Firstly, your 3rd grade school sucked, Beef, if they taught you that.
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that if something happens more frequently than normal during some period, then it will happen less frequently in the future (presumably as a means of balancing nature). In situations where what is being observed is truly random (i.e. independent trials of a random process), this belief, though appealing to the human mind, is false.
Before 2004, my parents had 2 children, both girls. The fact that two female sperm were the ones that got to the centre of the egg before has ABSOLUTELY NO IMPACT WHATSOEVER on any sperm later on. It was a COMPLETE 50/50 CHANCE whether my newest sibling was going to be a boy or a girl. (Sorry for using genetics as the example - it's what's fresh on my mind atm.)
Being mafia in a previous game does not make my chance of being mafia ths round any lower than 25%, just like the rest of you. (I'm not, but that's beside the point.)
The two events are INDEPENDENT. No, that does not mean there is a 1/6 chance of rolling 100 sixes. It means EACH INDIVIDUAL ROLL has a 1/6 chance of being a six, and added up, this results in a much lower chance.
THE DICE, RAMDOM.ORG, AND OTHER FORMS OF RNG HAVE NO MEMORY. This is stuff
I learnt in year 4. (Turned 8 that year)
Sadly, stuffed up statistics isn't a reason to kill a person. Acting suspiciously, while still not a very good reason, is a better reason than the former.
BeefSupreme (3) - Mort, Fippe94, Demagog
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