A Three Card Trick.

if you deal three cards off a shuffled pack they will come out in one of the following 2x2x2 = 8 possible ways:


(R = red; B = black)


RRR

RRB

RBR

RBB

BBB

BBR

BRB

BRR


if you keep dealing, they might come out, say:


RBBRB RBBBR RBBRR etc (they are only put into groups of five for ease of reading)


now here's the game:


ask your opponent to choose any one of the eight groups of three above and tell him that you'll choose one of the seven remaining groups - he can choose whichever he feels is the best group


then you'll start dealing cards off the top of the shuffled deck one at a time keeping track of the R/B order


whose ever chosen group of three is dealt out in order first wins $1 from the other


if there has been no winner after having dealt out about half the deck, it is reshuffled - this is to try to keep the chance of an R or a B being dealt next near to 50%/50%


so, if he chose BBB and you chose RRB he would win $1 from you, as his group came out as cards 7,8,9 before yours at 10,11,12 in the above example series


what best strategy would you use and who would win how much in this game?