Here is another problem from the Sherlock Holmes puzzle book by Dr. Watson (aka Tim Dedopulos).
“Wiggins grinned at me. ‘You’ve not played Rock Paper Scissors before, Doctor?’
‘Doesn’t ring a bell,’ I told him.
‘Two of you randomly pick one of the three, and shout your choice simultaneously. There are hand gestures, too. If you both get the same, it’s a draw. Otherwise, scissors beats paper, paper beats rock, and rock beats scissors.’
‘So it’s a way of settling an argument,’ I suggested.
‘You were brought up wrong, Doctor,’ Wiggins said gravely. ‘Look, try it this way. I played a series of ten games with Alice earlier. I picked scissors six times, rock three times, and paper once. She picked scissors four times, rock twice, and paper four times. None of our games were drawn.’ He glanced at Holmes, who nodded. ‘So then, Doctor. What was the overall score for the series?’ ”
See the Rock Paper Scissors Problem
(Update 7/29/2021) This problem in a different guise was presented by Futility Closet (7/28/2021) and attributed to Yoshinao Katagiri in Nobuyuki Yoshigahara’s Puzzles 101: A Puzzlemaster’s Challenge, 2004.