The rules of the game are as following: a player draws one card from a standard 52-card deck. if the player picks a heart, they win $10. if they pick a face card that is not a heart, the player wins $8. picking a face card heart counts the same as picking a heart. if a player picks another card, they lose $6. is this gambling game a good way to make money for someone or not?

Let's suppose "good" here means that the amount a player can expect to win is positive.

The probability of drawing a heart from the deck is 13/52 = 1/4.

The probability of drawing a face card that is not a heart is 9/52.

The probability of drawing anything else is 30/52 = 15/26.

The expected winnings are then 10(1/4) + 8(9/52) - 6(15/26) = 11/26, meaning on average the player can expect to win about $0.42 per game, so by our definition this game is a "good" way to make money.

-2

7 - 9 = -2

reversed:

-2 + 9 = 7