Cheated or Credulous?
Astonishing - for Friday

The Mathematics of Cluedo

Actuaries and other more amateur number fans may enjoy Cleudo, sometimes known as Clue, the popular murder mystery game in more ways than the average Joe. I have just enjoyed the long weekend in part rediscovering this excellent game -- and even an effort to teach it to my two elder children (aged 7 and 5) which was not a total failure :-)

I quickly figured that mathematics could help. I started down the track of the grids used in popular paper based logic problems. The journey home gave me a better idea - look to the web - and was delighted to find this quote, and a feast of resources.

"Beginning in 2000, the University of Oregon gaming club began holding Clue/Cluedo games three nights a week for nearly a full year. Since most of the players were geeks who had a computer science background, What transpired was a brilliant 'arms race' with players devising new paper systems to get better and better at the game.

The strategies evolved, at first just writing a few known facts on the included detective sheet, but eventually several sheets of paper would be consumed as all players recorded every possible fact, drew every possible conclusion-- during the latter phases of the game, it was not uncommon for ten minutes to pass between suggestions, as players deduced as much as possible.  What started with the provided Clue Detectives Notepads transformed into elaborate custom-printed forms and finally into layers of transparencies so whole sets of data could be both view seperately and conjunctively.  Ultimately, players began simulating not only their own knowledge, but the potential knowledge of each of the other players, in order to avoid asking questions which would help other players. 

An art major become one of the most competitive players. Meanwhile, a true genius computer scientists would inevitably lapse into his explictive of choice, "rassin frassing", each game when he had 'proved' something he knew to be false, thereby signallying that he has made an error.  Another savant refused to use paper, but instead tried to read the faces of those around him to deduce the solution-- with astonishingly succesful results.  Finally, one player had a knack to correctly guess which of the 216 possible solutions was correct on her first suggestion. 

As the paper systems grew in complexity, it became increasingly apparent that the paper systems were both prone to errors and were incomplete.   Users of the systems would often make simple errors which would undermine their entire deductions.  Situations occured where the human players could see something was 'true' which the paper systems were unable to deduce.   All this begged the creation of a perfect and complete solver.  After six years, this is a dream which was finally realized."

Links to the Solver

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