Suppose that you and a friend are playing cards and decide to make a bet. If you draw three non-face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards with replacement, you win $\$ 50$. Otherwise, you pay your friend $\$ 50$. If the same bet was made 30 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary.

Step 1 ：First, we need to calculate the probability of drawing a non-face card from a standard deck of 52 cards. There are 12 face cards in a deck (4 Jacks, 4 Queens, and 4 Kings), so there are 40 non-face cards. The probability of drawing a non-face card is therefore \(\frac{40}{52}\).

Step 2 ：Since we are replacing the cards after each draw, the probability of drawing three non-face cards in succession is \(\left(\frac{40}{52}\right) \times \left(\frac{40}{52}\right) \times \left(\frac{40}{52}\right)\).

Step 3 ：Next, we need to calculate the expected value of a single bet. The expected value is the sum of the possible outcomes, each multiplied by its probability. In this case, the possible outcomes are winning $50 and losing $50. The probability of winning is the probability we calculated above, and the probability of losing is 1 minus the probability of winning.

Step 4 ：Finally, to find the expected winnings or losses after 30 bets, we multiply the expected value of a single bet by 30.

Step 5 ：Doing the calculations, we find that the expected value of 30 bets is approximately -$134.50.

Step 6 ：Final Answer: You would expect to lose approximately \(\boxed{134.50}\).