Gamblers Always Lose - Round 4

Discrete Mathematics Level 3

The Las Vegas Casino Magnicifecto offers an “even value” game, with the catch that players may not leave the game players may not leave the game if their (total) winnings are positive. See previous question for more details.)

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?


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