You are playing a game with your friend using a standard deck of 52 playing cards. Each round, you flip over two cards:

- If both cards are black, you keep the cards and earn one point.
- If both cards are red, your friend keeps the cards and earns one point.
- If one card is red and one is black, the cards are set aside in a discard pile.

What is the probability that you end up with more points than your friend when all the cards in the deck have been used up?

#### Solution

0%

The deck starts with the same number of black and red cards. Whenever one card is red and one is black, it reduces the number of black and red cards remaining in the deck by an equal amount. It is therefore impossible to change the balance of black and red cards in the deck except by earning points – so both players always end up earning the same number of points.