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 \(\boxed{134.50}\).