The possible observer instances and their probability are:
Heads 50 %
Red room 25 %
Blue room 25 %
Tails 50 %
Red room 50 % (On Monday or Tuesday)
Blue room 50 % (On Monday or Tuesday)
If I choose a strategy “bet only if blue” (or equivalentely “bet only if red”) then expected value for this strategy is (−300)∗0.25+200∗0.5=25 so I choose to follow this strategy.
I don’t remember what halfer and thirder were or what position I consider to be correct.
Halfer and thirder are about answer to the initial question of the Sleeping Beauty problem: What is the probability that the coin landed tails when you awake in the experiment?
The possible observer instances and their probability are:
Heads 50 %
Red room 25 %
Blue room 25 %
Tails 50 %
Red room 50 % (On Monday or Tuesday)
Blue room 50 % (On Monday or Tuesday)
If I choose a strategy “bet only if blue” (or equivalentely “bet only if red”) then expected value for this strategy is (−300)∗0.25+200∗0.5=25 so I choose to follow this strategy.
I don’t remember what halfer and thirder were or what position I consider to be correct.
What is the probability of tails given it’s Monday for your observer instances?
Good formulation. “Given it’s Monday” can have two different meanings:
you learn that you will only be awoken on Monday, then it’s 50%
you awake assign 1⁄3 probability to each instance and then make the update P(T|M)=P(M|T)P(T)/P(M)=(1/2)(2/3)/(2/3)=50%
So it turns out to 50 % for both but it wasn’t initially obvious to me that these two ways would have the same result.
Well done!
Halfer and thirder are about answer to the initial question of the Sleeping Beauty problem: What is the probability that the coin landed tails when you awake in the experiment?
I’d say P(Tail|Wake-up)=2/3