If you are not familiar with the Parker Brothers board game called CLUE, it is a game where winning involves figuring out which suspect committed the murder, what weapon they used, and in what room the murder took place. In the classic version of the game, there are six suspects (Miss Scarlet, Colonel Mustard, Mrs. White, Mr. Green, Mrs. Peacock, and Professor Plum). There are also six weapons (knife, rope, lead pipe, candlestick, revolver, and wrench) and nine rooms (hall, lounge, dining room, kitchen, ballroom, conservatory, billiard room, library, and study). At the beginning of the game, one suspect, one weapon, and one room are randomly (and secretly) removed from the deck and “hidden” during the game. The game involves determining which three items are “hidden” by trying to find out the rest of the cards in play.
Assuming that there is a full game (six players), each player will be dealt three of the remaining cards. Depending on what cards you are dealt, you may have an easier or harder time winning the game. It all depends on what you are given and how many possible correct answers are left. If you use all of the cards (6 suspects, 6 weapons, and 9 rooms) and the understanding that you will have one of each in the answer, you multiply these numbers together to determine the number of possible combinations of suspect/weapon/room that could be a possible answer. This would be 6*6*9 = 324 possible options.
I like to use this example in my Statistics class when we are covering the different counting techniques. Quite often “book” problems on this topic are boooooring! However, many students are familiar with this game and have fond memories of it…..at the very least it is a more happy example.
When I tell them that I am going to give them a strategy to make it a little easier to win the game, their interest is piqued. They are now ready to learn something that they can take with them of value for the next time they play the game. I expand on the original problem and then explain how they can analyze their hand.
Once you know what you have in your hand, you can eliminate some of these options. For example, if you are dealt the “knife” card, you can eliminate all of the 324 options which use the knife as the weapon. If you are given one suspect, one weapon, and one room card, then that leaves 5 suspects, 5 weapons, and 8 rooms that you do not know and can be used to make the correct answer. This leaves you with 5*5*8 = 200 possible options. Is this a good hand or not? The answer to that can be determined by listing all of the possible sets of cards that you can be dealt to begin a game. Without listing all of the options here, we will just go straight to the “best” starting hand and the “worst” starting hand.
The best hand you could be dealt is either getting three suspect cards (or three weapon cards). That will leave you with three more suspect cards (or three other weapon cards), all six weapon cards (or all six suspect cards), and all nine rooms. This gives you 3*6*9 = 162 possible options….38 fewer than the 200 from the earlier example. The worst hand you could be dealt is three room cards. This would leave you with all six suspect and weapon cards that you don’t know as well as six of the rooms still to figure out. That means there are still 6*6*6 = 216 options to have to figure out. How does this help a player once they already have their cards? Well, I jokingly tell them that if they get three room cards to fake a violent sneeze which causes them to toss their cards up and expose them……necessitating a re-deal of the cards and hopefully a better starting hand.
Good luck sleuthing! –Pat
pleasureteam notes: Clue has been used in a number of different educational settings. You might want to visit http://cs.gettysburg.edu/~tneller/nsf/clue/ to see how it has been used in a class on artificial intelligence.
To learn about Hasbro’s 1998 makeover of Clue, check out http://www.npr.org/2008/08/08/93417780/hasbro-gives-clue-board-game-a-makeover for details and the audio file of All Things Considered featuring the story.
Finally, Anne is also ready for a game of Clue. Check back later this week for our resident psychologist’s take on using the characters in her class.