"I claim the odds of flipping a fair coin 100 times in a row and getting heads every time is 50/50, but only in the situation where you happened to flip 99 heads in a row already".
If I'm told that I'm in a coin flipping contest and (1) in my first flip I got heads, (2) in my second flip I got heads, ..., (n) in my n-th flip I got heads, ..., (99) in my 99-th flip I got heads and then I'm asked what's the probability that I get to 100 heads in a row there are different answers that I could give.
I could assume that the probability of every single flip is 50/50 and then my answer will by 50%. Or I could give an answer higher than 50% if I'm able to control the outcome - or if by now I suspect that the coin has two heads. Or I could give an answer lower than 50% if I suspect the game is rigged and they are going to make me lose now.
Whetever my assumptions about the upcoming flip, my answer will be conditional on (1),(2),...,(99) having happened already. There is no point in thinking about the "whole game" at this point in time. I already got heads 99 times - just like in the Monty Hall problem I already picked a door and he already picked another door with a goat.
I'm not sure what is "this".
> See the coin flipping example.
"I claim the odds of flipping a fair coin 100 times in a row and getting heads every time is 50/50, but only in the situation where you happened to flip 99 heads in a row already".
If I'm told that I'm in a coin flipping contest and (1) in my first flip I got heads, (2) in my second flip I got heads, ..., (n) in my n-th flip I got heads, ..., (99) in my 99-th flip I got heads and then I'm asked what's the probability that I get to 100 heads in a row there are different answers that I could give.
I could assume that the probability of every single flip is 50/50 and then my answer will by 50%. Or I could give an answer higher than 50% if I'm able to control the outcome - or if by now I suspect that the coin has two heads. Or I could give an answer lower than 50% if I suspect the game is rigged and they are going to make me lose now.
Whetever my assumptions about the upcoming flip, my answer will be conditional on (1),(2),...,(99) having happened already. There is no point in thinking about the "whole game" at this point in time. I already got heads 99 times - just like in the Monty Hall problem I already picked a door and he already picked another door with a goat.