Answer Happy

A4. Consider the following two-player card game using a standard deck of cards. • Players A, B each choose a length-two sequence of colors (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 se- quence. The player who observed their sequence wins! This game can end in a draw. (a) 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. (b) Answer the following questions: i. Imagine player A needs to choose first and must announce their choice to player B. What sequence would you choose as player A? ii. Imagine player A chooses first and announces their choice to player B. What sequence would you then choose as player B? iii. Imagine players A and B both choose in secret and are forced to simultaneously announce their choices (via envelop, for example). Consequently, neither player can use additional information. What would you advise player B to choose?