King Coin Flips the Third, of ToM
Two players play the following game with a fair (!) coin.
Player 1 chooses and announces a sequence of 3 heads and tails (HHH, HHT, HTH, HTT, THH, THT, TTH, or TTT) that might result from three successive tosses of the coin.
Player 2 then chooses a different sequence of three.
The players toss the coin until one of the two named ‘triplets’ appears. The ‘triplets’ may appear in any three consecutive tosses: (1st, 2nd, 3rd), (2nd, 3rd, 4th), and so on. The winner is the player whose triplet appears first.
a. What is the optimal strategy for each player? With best play, who is most likely to win?
b. Suppose the triplets were chosen in secret? What then would be the optimal strategy?
c. What would be the optimal strategy against a randomly selected triplet?