Zizka There are waves of
Resident Evil-type games that use similar save mechanics.
monilloman already mentioned
ALISA, a game so good that the rest of you are all officially criminals for not having played it yet. Also there's one called
Them and Us, which I didn't like, and the excellent
Tormented Souls. Plus many more I'm sure.
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gurugeorge, the difference between "limited saves" and "limited slots" is simple but important. A "save slot" is just another name for a save file.
Example, you and your roommate can each have your own saved game in
Resident Evil, each on a different slot. Or you can have one playthrough, where you have let's say Game State A saved in Slot #1, then play for a while and save the game (in Game State B) either in Save Slot #1 (overwriting Game State A), or in Save Slot #2 (creating its own timeline branch). If you save State B in Slot 2, you can still load Slot 1 and return to State A, then make different decisions and in effect create a new timeline: C, distinct from B. If you save
that in a new Slot then you can still go back to A and create timeline D, etc.
Some games only have one Slot, meaning you and your roommate can't each have your own save at the same time, or just a few Slots so you can't keep a million different save states on file. This is a completely different limitation than spending in-game resources, such as typewriter ribbons, to save your game; or only being able to save in certain locations, etc.