Assuming we randomly use 50% paper and 50% rock, we get:

- on rounds he is forced to play rock, we get half victory and half tie, so 25% win, 25% tie so far

- on other rounds he can:

- always use scissors, which will turn into our 25% win, 25% lose - we win overall, 50% win, 25% tie, 25% lose

- always use rock, which will turn into our 25% tie, 25%win - we win overall, 50% win, 50% tie

- always use paper, which will turn into 25% win, 25% lose - we win overall, 50% win, 25% tie, 25% lose

- any kind of random mix of above, which can only move between results above, as our picks are completely random as well

So, he best strategy is to always play scissors or rock, for 50:25:25 result. If ties are repeated, we win 2 out of 3 times.

Any better strategy?