I think I posted this before about how some video games, you can learn the RNG pattern, and by doing a certain sequence of button pressing, save/reloading, you can guarantee a rare item in a treasure chest. Somebody told me some advantage was to be gained by doing this on Pacman. I remember doing this to cause a certain rare event to happen in game as well.
Use your phone to time the older Aristocrat slot machines for wins.
It might have been another game that came out in the 80's, but that's before my time so I don't remember the exact game. However there is an RNG glitch you can do in Final Fantasy XII.
"You must not open the following four chests from the
beginning of the game until reaching access to the
Necrohol Of Nabudis, where the spear resides:
1.The chest in front of Old Dalanís place in Lowtown.
2.Once inside the palace in the Cellars, the left
chest in the southeast corner contains an elixir.
Do not open it. Or either just to be safe.
3.Once youíve been captured and thrown in Nalbina
Dungeon, one of the chests looks slightly different
than the others. Do not open it. The other two chests
will contain a gambit and a Tourmaline Ring.
4.There are 16 chests on Phon Coast aligned in four
rows of four. One of these is the forbidden chest.
Do NOT open any of them, period."
It was the first one of it's kind where not opening certain chests in the game led you to getting the best weapon. There were more ways to manipulate the RNG in this game to get the best stat increases in a level up, or to force a certain item in a chest.
The only "rare event" I can think of in Pac-Man is the "kill screen" - the game designer probably never expected anybody to get through level 255, so he saved the level number as an unsigned byte; as a result, when you get past level 255, the game thinks the next level is "level zero" and half the screen is garbage.