The Boggle cube redesign and its effect on the difficulty of Boggle

I wanted to buy a copy of Boggle. This seemingly simple mission was complicated by the facts that a) there are different kinds of Boggle out there and b) I like to make things complicated.

If you exclude variations such as Big Boggle and the recently introduced 6-by-6 Super Big Boggle and just limit yourself to the original 4-by-4 Boggle configuration, there are three principle versions of Boggle:

1) Boggle Reinvention (now sold as just "Boggle") - While the new sealed case design and the integrated timer mean that you don't need to worry about losing any of the pieces, there are reports that it is possible for two dice to become jammed together in such a way that it is essentially impossible to separate them without opening up the case and destroying the game. In my opinion, Boggle should not be a game that can break.

2) Plain old Boggle, made from about 1976 to 1986 (which I will call "classic Boggle").

3) The version of Boggle sold from 1987 to ~2008 - essentially the same as classic Boggle except that the letter distribution on the cubes was completely redesigned. I'll call this "New Boggle".

Below, you can see a side-by-side comparison of the classic and new sets of Boggle dice.

Classic Boggle Dice	New Boggle Dice
AACIOT	AAEEGN
ABILTY	ABBJOO
ABJMOQu	ACHOPS
ACDEMP	AFFKPS
ACELRS	AOOTTW
ADENVZ	CIMOTU
AHMORS	DEILRX
BIFORX	DELRVY
DENOSW	DISTTY
DKNOTU	EEGHNW
EEFHIY	EEINSU
EGKLUY	EHRTVW
EGINTV	EIOSST
EHINPS	ELRTTY
ELPSTU	HIMNUQu
GILRUW	HLNNRZ

To help visualize the differences between these distributions, I sorted the classic letter distribution by number of letters (shown on the left below) and used that order to sort the new letter distribution (shown on the right).

<= Classic New =====>
EEEEEEEEEE EEEEEEEEEEE
  AAAAAAAA AAAAAA
   IIIIIII IIIIII
    OOOOOO OOOOOOO
     LLLLL LLLL
     NNNNN NNNNNN
     SSSSS SSSSSS
     TTTTT TTTTTTTTT
      DDDD DDD
      RRRR RRRRR
      UUUU UUU
       BBB BB
       CCC CC
       GGG GG
       HHH HHHHH
       MMM MM
       PPP PP
       YYY YYY
        FF FF
        KK K
        VV VV
        WW WWW
         J J
         Q Q
         X X
         Z Z

In some ways (such as increasing the number of Ts and Hs), the new distribution is closer to the letter frequency in English words, but that motive alone would not explain why the number of As was decreased and the number of Os was increased. It has been suggested that this change was designed to reduce the frequency of harder letters (like K and G) and make finding words easier.

One other interesting property of the new set of dice is that since it concentrates certain letters all on the same die, it is never possible to make words that combine F and K (like FAKE, FORK, SKIFF,...) or words that combine B and J (JOB, JAB, BANJO,...). It is also not possible to make words with three Ps (like PINEAPPLE) or two Ks (like SKOOKUM, which is a slang term in the Pacific Northwest, derived from the Chinook language, and having multiple meanings: as an adjective it refers to something that is massive or powerful or reliable or simply really cool; as a noun, it can refer to an evil spirit or demon or a monster somewhat like Bigfoot or Sasquatch; it is pronounced /SKOO kum/).

So does this change in letter distribution have an effect on the game? To find out, I ran some simulated Boggle games, generating random boards with each set of dice and using a Boggle solver (written by GitHub user cespare) to determine the number of words in each board, the resulting Boggle score, and the longest word in each grid.

[The default word list used by the Boggle solver only contains words that are 15 letters long or shorter. While it's highly unlikely to find a random 4-by-4 Boggle board containing a 16-letter word, I decided to augment the word list to include 16-letter words, as well as the 17-letter words that could be made with the Qu cube (like QUATTUORDECILLION [which means 10⁴⁵ in the U.S. and 10⁸⁴ in Britain] and SESQUIPEDALIANISM).]

Dice set	Average  # of words	Average  Boggle score	Average length of longest word
New Boggle	~104	~150	6.8
Classic Boggle	~93	~128	6.6

The results show that there are about 12% more words to be found in a New Boggle board. These results are from simulating 10,000 boards for each set of dice, so the numbers in the table may be off by a few percent.

To try to give a little more insight into the difference between these versions of the game, I ran simulations for a New Boggle board in which a randomly chosen cube from a corner of the board was removed. The corresponding results,

Dice set	Average  # of words	Average  Boggle score	Average length of longest word
New Boggle w/o one corner cube	~92	~131	6.6

are really close to the classic Boggle results, suggesting that if you want to make your New Boggle game about as hard as a classic Boggle game, you can just remove a die from the corner of the board before hunkering down to find words.

Out of curiosity, I also ran simulations for 5-by-5 Big Boggle, using the requirement that words be at least four letters long (unlike the three-letter limit in regular Boggle) and using the Big Boggle scoring system, which yielded these results:

Dice set	Average  # of words	Average  Big Boggle score	Average length of longest word
Big Boggle	~190	~395	8.3

(For comparison with 4-by-4 Boggle, if you include the three-letter words that are in Big Boggle boards, the average number of words increases to about 260.)

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Of course, these calculations only confirmed what I already knew: the older version of the game is harder and is the one for me. I bought a copy of classic Boggle from eBay. The dice are made of wood rather than plastic. The timer has sand in it and doesn't make some noise to tell me when time is up. Succinctly, I think it is skookum.

A review of the word-tree building game Konexi

I previously posted about how intrigued I was about a new game that involved assembling letters into a precarious tree of words. Now, I have finally played this game (Konexi), and it exceeded my expectations.

The first player places a letter on the table, and then every successive move involves building letters off of that first letter, such that no other letter touches the table. The letters have little notches and also little isolated teeth, like the teeth of a gear, that fit nicely into the notches, while allowing a little bit of movement. By matching up a tooth of one letter with a notch of another letter, you can add the new letter to the tree, subject to the physical stability of the placement.

On your move, you have a choice between two (effectively) randomly chosen letters. You take one and try to add it to the tree in a way that allows you to connect together a set of letters that can be anagrammed to form a word. The letters must be a contiguous set. Your score is the number of letters in the word that you were able to make.

Even once you find a set of letters in the existing tree that you can connect your chosen letter to, to form a new word, it can often be a huge challenge to place that new letter. It must connect one of its notches or teeth to a complementary tooth or notch of one of the letters in your word, and it must result in a balanced structure that continues to stand on its own. Consequently, whenever someone is placing a new letter, there is a tension to the process that is similar to those moments when someone is removing a piece from a Jenga tower (though it is generally not at the Jenga level of pressure). However, Konexi is actually better than Jenga because you have far more options as to where and how you can place letters. It's also a good game for building intuition about concepts like the center of mass of an object.

This game can play out in very different manners, depending upon the structure of the tree that the players form, and the letters that they choose. With enough vowels in your tree, you may find that it is easy to make four- and five-letter words on every turn. If insufficient vowels are available, players may at times struggle to form any words at all.

If someone accidentally knocks down the tree, that player loses three points, and a new tree is started on the next play. Play continues until someone scores 20 points.

This game is basically exactly as cool as it looks, so if you think it might be your kind of game, you will probably enjoy it.

Lexcavator: A cool word-exploding arcade game

A great new arcade-like word game has just been released for desktop computers. It's called Lexcavator, a name that evokes the idea of digging for words. In this game, you tunnel down through a bottomless grid of letters by forming words Boggle-style. Then you jump your little avatar (represented by the "@" symbol) around in the various tunnels that you create, as you try to avoid being pushed up to the top of the screen by the constantly rising letter grid.

The game feels like a hybrid of Boggle and an inverted Tetris. Once you get used to using the mouse to click and drag through letters to form words and navigating with the keyboard, the interface becomes quite intuitive. There are power-ups in the form of other symbols: "!" creates a deep one-column-wide vertical shaft, ">" clears all the letters in the row that it is sitting on, "_" destroys a random set of tiles, "?" randomizes all the letters, and "*" takes out all letters in a 5-by-5 grid.

You don't necessarily need to activate the power-ups when you uncover them. I find that using the "?" power-up usually causes the resulting letters to be harder to make words out of. You also have the option of delaying usage of a power-up by guiding it down with you: for instance, standing next to the power-up and excavating under both yourself and it works nicely.

Once you finish a game, you get a report of various statistics about your performance. If you enable the "Internet" option in the Settings, the game will also report your scores to the central server and tell you how well you did compared to other players...

and what words you were the first in the world to find:

As of today, only 2% of the words on the word list had been found, according to the Lexcavator Twitter account. According to the developer's blog, the leaderboard is completely anonymous, so you don't have to worry about generating a login or a password or recovering a password when you've forgotten it. It's simple and done the right way, just like everything else about the game.

This is the kind of game that you will find yourself wanting to play repeatedly. There is also a Quest Mode which consists of a series of untimed challenges (like, find four 4-letter words, all in lines, without finding any other words).

You can get the game at lexcavator.com. It is being distributed on a pay-what-you-want model. I initially downloaded it for free, but I'm going to go back and pay for a copy to support the developer.

Lexicographer: the iPhone version of Guess My Word

As an addendum to my review of the online Guess My Word game, I'm reviewing the iPhone companion game, Lexicographer. Just as with Guess My Word, Lexicographer allows you to guess words and tells you whether your guess is before or after the secret word ("my word").

But rather than having two daily words to guess, Lexicographer will let you keep playing new rounds of "Guess my word!" all day long.

Once you start, there is a running timer (counting tenths of a second!). I found that this totally changed the guessing experience for me. Without a timer, I try to minimize the number of guesses I need to guess the word, choosing guesses in a calculating but leisurely fashion. With the timer constant ticking away, I guessed words in a more frenzied manner.

There is an option that allows you to see how many words are left in the range that you have bracketed. This is a useful way of sharpening your sense of how words are distributed in the alphabet and where the best bisection point is.

We increased the difficulty level from 1 (where a typical word was "talent") to 10 and then struggled on the last few guesses until we narrowed the word down to four possible words (between "parapets" and "paraphrase"). But we were totally stumped at that point. After guessing "paraphobia" (which I hoped to be defined as the fear of parallel lines) and finding that it was not actually a real word, I randomly guessed "paraph". And it was, to my stunned triumph, correct.

(It turns out that a paraph is a flourish someone adds below or to the end of their signature. The example that first comes to mind is below John Hancock's signature on the Declaration of Independence:

It's believed that paraphs originated during the Middle Ages to discourage forgery. I wondered how effective this might have been until I read in Joe Nickell's Detecting Forgery (browsable in Google Books) the following:

It might also be noted that the concept of individuality that today may be expressed in a distinctive signature was less valued in the penmanship of an earlier time, when adherence to strict copybook form was regarded as a virtue. As Jonathan Goldberg notes in Writing Matter: From the Hands of the English Renaissance, "in fact, what differentiated one italic signature from another is more often a paraph, flourish, than the letter itself." [...] Indeed, sometimes so distinctive was the eighteenth-century paraph ([...] like that of John Hancock's or Benjamin Franklin's) that it was sometimes used instead of the signature, thus concealing one's identity except to the initiate.

That was a really interesting word to learn about, but given that I got it through sheer luck, I think I'll be reducing the Lexicographer difficulty level to something more like 5 for now...)

I think that each version of the game has its merits. Guess My Word is fun because you can compete against other people (mostly just names on the leaderboard, unless you happen to know them or invite your friends to play) and see what sequence of words they chose by mousing over their guess history. Guess My Word words often feel more special, as though I can develop an intuition about the kind of words that are likely to be chosen; it's possible that Lexicographer words have a similar property, and I just haven't played enough to pick up on it. Lexicographer's strength is that it can be pulled out anytime and played with a group of friends, as many times as you like. Showing the number of words that you have bracketed allows you to get better at picking the word to bisect the range. Not only does this improve your Word-Guessing ability, it also adds an extra layer to the game, making for a nice complement to Guess My Word.

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Update:

• You may notice that Lexicographer no longer seems to be available on its former iTunes Store page. My guess is that the developer decided not to renew his ($99/year) iOS developer license, and Apple has nixed his apps. Which is a pity.
• You can no longer play the original Guess My Word game, but there is a functioning direct descendent here. You can also read my previous post about Guess My Word.

Guess My Word - a fun word-guessing game

Important notice: This post is about an online game that no longer exists at the linked URL, but you can find the same game (now maintained by someone else here.

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Imagine if you were trying to play Twenty Questions but weren't allowed to ask about the meaning of the word, only its position in the dictionary. Well somebody else imagined it first, wrote it up, and put it online.

It's called "Guess my word!", and each day there is a new word to guess.

You start by making some initial guess about where the word might be in the alphabet:


You find out where the word is with respect to your guesses (with the closest words being highlighted in blue and red (indicating before and after, respectively)):


And after a number of guesses, eventually you should converge on the word:


...after which you can enter your name to appear on the leaderboard and check out other people's times and guesses. It's a good way to work on your active vocabulary when you are not playing Bananagrams...

You can play Guess My Word by clicking here. If you really like it, there are now two separate words you can play each day. Plus there is a new iPhone app called Lexicographer which is a little different, and for which I have written a separate review.

The best thing about this game is that you can also easily play it offline as a two-person game. You can take turns thinking of the secret word and guessing, and since this can be played without pen and paper (as long as you can remember the two current bounding words), it makes a great game to play in the car.

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Further reading:

• My Lexicographer review - which includes further discussion of Guess My Word

Ghost, Superghost, and Disorder: Word-dodging games

I recently played a game called Disorder, which is a neat little word-building (or more accurately, word-avoiding) game. To explain it, it's best to start with the simpler games that it is based on:

We begin with an old parlor game called Ghost. In Ghost, players take turns adding letters to a word they are building, trying to avoid being the one to actually finish a complete word. If a player adds a letter that makes it impossible to form a real word (e.g., T-R-I-C-J), another player can challenge him. If the first player cannot name a legitimate word that he's trying to make, he loses the game. But if the challenger is wrong, he loses instead.

Example gameplay:

Player 1: A
Player 2: M [A and AM are words, but words shorter than 4 letters are permitted.]
Player 1: B
[At this point in the game, there are lots of words that players may be thinking of like AMBITIOUS, AMBULANCE, AMBUSH, AMBIGUOUS, AMBLE. But with each new letter the options narrow.]
Player 2: E
[This is a brilliant play because the only common words that can be formed starting with AMBE all have the root AMBER which is a valid word. The options for Player 1 are to choose the R and lose or choose another letter and try to bluff. Bluffing adds an interesting gameplay dimension to Ghost and related games.]

A Ghost variant called Superghost allows players to add letters to both the beginning and the end of the proto-word, opening wide the strategic possibilities and making for a game that you really have to think about.

The writer James Thurber enjoyed playing Superghost with his friends and wrote a New Yorker essay about it back in 1951 (delightfully titled, 'Do You Want to Make Something Out of It? (Or, if you put an "o" on "understo," you'll ruin my "thunderstorm")'). The essay can be found on the New Yorker site (behind a paywall) or in a collection of Thurber's writings called Thurber Country).

Finally we come to Disorder, which is a board game that comes with 1) cards that players get dealt so that they have a hand of letters to choose from, 2) a long skinny board with slots for each card to go into as the word is being built, and 3) chips for keeping score. In addition to giving players a set of letters that they can use for word-extending, Disorder introduces a few more twists on Superghost. Mixed into the deck of letters are four types of power cards. The Exchange card lets you swap a card in your hand with a card on the board. The Switch card lets you take two cards on the board and switch their positions. The Squeeze card allows you to make a one-card gap anywhere in the word and insert a card from your hand. And the Pass card lets you skip a turn.

And finally, any card can be used as a wild card, simply by flipping it over (they all say "wild!" on the back) and laying it down as part of the word. Wild cards can be tricky to deal with since (unlike in Scrabble, where a player declares what the blank tile represents) in Disorder, the wild card can be any letter. This makes it easier to build toward a word without giving away to your opponents what you are planning, but it also makes it difficult to think of all the possible words that could be in play.

Scoring is simple. Each card has a point value on it, with harder letters like Q and Z having correspondingly larger point values (roughly like in Scrabble). At the end of the round, the point values of the cards that have been played on the board are summed, and the total is awarded to whoever lost the round. After how ever many rounds are played, the winner is the player who accumulates the least points. I enjoy playing Disorder so much that I am willing to play without keeping score (though that may just be the Bananagrammer in me).

Disorder is a great game. I have already bought someone a copy for Christmas.

I like having the cards and the board, but in a pinch, this could be played with Bananagrams tiles with a few modifications: Each player can take 7 Bananagrams tiles and, in the absence of racks, just stand the tiles up on their edges. Note that Disorder has a flat letter distribution (4 cards for each letter of the alphabet). While I haven't tried it, I think that using the standard Bananagrams distribution of letters will still be fine. The important adjustment I would recommend borrowing from Disorder is the notion that you can play a tile face-down and have it act as a wildcard. If you're playing for the first time, I suggest starting off with the regular Ghost version until you are ready to graduate to the Superghost variety.


Ghost lends itself to rule variation, spawning games with names like "Superduperghost" and "Spook". My ambition is to come up with a mutation that will best them all. I think I'll call it "Pac-Man".

The new crop of games from the makers of Bananagrams: Zip-It, et al.

First they brought us Bananagrams. Last year they introduced Appletters and Pairs in Pears. This fall, they released so many new items that I feel like I am going to have to make a list:

1. Zip-It is like an accelerated version of Bananagrams, except instead of tiles, you get twelve letter cubes. And unlike in Boggle, you can turn each of those cubes and use whichever side you want. A typical time for forming those cubes into a grid of words is reported to be about twenty seconds! It sounds super-frenetic, like playing Bananagrams on a roller coaster. Zip-It comes with Weords, a small book containing game-winning weird words.
2. The 4th Bananagrams book has been released: 10-Minute Bananagrams, in which each puzzle is designed to be solved in 10 minutes or less.
3. The Bananagrams 2011 Page-a-day Calendar - perfect for your favorite Bananagrams addict.
   
   

2014 UPDATE: More recent games from the makers of Bananagrams: Bananagrams WildTiles - a new version of Bananagrams with extra monkey-themed wildcard tiles.

Also available are the French version of Bananagrams, for the family Francophile or polyglot, and the German version of Bananagrams.

UPDATE 2: The release of Oh-Spell is apparently not as imminent as I had wishfully thought. But in the meanwhile we have, coming very soon... Fruitominoes, the first non-word-game game from the makers of Bananagrams.

Boggle + Jenga = Konexi

One new game that caught my eye is called Konexi. It has the word formation aspect of Boggle and the balancing act aspect of Jenga. But instead of Jenga-style (also Operation-style, I suppose) delicate removal of parts, in Konexi you have to carefully add letters to an existing tree-like structure without causing it to collapse.

Gameplay is simple. You start by laying out the twenty-six plastic letters in a big circle. Then on each turn, you throw a die and move a special marker the indicated number of positions around the circle. The letter you land on is the one that you have to place in the tree. The object is to position the letter so that it connects to a set of letters that you can anagram to form a word. So for instance, in the illustration on the box, you can see that the words WORD and GAME could have been claimed (by the players who played the W and the E respectively), but if the D had already been there when GAME was formed, a better play would have been to claim GAMED since you get an extra point for each letter in the word. First player to twenty wins. Knocking down the tree loses a player three points and requires a new tree to be started.


And yes, it's not just a trick of perspective; the game box really is a trapezoid.

I really like the dual challenge of forming anagrammed words while maintaining a balanced structure. This may wind up being my new favorite game.

Scrabble Flash: An entire game in 5 electronic pieces

Last year, a cool new technology from the MIT Media Lab called "Siftables" was demonstrated in a TED Talk. It consists of little computerized blocks that you can move around with your hands. Touching them together makes them interact, and they can give feedback via their built-in screens and speakers.

At around 2:40 in the TED Talk video (below), the speaker shows how these Siftables can be used to play a word-formation game, referred to as being "like a mash-up of Scrabble and Boggle".



Now this technology has been licensed to Hasbro for a game called Scrabble Flash. There are three games that you can play with these tiles:

1. Scrabble Flash is similar to Boggle. The tiles are locked into a random set of five letters for 75 seconds, during which time you try to make as many 3-, 4-, and 5-letter words as possible. Whenever you form a new word, the tiles flash at you and make a pleasant reward sound. At the end of the round, the tiles will display the number of words you formed and also the maximum number of words you could have formed.
2. Scrabble Five-Letter Flash is an anagramming game in which you're just supposed to find one single 5-letter word, after which the tiles will flash and then switch to a different set of five letters.
3. Scrabble Pass Flash is a multi-player version of Scrabble Five-Letter Flash. If someone fails to find the five-letter word within a set time, they will be knocked out from the game. The speed of the game increases, and the player who avoids elimination wins.

The speed and simplicity of these games reminds me of Bananagrams. It might be even more fun to have one set for each player, so you could play head-to-head. This looks to be easily the most fun new Scrabble-branded game in years.

UPDATE: It is now possible to buy the Siftables blocks shown in the TED Talk. They are sold under the name Sifteo Cubes. They are expensive ($149 for a set of 3), but they are much more colorful, dynamic, and amazing. You can buy "apps" for them, and in principle, program your own games or uses for them.

Scramble: Part word game, part scavenger hunt, part Easter egg hunt

If you travelled back in time to the 2010 ARGfest in Atlanta (a conference for Alternate Reality Game designers and fans), you could have played in an original mutated word game called Scramble, masterminded by ARG designer Brooke Thompson.

Large letters have been scattered around the park and it is your job to find one. Once you do, you've got to find enough other people who have found letters so that you can form a word... a real word... not just one of those made up ones... well, not unless you can convince the Word Master that it’s a real one. Once you've gathered a word, head to the Word Master. Simple, right?

Not so much! Like Scrabble, each letter is worth a certain number of points... do you keep that Z you found or trade it in for an E? How many words, real words, can you spell with your letters? How many little tasks you were able to compete on the way? And... how quickly did you get back to the Word Master? Oh yes! It’s a battle between time & creativity. And it’s up to you to win.

Further event details may be found here. The exact rules of the game are not specified, but given that it was an experimental game, I don't think they need to be. The essence of the idea is enough for anyone who wants to try this. It seems like it would be well-suited to a party or also in a classroom, as it is the kind of challenge that also has educational value and teaches kids how to work together and think creatively.

I'd probably modify the game to make it more Bananagrams-like, requiring each group to form a single grid, and getting points for each word that they also can find a physical example of. Even I would like to play in that game!

I found a blog posting from someone who played in this game who writes:

The game was called Scramble, and the letters were valued like Scrabble tiles, the goal being to grab a group of people and get good letters to maximize your Scrabble score with them. Given that you could get credit for multiple words with the same letters, I picked up pretty quickly that the thing to do was to get 4-5 people, nab some good letters, and make lots of anagrams. You also got a double score for taking a picture of your word with an example of the word. My team went for C-O-D-E-S (and coeds, decos, and edocs), got pictures for all our words, and totally stomped on the other team, who only had one word, even though it was longer.

High marks to that team for devising a winning strategy on the fly, though if I were Word Master, I would have given the thumbs-down to the dubious "decos" and the hideous "edocs". A few more words like that, and I might think this was part of the ARGHfest.

Three-dimensional word games may be on their way

I've spent some time trying to think of a way to make a three-dimensional word grid for Scrabble or Bananagrams purposes. (The added challenge that an extra dimension would pose in such a game is very tempting!)

Cubical blocks with the same letter on all sides would almost work. Except that it wouldn't allow words to be build sideways from an upper level without other blocks acting as supports.

There are in fact, a lot of other games from the past that have been referred to as "three-dimensional Scrabble" or something similar, but they never seem to be successful, truly three-dimensional implementations.

Upwords is sometimes included in the category of 3-D word games, but it's physically more like layered Scrabble with corresponding differences in strategy. I mean, yes, technically it's three-dimensional, in that you need three-coordinates to locate a piece (row, column, height), but at any one time, it's only the topmost letter that matters. It's not really what people want when they think of 3-D Scrabble.

This patent from 1997 is for methods of making a three-dimensional Scrabble game.

A figure from the patent documents illustrates what I would consider closer to a true 3-D word game:


This patent laid out a bunch of ways that three-dimensional constructions might be done (connecting letter spheres together with magnets, velcro, and various mechanical tricks). As far as I can tell, none of these ideas ever made it to production.

Another patent was quite recently applied for for a three-dimensional word game. The inventor is listed as Joseph Elie Tefaye with Games R Us of Australia.

This figure shows the essence of the idea:


The design is reminiscent of the two-dimensional Typ-Dom, a predecessor of Scrabble invented in Austria in 1936. In Typ-Dom, the letter tiles are shaped like jigsaw puzzle pieces, so that they all link together. It's an interesting way of keeping letters in place without a board. This actually strikes me as superior to having a board in some ways: You can extend the grid as far as you want in any direction, and if your table gets jostled, the tiles won't be thrown out of position. In fact, you wouldn't even need a particularly flat surface to play on.

The extension to making Typ-Dom into a three-dimensional word game just required two main ideas: 1) Using a base to build the three-dimensional word grid from, and 2) modifying the pieces so that one can link up with another at a 90 degree angle. It looks like this might work out nicely.

But if you can't stand waiting for someone else to manufacture the perfect 3-D word game, you could always make your own, Star-Trek-style:

Zip-It and Oh-Spell!: Two new games from the makers of Bananagrams

The makers of Bananagrams unveiled their latest creations at the American International Toy Fair this month.

Zip-It is a two player game in which each player gets 12 letter cubes (dice with letters on all sides) and then has to assemble them into a grid of words as quickly as possible. The first to finish their grid says "Zip!" and scores one point. You can keep track of the score by incrementing the two zippers built into the bag for the game pieces.

Coincidentally, I have been recently thinking that it would be neat to make a game with letter cubes, like in Boggle, except that the player would get to choose which side to use. The cube aspect of Zip-It is tantalizing. Imagine playing Bananagrams with letter cubes. I imagine that there might be a lot of head-tilting to look at cubes from the sides. If you don't like one of the face-up letters, you could just rotate it until you found a letter that you liked. But is that the fastest method? I really want to play this right now and find out!

Oh-Spell! is the first card game from Bananagrams International. It sounds somewhat like Quiddler in the sense that the cards have letters rather than numbers, and the objective is to form words. There is a twist involving the cards having suits... It's not yet clear how that will play into the game. And I have a suspicion that rather than making separate words, players will form a word grid from the cards in their hand. But at this point, that's just a rumor (which I started because I think it will make a cool game).

I will report back when I have more details on these games.

Zip-It and Oh-Spell! should be available in a few months.

UPDATE: OK, these games were not released by the summer, as I had expected. Oh-Spell has been delayed indefinitely, but Zip-It is now out. Get it while it's hot!

My first Q-without-U word and Academic Games

I once played a game called LinguiSHTIK in a competitive situation. The other players were clearly veterans, and I was the rookie. They must have decided among themselves that they were going to take advantage of the newcomer. A big part of LinguiSHTIK is placing constraints on the word to be formed (e.g., must be four letters long, must be a noun, must contain a certain letter) while moving cubes with letters on them into either the ALLOWED or FORBIDDEN areas of the board. The other players made the requirements that the word must contain a Q and must not contain a U. Then at some point, one of them decided to CHALLENGE WIN, essentially saying that it was possible to make a word from the ALLOWED letters that satisfied all of the constraints. Fortunately, I had already come up with a word spelled with a Q but without a U - something I remembered from browsing through the Q section of the dictionary: QOPH (the 19th letter of the Hebrew alphabet). Somehow, I had managed to get the letters I needed into the ALLOWED set. When everyone revealed their words, the other players were kind of irritated: they had both been thinking of QAID (which was presumably the accepted Q-without-U word in that group) and they had never heard of QOPH. They challenged my word, but fortunately the dictionary contained the word QOPH, and I was vindicated.

WFF 'N PROOF, the manufacturers of LinguiSHTIK, have produced many other games, all having the same parallel-universe board game feel, probably because most of them have educational value as their primary design goal. These games do a good job of challenging the player while being fun enough as a game to suck the player in. Equations: The Game of Creative Mathematics is similar to LinguiSHTIK in that players are setting constraints and trying to find a solution that meets them, but with numbers and mathematical operations instead of letters and words. WFF 'N PROOF cites research suggesting that students who sometimes get to play Equations in math class skip classes less often and are better at applying math concepts.

The even more interesting claim is that another game boosts I.Q. test scores:

The first studies published (in 1972) on the effects of resource allocation games involved I.Q. tests on groups of students playing WFF 'N PROOF: The Game of Modern Logic intensively for three weeks in summer school classes. The average increase in the non-verbal I.Q. scores was more than 20 points. Although researchers have questions about the sort of intelligence actually measured by such tests, it is clear that there was a dramatic improvement in the problem-solving skills utilized in such exercises.

Another game that seems really compelling to me is Queries 'N Theories: The Game of Science & Language. It's the closest thing I have ever seen to a code-cracking game. One player makes up a "language" (consisting of fundamental allowed sentences and rules for transforming those sentences to other sentences). It's a bit like Mastermind except that where Mastermind has one secret sequence of colored tokens that the player is trying to infer, Queries 'n Theories starts off with such a sequence (a "sentence") which the first player morphs according to his transformational rules (like, every instance of GREEN RED transforms to RED YELLOW GREEN) and then presents the result - a more complex sentence in the language - to the other players. The other players then try to figure out the principles of the language by proposing possible sentences which are then accepted or rejected by the player who made up the language.

Like most of the WFF 'N PROOF games, Queries 'n Theories can be scaled down in complexity for the younger part of its age range (only sentences of length four for 12-year-olds) or scaled up to challenge more experienced players (sentences of length thirteen!). The most appealing part about this game, to my mind, is that it teaches scientific thinking and inductive reasoning.


There are two organizations that allow students to play some of these games against each other in a regular tournament: The Academic Games League of America and National Academic Games.

You can buy these games directly from Wff 'n Proof.

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Further reading: My previous post on Q-without-U words and a reference to another game about logic, invented by Lewis Carroll.

Scrabble Me: The chimera of Scrabble games

I recently ran across the strangest official Scrabble mutation that I have ever seen: "Scrabble Me"

It looks like, in addition to Scrabble Apple, the makers of Scrabble decided to make another game that fuses elements of Bananagrams with those of conventional Scrabble. This one is kind of a Frankenstein hybrid, so don't say I didn't warn you.

The game is divided into rounds. In each round, everyone uses up their tiles by building words on independent mini-Scrabble-boards. Then players score their words, draw new tiles, and continue building up their grids.

Unlike Scrabble Apple, which seemed to be fairly close to Bananagrams, with some Scrabble elements thrown in (scoring and double word score squares), Scrabble Me seems like it is deviating from the Scrabble - Bananagrams continuum. It's more random, in the sense that when someone uses a blank tile (called "wild" in this game), they have to swap their grid with someone else's. However, it is less random in the sense that there is a pool of face-up tiles that one can opt to draw from, instead of from the bag. It somehow reminds me of the card game Uno.

In the interest of trying to categorize these games, I've made this ASCII chart:

   ^                     BANANAGRAMS
S  |
P  |
E  |
E  |
D  | SCRABBLE          SCRABBLE ME
   |
   |---------------------------------->
         DECOUPLING OF PLAYERS        

And there really ought to be a third-dimension where Scrabble Me towers above the others on the Uno-ness axis.

The reviews I've read are sort of favorable though. In spite of the Frankenstein quality, I would like to try this game.

The games of Lewis Carroll

In addition to his anagramming prowess and his wonderfully surreal and whimsical stories, Lewis Carroll is known for creating numerous games and puzzles.

He is credited with the invention and popularization of the doublet (a.k.a, Word Ladder) in which one transforms one word into another, one letter at a time, with all the intermediary steps being legitimate words. Two examples:

          EAST          CAT
          FAST          COT
          FEST          COG
          WEST          DOG

Admittedly, this is really more of a puzzle or a pastime than a game.

He spent much of his professional life tutoring students in mathematics and logic. He invented a game called The Game of Logic designed to teach the fundamentals of formal logic, using a unique way of representing logic propositions with a game board and colored tokens. The game is described in a book of the same name (available from Project Gutenberg (though they seem not to have gotten the figures right)). Ultimately though, it seems to be for one player and seems rather like a puzzle.

Carroll also thought about and devised rules for playing billiards (the British sort, played on a table without pockets) on a circular table.

In 1880, he wrote in his diary that "A game might be made of letters, to be moved about on a chess-board till they form words.". Martin Gardner (famous for his writings on recreational mathematics) took such notes from the writings of Carroll and fleshed them out into a board game in which, as I understand it, letters are placed on the first row of a chessboard and can be moved like queens to form a word in the fifth row. Meanwhile your opponent is trying to do the same thing while blocking you. (Rows 2, 3, 6, and 7 are open to everyone.) Like Scrabble, once a word has been formed, more letters are drawn from a bag, and the first row is replenished. You can buy the game here. I am thinking of playing an improvised version with a chessboard and a set of Bananagrams tiles.

Description of the Pairs in Pears game

Now that the new Pairs in Pears game is available, some new information has surfaced. The tiles come in four designs: solid, outline, lines and dots. The different patterns function like different suits of cards. As there are four suits, each containing a complete alphabet, there are a total of 104 tiles. Just as in a deck of cards, each tile is unique (e.g., the G of solids or the H of dots). This adds an interesting new dimension to play with.

The "Pairs in Pears" game involves making pairs of intersecting words that consist of tiles of all the same pattern (as shown in the picture). Whoever makes a certain number of word pairs first, wins. "Pairpoints" is a variation that includes a more elaborate scoring scheme.

I will post more information about gameplay here, as I find it.

Appletters details revealed!

The online version of the Toy Directory trade magazine reports that Appletters (one of the new games from the makers of Bananagrams, previously mentioned in this post) will come with 110 tiles in a cloth apple and will come with instructions for three separate games:

In Appleletters, for two to six players ages 5 and up, players alternately add tiles to the first or last letter of a word in the middle of the table, creating a continuous "snake" of new words. Apple Turnover, for two to four players ages 7 and up, is similar to Appleletters. However, each player begins with 21 tiles instead of nine, and may actually replace an opponent's word with a longer word. The goal is to be the first player to get rid of tiles. In Applescore, for two to four players ages 7 and up, players build words as long as possible in crossword-like fashion and get bonus points for length, palindromes and going out first.

If the spelling above is correct, this means that the overall physical package is called "Appletters", while one of the three games that can be played with the equipment is called "Appleletters". We'll see... All of the games sound interesting. Applescore, in particular, sounds like a sort of Bananagrams-Scrabble hybrid that incorporates the emphasis on long words and scoring of Scrabble while retaining the free-flowing nature, individual grids, and speed of Bananagrams. Adding extra points for palindromes is probably the twist I like the most.


UPDATE: According to the rules of Appleletters, players build a single zigzagging chain of words, like the formation used in dominos:

          TOCK
   GIANT  I  E
   O   A  C  Y
   A   BOOK
   L

The object of the game is to be the first to use all your letters. If, on a given turn, you cannot add a word to one of the two ends, you must draw three more tiles.

The tiles are about twice as thick as Bananagrams tiles, so they can stand up on their own without need for a rack.

The game of Snatch (a.k.a., Anagrams)

I recently learned a great game that can be played with the Bananagrams tiles. It is currently sold under the name "Snatch", but earlier versions actually pre-date Scrabble and, if the Wikipedia entry can be believed, has existed in some form since the Victorian era.

Like Bananagrams, it can be played with 2 to many players, but also like Bananagrams, it seems like (tentatively) 4 is the optimum number.

The object is simply to build words from the available tiles. Start with all the letters face down in the center of the table. One player starts turning over tiles until someone sees a combination of tiles that make a word (at least 3 letters long). They shout out the word and claim it. Then the next player starts turning over tiles. What makes the game interesting is that, even a word that have been claimed by a player can be snatched away if someone sees a way to combine all of its letters with one or more tiles from somewhere else on the table to make a new word. New words must have a different meaning. (You can't just use another form of the word. For instance, if someone has the word TONE, the variations TONES and TONED are not allowed. STONE, on the other hand, would be a legitimate snatch.) You can build off of your own words, and you can combine the letters from multiple words to form a single new one.

The rule that I really like is that, if you see a word, you can snatch it at any time. For example, Alice turns over a tile. Bob sees a word and snatches it. Your first reaction (from the paucity of options when the game first starts), is to wait for Bob to take his turn flipping tiles. But if you see a word, you can grab it immediately.

Ties: If Alice and Bob both call out words at the same time and the words share at least one tile, the conflict can be resolved by yielding to whoever has the longer word. You should make up your own house rule for when two players call out the same word (or words of equal length) at the same time. (One idea is to throw those tiles back into the pool.)

When all the tiles have been turned over, play continues until everyone decides that there are no more moves to make and quits. Scoring is completely arbitrary. I like counting the number of words, but admittedly, this penalizes for combining two of your own words to form one longer one.

You can play Snatch with Bananagrams tiles (which I call "Bananasnatch"), but you may find that there are a few too many vowels as the Bananagrams set is optimized for Bananagrams while the Snatch set is designed for playing Set. I threw out about 12 of the vowels and found that we had a pretty good game. Throwing out more may make the game steadily more challenging. I will have a more detailed analysis of the letter distributions in a forthcoming post.

After playing one round of Bananasnatch, everyone wanted to play again. It is tremendous fun! It's perfect for when you've played six or seven rounds of Bananagrams and you want to change things up a little bit.

Other games: Scrabble Apple and Los Bananagrams

The makers of Scrabble have released a game that is packaged as a bunch of tiles in a fabric piece of fruit: Scrabble Apple. (I like to call it "Scrapple" for short.) It came out in January of 2009, so it is clearly a response to Bananagrams. Some of the 100 tiles are red, indicating that they are "double word score" tiles. The rules make it sound something like "Snatch", a game I am interested in trying.

[UPDATE: I have played Snatch with Bananagrams tiles, and it is awesome! See this post.]

Also there is now a Spanish version of Bananagrams. It has special tiles for "rr", "ll", "ch", and the n with the tilde over it (a.k.a., the /en yay/).