Since game theory can be loosely considered to be part of the main subject of these columns, and since games are fun, today I want to share a game invented by my wife, Patricia Mehan (She is a stubborn Irish woman who did not take my name when we married), and me on a long, otherwise boring drive. This game is both fun and educational.

The essence is similar to a standard puzzle (for instance, see puzzle #6 here, but while you are there, do not try puzzle #2. You will be sorry.). In this type of word puzzle, one can change a letter in a word to make another word in a ladder that goes from the start to a desired new word in a specified number of moves with the proviso that after each move, you must have created a new valid word.

We turned that old puzzle into a competitive game tentatively called “Latex” because we initially thought that playing “latex” would end the game. It turns out that is not so, but until we think of a better name, that will have to do. Since the rules are not yet fixed, I will present a couple of variations. We tried to make the game suitable for any number of players from two up to however many you want.

Version without points: Play starts with one player chosen by lot picking a five letter word. The next player must either change one letter to make a new word or add or subtract one letter to make a new word. The next player does the same. Play continues until someone cannot make a new valid word (repeating a previously used word is forbidden). Then that player is eliminated. So far so good, but here is the interesting part. When a player is eliminated, the last person to play (the eliminator) must make a proper word where the other player failed or state that no other is possible. If the eliminator says no word is possible, then anyone left playing can eliminate the eliminator by calling out a valid word. Alternatively, failure to make a valid word results in the eliminator also being eliminated. If the eliminator succeeds in making a new word or no one else has a valid word, play continues as before. If the eliminator says no word can be made and no one else has a new word, then the eliminator introduces a new and play continues. If the eliminator is eliminated, the next player in line makes a new starting word and play continues. The winner is the last person to be still in the game.

Version with points: This version is less well-defined. I solicit readers to submit better variations. Play is as before, but if a person cannot make a new word, the one who generated the last valid word gets a point. Play then goes to the next player. If that player also cannot make a valid new word, another point is awarded to the originator, and so on. However, if a person is unable to make a new word and doubts that any valid word can be made, that player can challenge the originator. If the originator cannot make a new word, a penalty is levied and the challenger gets all the originator’s points that have accumulated to that point in the game: the challenger makes up a new word and play continues. A originator who does make a new word gets all of the challenger’s points and one additional point for each player still in the game. Play continues, starting with the challenger selecting a new starting word. Play continues until a set number of points is earned by one of the players. A small multiple of the number of players is a good starting point. For five players, one might set the goal at 25 points.

Remember that new words can be made by changing a letter (as in changing “lash” to “lush”) or by adding a letter (as in changing “lash” to “slash”) or by removing a letter (as in changing “lash” to “ash”). This is subject to the prohibition against words with fewer than three letters. If the players wish, they can also define an upper limit for the total number of letters in a word, but making longer words can be a good strategy.

Other variations: (1) Points awarded in proportion to the number of letters in a word. That is, for words of 3-5 letters, only one point is given as above, but 6 letter words earn 3 points and 7 letter words earn 5 points. (2) Rapid point accumulation: in this version a player gets points for every valid word passed to the next player in addition to the various penalty points. The total number of points needed to win should be a bigger number than in the original version.

We had fun playing around with these and other variations. If you like the idea and have better variations, let me know.

This game and several of its variations are obvious candidates for transporting to computer gaming. If anyone is interested, let’s talk.

Have you thought of at least three words that link to “latex?” Generally, a word is safe if there are at least three other words leading to it. For instance, both “late” and “later” lead to “latex.” In a game, the progress could be “late” to “later” to “latex.” And that would be the end of it, but both “laten” and “lated” are listed in some dictionaries. It’s good to agree on a dictionary before playing if the contestants are serious or likely to be drinking.

In response to the interest my original tutorial generated, I have completely rewritten and expanded it. Check out the tutorial availability through Lockergnome. The new version is over 100 pages long with chapters that alternate between discussion of the theoretical aspects and puzzles just for the fun of it. Puzzle lovers will be glad to know that I included an answers section that includes discussions as to why the answer is correct and how it was obtained. Most of the material has appeared in these columns, but some is new. Most of the discussions are expanded compared to what they were in the original column format.

[tags]latex, word puzzle, long car trip, decision theory[/tags]