Rationalist Clue

(not by Parker Bros., or, for that mat­ter, Wadding­tons)

A re­sponse to: 3 Levels of Ra­tion­al­ity Verification

Re­lated to: Di­plo­macy as a Game The­ory Laboratory

It’s a clas­sic who-dun-it…only in­stead of us­ing an all-or-noth­ing pro­cess of elimi­na­tion driven by dice rolls and lucky guesses, play­ers must piece to­gether Bayesian clues while strate­gi­cally di­vid­ing their time be­tween gath­er­ing ev­i­dence, perform­ing ex­per­i­ments, and in­ter­ro­gat­ing their fel­low play­ers!


ROOMS:

He­ma­tol­ogy Lab—bring a blood sam­ple over here, and you can find out one bit of in­for­ma­tion about the serotype…is it A or O? B or O? + or - ? The micro­scope knows. Don’t know how to use a micro­scope? Try read­ing up on it in the Library.

Au­topsy Table—bring a body part over here, and you can take an ed­u­cated guess as to what kind of weapon caused the mur­der wounds. (Flip over 1 of 10 cards, 4 of which show the cor­rect mur­der weapon and 6 of which are ran­domly dis­tributed among the other five weapons.) The er­ror in guesses doesn’t cor­re­late across body parts, so if you per­son­ally ex­am­ine enough of them, or if you can per­suade your fel­low din­ner-guests to bust out all the body parts at the same time, you should be able to get the right an­swer.

Lie De­tec­tor—bring a fel­low player over here, and you can ask him/​her a yes-or-no ques­tion and get some ev­i­dence as to whether it was an­swered hon­estly. Have the an­swerer roll a D10, add a se­cret con­stant unique to his/​her char­ac­ter, mul­ti­ply the sum by the truth value of his/​her state­ment (1 for true, 2 for false), and then look up the num­ber on a chart that re­turns the value “stress” or “no-stress.” It’s up to the in­ter­roga­tor to figure out the cor­re­la­tion (if any) be­tween stress and ly­ing for each player! How do you get the other player into the Lie De­tec­tor room in the first place? Good ques­tion! When you figure it out, let me know…I have a pa­per I’d like you to co-au­thor with me on the Pri­soner’s Dilemma.

Plus the usual col­lec­tion of Kitchens, Billiards Rooms, Par­lours, and so forth. One room is in­ac­cu­rately la­beled.

PIECES OF EVIDENCE:

If you spend your turn search­ing a room, you might find…

Blood stains—most of them are ei­ther from the mur­derer or the vic­tim, but some are not. You can take a sam­ple so as to carry it with you to the He­ma­tol­ogy Lab.

Body parts—all of them be­long to Mr. Boddy, and all the parts are nice and portable…just the right size to shove one in your pocket and dash back to the au­topsy table to sneak a peek by your­self. Of course, if you’re feel­ing co­op­er­a­tive, it might be more effi­cient to get the gang to­gether and lay all your cards, er, on the table, at the same time.

Video footage of the mur­der—just kid­ding. What kind of game did you think you were play­ing here, any­way?

WHERE DID THE MURDER TAKE PLACE?

The game rules chat­tily as­sure you that the mur­der did not take place in the Lab, on the Table, or by the De­tec­tor…but of course this is sim­ply dis­in­for­ma­tion com­ing from a source that you are likely to er­ro­neously as­sume is au­thor­i­ta­tive, even though you have no firm ev­i­dence that the rule­book is a re­li­able nar­ra­tor.

You don’t need to know where the mur­der took place to win, as each player only gets one guess, and there are 36 weapon * char­ac­ter pos­si­bil­ities, which is a lot to sift through with just a hand­ful of sadis­tic clues. How­ever, for bonus points, you can try notic­ing that most of the use­ful clues come from the same room, and that the mur­derer knows where (s)he kil­led Mr. Boddy, so if you ask real nicely you might be able to ask him/​her a few thought­ful ques­tions over at the Lie De­tec­tor.

HOW DOES THE GAME END?

Once you re­al­ized Mr. Boddy had been kil­led on a dark, snowy night that shut down all travel in and out of the man­sion, one of you took the pre­cau­tion of ac­ti­vat­ing the house’s high-tech se­cu­rity cam­eras—the mur­derer will not kill again this night. Rather, you will all dither end­lessly un­til all but one of you can agree on a prime sus­pect, at which point you will join forces, hand­cuff him or her to the telescope in the Ob­ser­va­tory, and wait for the snow­plow to come through and the po­lice to ar­rive, at which point you will find out just how right (or wrong) you were.

This has the dis­tinct ad­van­tage that if most peo­ple want to stop play­ing they can rule-fully end the game at any time.


Note, by the way, that while I hope at least some parts of my de­scrip­tion are funny, this is not re­ally a joke—I would like to de­sign this board game and then playtest it with ca­sual Less Wrong read­ers to see if it mo­ti­vates us or oth­er­wise helps us to test, de­velop, or prac­tice ra­tio­nal­ity skills. If you have feed­back about ei­ther the game’s playa­bil­ity or its ed­u­ca­tional value, I’d love to hear it.