A standard 52-card deck of French playing cards consists of 52 unique cards, each identified by a particular suit (hearts, spades, clubs, diamonds) and rank (2 through 10, along with an ace, king, queen, and jack). Suppose there is a game in which the player draws 6 cards from the deck, one at a time, without replacement. The cards are recorded and returned to the deck. The dealer then draws 12 cards from the deck, one at a time, without replacement. If the dealer draws 3 or fewer of the cards the player selected, the player does not win any money. If the dealer draws 4, 5, or 6 of the cards the player selected, the player wins a certain amount: $100, $1,000, and $10,000, respectively. It costs $5 to play the game.

Your friend is interested in trying their luck at the game. Based on your understanding of probability, advise your friend as to whether it seems profitable to play the game. Explain reasoning and reference any necessary numerical support.