The expected number of cards that you need to flip before you see the first ace is known as the expected value or expected number of trials. To find the expected value, you can use the formula:
E = (probability of success) * (number of trials)
Where E is the expected value, probability of success is the probability of seeing an ace on a single card flip, and number of trials is the number of cards that you need to flip.
Since there are 4 aces in a deck of 52 cards, the probability of success is 4/52 = 1/13. Plugging this into the formula above, we get:
E = (1/13) * (number of trials)
To find the expected number of trials, we can solve for number of trials:
number of trials = E / (1/13) = 13 * E
So the expected number of cards that you need to flip before you see the first ace is 13.