Gamblers Always Lose - Round 4
Scrooge wasn’t too happy that the previous game didn’t go too well. He decided that he wasn’t daring enough, and so decided to triple up, instead of just doubling up. His strategy is as follows:
He first makes a bet of \($10 \). If he wins, he will triple the size of his bet. If his total winnings is ever non-positive, he will leave the game.
Now, what is the expected dollar amount of Scrooge's (total) winnings from this fourth round?