I don’t know about you, but growing up I always played rock-paper-scissors with just three weapons … you know, the three in the title. But my wife is French, and as Wikipedia explains:
Similarly, the French game “pierre, papier, ciseaux, puits” (stone, paper, scissors, well) is unbalanced; both the rock and scissors fall in the well and lose to it, while paper covers both rock and well. This means two “weapons”, well and paper, can defeat two moves, while the last two weapons can only defeat one of the other three choices.
So I have questions for you.
1. There is a weapon in the French version that should never be used (in an optimal strategy). Which one is it and why?
2. Is it possible to add one weapon to rock-paper-scissors without rendering one weapon inferior to all the others? If so, give an example; if not, show why not. (Fans of The Big Bang Theory know it’s possible to add two.)
August 4, 2013 at 2:06 pm
1) Rock should never be played. Playing the well is otherwise equivalent to playing the rock (both defeat scissors and are defeated by paper), but well defeats rock.
2) No, it’s not possible. If I add a new move to RPS, there are two possibilities:
* The new move M defeats two other moves (A, B), where A defeats B. Playing M is equivalent to playing A, except for that M defeats A; A should never be played (in favour of M).
* The new move M defeats one other move (B); A defeats B. Playing M is equivalent to playing A, except for that M loses to A; M should never be played (in favour of A).
* There are also two other pathological cases: M defeats no other moves (in which case it would never be played), or M defeats all the three other moves (in which case it would always be moved, rendering the game pointless).
Along these lines, I invented the move “glue” when I was a child: it defeated each of rock, paper, and scissors. When told that it wasn’t fair, I added “solvent”, which defeats glue but loses to each of the three basic moves.
December 11, 2013 at 10:49 am
You can assert by saying that even animals do
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