Streaky dice
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Here is one of my favorite probability puzzles.
Puzzle
You decide to introduce a new game to your casino called Streaky Dice. The rules are simple: the patron selects any fair six-sided die and rolls it. As long as they roll an even, they get to keep playing. Every time they roll an even, they win $1. However, as soon as they roll an odd, they must pay you $1 and the game ends.
Assuming everyone plays until they lose, will your casino make or lose money in the long run?