$\textbf{Casino Game's Fair Price}$
A casino offers a card game using a regular deck of $52$ cards. The rule is that you turn over two cards each time. For each pair, if both cards are black, they go to the dealer’s pile; if both cards are red, they go to your pile; if one card is black and the other is red, they are discarded. The process is repeated until you two go through all $52$ cards. If you have more cards in your pile, you win $\$100$; otherwise (including ties) you get nothing. The casino allows you to negotiate the price you want to pay for the game. How much are you willing to pay to play this game?
$\textbf{Answer}$
If I were you, I would not pay for playing this game because I would always lose.
$\textbf{Analysis}$
Because the discarded cards always have the same number of red and black cards, the remaining cards of these two color must have the same number as well. This means the result is always a tie, or I lose.
$\textbf{Note}$
This problem appears to require some calculation. In fact, it does not. Therefore, it is a brain teaser.