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Rock, Scissors, Paper

Starting off with the most simple example, where the idea is that no one has an advantage. Not much of a game, but simple to understand.

Two players play this games, each secretly selects one of the three pieces (rock, scissors or paper (symbolised by a resp. a closed fist, a V-sign with pointing and middle finger, and an open hand); they simultaneously announce and compare their choices. If both made the same choice the result is a draw and the game is repeated. If they make different choices, then rock breaks scissors, scissors cut paper, and paper enfolds rock (to be interpreted as "wins over"). As such a classical example of non-transitivity.