Consider the following two-player card game using a standard deck of cards. • Players A, B each choose a length-two sequence of colours (e.g. RB, BR). • Cards are then revealed from a standard deck of 52 cards one by one. • Revealed cards are placed on the table and not returned to the deck. • The game is immediately stopped once either player observes their sequence. The player who observed their sequence wins! • This game can end in a draw. For all sixteen pairs of length-two sequences of red and black cards (that is: RR vs RR, RR vs RB, ..., BB vs BB), find the probability that player A wins. For example: for the pair RR vs RR, this probability is zero because the game will always end in a draw.
I found by symmetry $P(RR vs BB)=\frac{1}{2}$ and $P(RB vs BR)=\frac{1}{2}$. I also found $ P(RB vs RR)=\frac{26}{51}$. Could someone tell whether i am right or not?