So isn't the correct answer to the problem is to contact the other
ticket owner and offer to split the winnings.... before they check the
ticket.   $500,000 better than $0.

Wirt Atmar wrote:
>
> Denys writes:
>
> > Now with the ticket, if I choose 1 ticket out of 1 million tickets and then
> > all
> >  the other tickets are shown as losers except for 1 which is still unknown
> > and
> >  my original ticket, will I switch?  In a heartbeat.  My original ticket
> had
> > and
> >  still has 1 chance in a million, the other ticket(s) has 999,999 out of a
> >  million of being correct.  The other ticket represents all the other
> tickets
> >  except mine.
>
> No, no, no, no, no.
>
> In the absence of any other information, all you've learned is that your
> current ticket now has a 50/50 chance of being the winning ticket -- and that
> the other ticket also has exactly a 50/50 chance.
>
> By showing that all other but one of the tickets was NOT the winning ticket,
> the odds that your original ticket is the winning one went up dramatically
> from 1 in a million to one in two, but then so did the other ticket's odds at
> exactly the same rate, at exactly the same time.
>
> This is a completely different -- and a more standard probability -- problem
> than someone who's flipping doors and who has special knowledge of what's
> behind each of the doors. "In the absence of any other knowledge" is the
> critical phrase in the sentence above.
>
> Wirt Atmar