$\textbf{Casino Game's Fair Price}$

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?