Colour-pair card game with a 10 dollar prize

A shuffled standard $52$-card deck is dealt two cards at a time. Two black cards go to the dealer, two red cards go to you, and a mixed pair is thrown away; this repeats $26$ times. You receive $10 only if your pile ends up strictly larger than the dealer's; ties and losses pay nothing. What is the game worth?

$0. Each discarded pair removes one red and one black card, so equal numbers of red and black cards survive. Those survivors are exactly your pile and the dealer's pile, so the game always ties and never pays out.