Hi, I'd like to solve the following problem, a version of Rock-Papers-Scissors:

Rock beats Scissors 100% of the time

Scissors beats Paper 100% of the time

Paper beats Rock 99% of the time

What is the Nash equilibrium (for choosing what to play)?

I know that it will be a mixed strategy equilibrium, but I haven't found a place that will help solving 3x3s without simplification / reduction (they always find dominated strategies, for example).

I'm pretty sure I'm just forgetting something simple...

Thanks for any help.