things I've learned, and would like to share from my personal experience-
The main aim is to avoid getting lynched. While playing like this, the mafia will most certainly leave you alive, thinking you're a liability. You must ensure that you don't get lynched at any point of time, which is what we will be focusing on.
before a game starts, always keep track of player's mindsets. If you wanna go the extra mile, have a look at their round record or their previous few games. If a player is raging in pregame you can pretty much reliably sheep them for a couple of days because they'll be putting in the effort for you(remember, the goal is to do as little as you can while still trying to win). If they happen to be mafia later on in the game, you're gonna be townread simply because "no mafia would buddy that hard"(a line I've seen almost every other game). If they were town they most likely won't be voting you so you have semi immunity. Once again, without doing anything ;)
use ISP as much as you can. ISP makes you null so you won't be lynched based on your lines, you'll be lynched on your votes(which we know has a very small chance of happening)
the most logical thing to do while using this approach is play using POE. Now you can go full IDGAF mode and select a random person, mark them as town and proceed with the day(very luck-based, even though in most games there will be roughly a 25% chance of them being mafia) or you can look for the towniest daystart. Keep in mind we're doing luckbased mafia so don't go in too hard.
if there's a bandwagon happening, fake AFK. Someone is going to unvote and ping you so that you don't veg. The trick here is to not respond to their pings and just have them give up towards the end. Now obviously you're going to be hammering but the hard part is hammering at the correct time. If you hammer too early or too late you will be lynched, for sure. According to me the ideal time to hammer would be with 25-10 seconds left in the day before kicks. Another thing to keep in mind while hammering is to use the 'ninja hammer' strategically; you can go "whoops I forgot about this" and still hammer but it won't have the same effect! When you hammer without saying anything, you will not be lynched the next day. Just act like nothing ever happened and if anyone asks, you were just clipping your nails or taking a or whatever(sometimes it's okay to admit that you came back around halfway through but never admit that you were here the whole time)
when you see someone being FOS'd, you need to townread them. These people happen to flip town 4 out of 5 times and are just either bad or deliberately being scummy. Townreading them earns instant favour from them(we're trying to not get lynched, over here). If they are mafia they won't kill you, obviously.
the LYLO. This is a very tricky situation(which you will end up in almost 70% of your games, if you followed the instructions above and if you aren't a confirmed PR or similar). What I'm about to say here will be deemed controversial and called OGI but really, nobody knows until you tell them. What I did was flip a coin and based my hammers on the flips. The important thing about the coin is that it's unbiased. You have to remember that you put in absolutely no effort this game so you don't have any real reads to hammer with. Flip a coin, say a prayer and go for it. I wish I was joking about it but coin-hammers really have gotten the job done, for me. However, if the person you marked town day 1 is still alive, you hammer them- no questions asked. I'm assuming you get to hammer here because that's what you should be doing. If someone votes you, just cross them and wait for the other guy to hammer(zero effort). If the one that voted you was mafia, you can always say you voted correctly and blame someone else for a mishammer. If the hammerer was mafia you just blame the one that voted you. The clever part here is making it sound like you're taking blame while subconsciously putting them in a bad position. something as simple as "my bad, sorry, but it's ok I voted mafia" will get the job done. Still, whenever possible, make sure you hammer. The reason behind taking a 50/50 in the dark is you being unbiased when you do it. Bias is what ruins a lot of mafia games
use the hammer as a way to clear yourself. This requires some skill because you need to hammersit in the correct manner or you're gonna get voted. I usually just chimed in with a couple of off-topic lines and then went "this guy is mafia" and voted him. I unvoted him around 1 min 30 secs before kicks to make it look like I was reconsidering(this will make them unvote you too if they were OMGUSing) and just stood on my vote right until the end. If you're lucky you might end up with a full-cross but mostly it'll be a 2 or 3 person cross for you. If you're able to force NL in this situation, point it out the next day and they'll mark you as town for not forcing it.
I don't expect you to take all of this very seriously, but it's what I've been doing and I have had an absolute blast playing like this. Sure, it isn't exactly a respectable way but I started to get bored while applying logic and reasoning and realized the game just wasn't as fun anymore if you went down that path.
Remember, the most important objective is to not get lynched, and then to lynch mafia. Obviously you have to use some common sense and take a few calculated risks but for the most part you will be doing absolutely nothing while looking like you've been doing the opposite.