Solve the puzzle using one bit of memory!

A task like this for sharing resources:
On September 1, 100 immortal elven Vorkuta convicts stood on a solemn ruler and suggested that they speed up the process of their liberation. So, in prison there is a camera with a hanging light bulb. Light bulb can be turned on or off. Every day, starting from September 1st, the jailer will launch one prisoner into this cell. At this point, the convict can see if the light is on.
The jailer will ask each prisoner: “Have all your comrades been here at least once?” If the prisoner answers “no,” the game continues.
If the prisoner answers “yes” and this is true, everyone is released into the tundra. If this is not true - capital punishment for all.
Prison officers may choose prisoners randomly and with repetitions. Prisoners sit in solitary confinement and can only agree once - on September 1st at a dinner after a solemn ruler. After that, they sit in "singles" without windows, do not see each other and light bulbs at all.
Find the optimal strategy for the behavior of each prisoner so that they are released early.

WARNING Two algorithmic solutions have appeared in comments, one probabilistic and one limit. Plus two or three cheaters. There are a few more possible answers based on quite difficult behavior of the cons. Also, I propose to all formally estimate the time of release.
Thank you xmolex for pointing out the possible source ! Under the link - a fundamental pdf-file with 10 solutions and a mathematical evaluation of each of them!
UPD cries of "dupe" are gaining power, and for good reason - this is the same task on the Eruditor , on the Moscow Olympiad and (oh my God, shame on my search skills) on Habré from the user ttim
UPD2 : for those to whom this task and all its solutions seem to be easy, a sequel has been published taking into account interference.