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Elemental game (Posted on 2005-06-16) Difficulty: 5 of 5
This game is similar to "rock, paper, scissors" in that two players independently pick one of the six things, and if one thing somehow "beats" the other, then that player wins. If both players pick the same thing, they repeat until someone wins.

Life grows on Earth.
Water douses Fire.
Air resists Cold.
Life drinks Water.
Fire consumes Air.
Cold freezes Water.
Earth smothers Fire.
Life breathes Air.
Fire and Earth both warm Cold.
Air and Water both erode Earth.
Fire and Cold both destroy Life.
Water displaces Air.

A program that plays this game has a single set of probabilities for picking each of the six things. Assuming that the program's opponent knows what these probabilities are, what probabilities will give the program the best chances of winning?

What if the rules of the game are changed so that "Water displaces Air" is replaced with "Air ripples Water"?

See The Solution Submitted by Tristan    
Rating: 3.6667 (6 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
solution question???Jason2005-07-14 03:32:58
No Subjectjeremy2005-07-02 06:13:26
re: Compliments, and correctionsTristan2005-06-22 01:11:32
Some ThoughtsCompliments, and correctionsSteve Herman2005-06-21 19:32:05
re(3): First part solution? / Second part solutionyocko2005-06-21 08:59:11
second solutionBob Smith2005-06-21 01:42:11
re(2): First part solution? / Second part solutionMatt2005-06-20 17:11:16
SolutionBoth solutionsFederico Kereki2005-06-20 15:56:44
re: First part solution? / Second part solutionyocko2005-06-20 04:17:39
Some ThoughtsPerhaps a solution...strange ods (even for me)Cougar Draven2005-06-20 02:14:54
First part solution?Matt2005-06-17 04:59:57
re: Expected resultSteve Herman2005-06-17 03:49:51
Expected resultFederico Kereki2005-06-17 02:29:42
re: Spoiler: Computers can be beat!Steve Herman2005-06-17 01:30:57
SolutionSpoiler: Computers can be beat!Steve Herman2005-06-17 01:03:13
Some ThoughtsHow to solve thisOld Original Oskar!2005-06-16 22:36:27
Some ThoughtsRanking the ElementsJer2005-06-16 20:10:33
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