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The officials have noted your position, and wonder why you did not elect to play as Blue. Let's evaluate the strategy for Red to play 1 twice as often as 2. We assume Blue is a profit-maximizing mofo and will play to win as many points as possible. When blue plays 1, Red expects to pay (2 x 3) + (1 x 6) = 12 over three turns, an average of 4 per turn. When blue plays 2, Red expects to pay (2 x 5) + (1 x 4) = 14 over three turns, an average of 4 2/3 per turn. No matter what Blue does, this is an improvement over Red playing 1 all the time, which has a worst case of 5 per turn.