1) I believe that playing each piece proportional to its potential winnings is ideal. In this case, Rock 9/13 of the time, Scissors 3/13, and paper 1/13...
Hm. Except that doesn't work. He still plays Rock all the time and wins an average of $2 per round. ($27 - $1 over 13 rounds.)
Gonna have to think some more...
2) This one's easier. I alternate Scissors and Rock. If at any point my opponent does not reciprocate with Rock and Scissors in alternating parity, I switch back to the optimal strategy from #1. We each make $4.50 per round, which is as good as it gets.
no subject
Hm. Except that doesn't work. He still plays Rock all the time and wins an average of $2 per round. ($27 - $1 over 13 rounds.)
Gonna have to think some more...
2) This one's easier. I alternate Scissors and Rock. If at any point my opponent does not reciprocate with Rock and Scissors in alternating parity, I switch back to the optimal strategy from #1. We each make $4.50 per round, which is as good as it gets.