GuaranteedDiscrete Mathematics Level pending
You and your friend are playing a card game. In this game, each player chooses an ordered sequence of three colors, either red (R) or black (B). Cards are taken from the top of a standard 52-card deck and laid onto the table, each card placed to the right of the previous card. Whenever the rightmost three cards match your color sequence, you may take these three cards, and cards continue to be laid down. Similarly, when the rightmost three cards match your friend's color sequence, your friend may take those three cards, and the game continues. When all the cards have been laid down, the game ends. At this point, the person with the most cards wins the game.
Suppose that you pick the sequence RBB, and your friend picks the sequence BBB. To the nearest integer, what is the probability, in percent, that you win the game?