To beat a rock-paper-scissors grandmasters:
Choose rock every single time.
Then, after many games,
choose scissors once.Statistically-speaking, the grandmaster will have a higher win rate.
Practically-speaking, the grandmaster lost once.
Choose a time when the grandmaster's loss matters the most. Use the grandmaster's crimes against humanity as justification for your betrayal.
If you play rock enough times, you'll beat the grandmaster.