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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.