Assignment:
Your opponent specifies 3 successives results of tosses of a coin, e.g. HHT. You then specify another such result, e.g. THT. The winner is the person whose sequence appears first when a fair coin is tossed successively and independently. Find the strategy which will allow you, the second player, to win at least 2/3 of the time. More specifically, for each possible choice of your opponent, find the choice that gives you the maximum probability of winning and calculate that probability.
Provide complete and step by step solution for the question and show calculations and use formulas.