Rock paper scissors
Pick your throw. The computer picks at random, without peeking.
Choose below.
Score
Why you can't out-think a random opponent
Whatever you throw, a random opponent has one move that beats you, one that loses and one that draws, each with a 1 in 3 chance. So your long-run record against this computer will drift towards a third wins, a third losses and a third draws, however clever your pattern. That is the Nash equilibrium of the game: mixing your three moves equally is the only strategy nobody can exploit.
Humans are a different story. A 2014 study of students playing for small rewards at Zhejiang University found winners tended to repeat their throw and losers tended to switch to the move that would have beaten them. Against a friend, that is worth knowing. Against a crypto-random computer, it isn't.
Settling who goes first between two people? A coin flip is quicker.
Questions people ask
Does the computer cheat?
No. The computer's move is drawn with crypto.getRandomValues before your choice is compared, and it never looks at what you picked. Each of rock, paper and scissors has exactly a 1 in 3 chance.
Is there a winning strategy against a random opponent?
No. Against a truly random player, every strategy wins, loses and draws one third of the time in the long run. Strategies only work against humans, who tend to avoid repeating a throw and often open with rock.
What beats what?
Rock blunts scissors, scissors cut paper, paper covers rock. The same throw is a draw.