Quote:
Originally Posted by Nate.
Ubercuber--
That strikes me as very improbable. If I see a frog fall from the sky and think "what are the odds of that?", it's pretty obvious what's going on. The event I'm surprised by is the frog falling from the sky. Now, if I see a frog falling from the sky today and tomorrow, and again I ask myself what the odds are, it's still pretty clear what I'm surprised about: frogs falling from the sky twice in two days. Perhaps it's some variant: frogs on two consecutive days or something like that. It's even conceivable that what I do care about is the conditional probability of a frog tomorrow given a frog today.
But just because event E is a necessary condition for E', or even a necessary condition to make you care about E', doesn't mean that when E' happens, and you wonder what the probability of "that" is, that you aren't referring to E'.
Of course there's a complex causal process leading to the woman asking what the probability of "that" is. And we can argue about where the clearest "joints in nature" here are. But this is, at the bottom, largely a psychological question. The woman got aces twice in a row, and I'd bet a whole lot of money that the "that" she asked about was the aces twice in a row. Mason's taken plenty of courses in statistics, but that doesn't mean he gets to choose what other people's pronouns refer to.
All my best,
--Nate
Nate,
Frogs falling from the sky on two days days are probably not much more surprising than falling on one... on day two I'm still surprised it's happening at all!
But back to cards, the fact that she was just dealt aces on the previous hand seems the most obvious reason that she was prompted her to ask the odds of getting them again the very next hand. Had she not been dealt aces on the previous hand and inquired the odds of getting them twice in a row I would feel differently.
She probably didn't know there was a difference, may very well have been satisfied with the answer, and perhaps cares very little for the reasoning, but the answer was, imo, not the best answer for the circumstances as they seem to have played out.
For two people who weren't there (and don't read minds), as you said, it is only speculation, but this rings of "OOH I just got em again, what are the odds?" to me. Operative word being "again", as in, it already happened once.
Quote:
Originally Posted by spadebidder
This.^^
"Aces twice in a row" is a specific event (one), with a precise probability, and only one answer to the question is possible. The woman absolutely was not asking about the probability of "being dealt a pair of Aces". Twisting the question to imply that is nonsensical, and in the circumstances it would require a belief in the gambler's fallacy to even ask it.
Absolutely? Even if you were there, how do you know absolutely to the point of all other views being nonsensical?
There is more than one answer because aces on the next two hands is much different than aces on the last two hands. When referencing the last two hands, the second pair is only noteworthy in the context of having already been dealt them on the previous hand. Ignoring that possible interpretation of the frame of reference for the question tosses out a perfectly reasonable interpretation.
Additionally, for aces twice in a row to have a precise probability with only one answer possible you need to be dealt a specific number of hands. If you are dealt two hands, you get one shot to get them back to back, if you are dealt four hands you can get them on the first two hands, the second two, or the third two, etc.