Gambler’s Fallacy - Round 2
Scrooge, who was on vacation, was eager to continue playing this game after his previous success. However, he was slightly confused about the new ruling, and decided to play it safe. He plays the second round of the game as follows:
He first makes a bet of exactly \( $10\).
If his (total) winnings are not positive, he will leave the game.
Otherwise, he will continue to make a bet of exactly \( $10 \).
Now, what is the expected value of Scrooge’s (total) winnings from this second round?