[cortesoft]

This sounds a lot like a Keynesian Beauty Contest (https://en.wikipedia.org/wiki/Keynesian_beauty_contest), where you are trying to make a selection based on what you think other people are going to choose.

If I really wanted to give an accurate answer in this case, I would probably choose some arbitrary source of a number (like my age or the number of days that have gone by so far this year), figure out the modulo 5 of that number, then say 'Right' if the modulo is 0, and 'Left' otherwise.

Obviously there are some flaws in this approach, but I think it would be as accurate as I could get.