- two cards have one gold badge on them,
- two cards have one silver badge on them, and
- one card has both gold and silver badges on them.
At the beginning of the game, all five cards are shuffled and set face down. In each round, one police card will be opened; if there are three badges of the same color, this indicates that the game ends after the current round is finished.
Determine the expected number of rounds played in the game.