At the casino, Andy is trying to decide if it is profitable for him to play a certain game: In this game, Andy chooses 6 cards from a standard deck, one at a time, without replacing them. Each card he chooses is recorded.

Then, the dealer proceeds to choose 12 cards, one at a time, without replacing them.

If the dealer ended up choosing 3 or less of the same cards that Andy chose, nothing happens and the game is over. However, if the dealer chooses 4, 5, or 6 of the same cards that Andy chose, Andy would win $20, $100, or $5,000 (respectively).

It would cost Andy 5$ to play. Is it profitable for him to play the game?