You are competing in a game with 2 other players, with a 21-faces dice (labeled 1-21). All three of you gets to choose a number and then roll the dice. Whoever chose the number closest to the outcome wins. What is your strategy if you three cannot communicate with others? another twist: what if all three of you can communicated?
2026-03-29 05:34:14.1774762454
Game Theory Puzzle
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I'll have another go:
Since there is complete symmetry w.r.t. the players and no hidden information, no strategy can give any one player the advantage.
If the players are allowed to communicate, it is difficult to say anything mathematically, since the complexity then greatens considerably (and human psychology and/or interpretations of what a rational player is comes into play).