You go to a casino with a dishonest coin, which you have hide
down in such a way that it comes up heads 51% of the time. You find
a credulous rube willing to bet $1 on tails for 1000 consecutive
throws. He merely insists in advance that if after 1000 throws
you're exactly even, then he'll take your shirt. You figure that
you'll win about $20 from this sucker, but instead you lose your
shirt. How could this happen? You come back every weekend with the
same proposition, and indeed, usually you do win. How often on
average do you lose your shirt?