I don’t understand how the halfer makes the wrong bet. If we are talking about probabilities, then a), b) and c) all have a probability of 1⁄2 of occurring. If we want the probabilities to sum to 1, then we need to do the following:
If heads occurs, Monday always “counts”
If tails occurs, we need to flip a second coin to determine if Monday or Tuesday “counts”.
So b) is “It’s Monday, and the coin landed tails and Monday counts”
And c) is “It’s Tuesday, and the coin landed tails and Tuesday counts”
So b) and c) are exclusive, so c) doesn’t override b).
On the other hand, if b) and c) aren’t exclusive, then then are both 0.5 instead. So b) being ignored wouldn’t matter as c) would suffice by itself.
The only way we get the wrong answer is if b) and c) overlap and are not 0.5. This makes no sense for the halfer model.
I don’t understand how the halfer makes the wrong bet. If we are talking about probabilities, then a), b) and c) all have a probability of 1⁄2 of occurring. If we want the probabilities to sum to 1, then we need to do the following:
If heads occurs, Monday always “counts”
If tails occurs, we need to flip a second coin to determine if Monday or Tuesday “counts”.
So b) is “It’s Monday, and the coin landed tails and Monday counts”
And c) is “It’s Tuesday, and the coin landed tails and Tuesday counts”
So b) and c) are exclusive, so c) doesn’t override b).
On the other hand, if b) and c) aren’t exclusive, then then are both 0.5 instead. So b) being ignored wouldn’t matter as c) would suffice by itself.
The only way we get the wrong answer is if b) and c) overlap and are not 0.5. This makes no sense for the halfer model.