Answer.
yes - the correct response is to make the first two of his choice the last two of yours - AND - never choose a palindromic set for your response
your wins are between 66% and 87% depending on what he chooses
if your sucker realises he is at a disadvantage you could offer to pay him $1 when he wins but collect only 80c when you win - as long as you can get away with at least $1 to 70c you will win in the long run
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