Good three-letter words for Bananagrams, sorted by rareness

When playing Bananagrams, 2-letter words are great for rapidly adding letters to a grid, like when you are running off a string of "PEEL"s, but it's hard to make an entire grid out of 2-letter words. In this post, I'm going to examine some of the 3-letter words and show you which are most commonly used and which you might want to add to your active vocabulary.

First, consider this list of some 3-letter words you can make with the letter V:

eve, ivy, ova, rev, van, vat, veg, vet, vex, via, vie, vim, vow

We don't have a good set of data of what words are most commonly used in playing Bananagrams, and Scrabble word choice would likely be a poor substitute since players' priorities in Scrabble are very different than in Bananagrams. WordSquared offers a good compromise: its gameplay shares score maximization with Scrabble, but also includes the rapid score-aloof word-building (such as when evading or outflanking opponents) that epitomizes Bananagrams.

If you sort the above V words by word count (as obtained from WordSquared word pages), you get

van, eve, vet, vat, vie, via, vex, rev, vow, ivy, ova, veg, vim

But sorting by raw word count is not the most useful ordering since the Scrabble tile distribution is going to skew the results. There are lots of As, Es, Ns, and Ts, so of course VAN, EVE, VET, and VAT will be popular words. I wanted to subtract out this bias to see what words would be most and least used if all letters were equally likely to be available. I accomplished this by just dividing each word count by the number of times that each of its letters occurs in a standard Scrabble tile set [which corresponded to the Word² distribution until the recent Word² redesign, which fortunately happened after I finished this post]. (For example, the word VAN had been used in WordSquared 24198 times (over about 2 months). In a 100-tile Scrabble set, there are 2 Vs, 9 As, and 6 Ns, so I divided 24198 by 2 and by 9 and by 6 to get a normalized count of 224.1.) Sorting the words by the normalized word count gives:

vex, vow, ivy, van, vat, vet, vim, vie, rev, eve, veg, via, ova

When people have a V, they are more likely to make VEX than any other three-letter V word. (In this case, 70% more likely than even the closest word (VOW).) On the other end, VIA is used fairly often in terms of raw word counts, but sparingly when considering how often it could be made.

Below are more word lists, all sorted by this effective word usage rate, starting from the most common words and ending with the most neglected:

3-letter words that contain the hardest letters, sorted from common to rare:

J words:
joy, jug, job, jam, jaw, jog, jay, jab, jig, jar, jet, jot, jut, jag, jib

K words:
key, kid, sky, kit, yak, kin, keg, wok, ink, ark, ask, oak, irk, ski, ken, ilk, koi, uke, eke, ska, auk

V words:
vex, vow, ivy, van, vat, vet, vim, vie, rev, eve, veg, via, ova

X words:
box, fox, wax, fix, mix, vex, fax, hex, tax, pox, six, sex, tux, lax, axe, lox, sax

Z words:
zip, zit, zoo, zap, zig, zag, fez


3-letter words that begin with vowels, sorted from common to rare:

Words that begin with A:
axe, ark, ask, any, awe, ace, arc, and, age, aim, arm, act, ash, ape, ago, ant, aye, art, air, all, aft, aid, ate, add, are, ail, ale, ado, apt, ass, asp

Words that begin with E:
elk, egg, elf, eve, eye, end, ego, elm, emu, ewe, eat, ebb, ear, eel, eke, era, eon, ere, eta

Words that begin with I:
ivy, ink, icy, ice, irk, ilk, ill, imp, inn, ire, its, ion

Words that begin with O:
off, owl, orb, oak, own, oil, old, owe, ova, one, oft, out, orc, our, odd, ode, oaf, opt, oat, oar, obi

Words that begin with U:
use, urn, ump, uke

Words that begin with Y:
you, yak, yam, yes, yet, yew, yap, yip, yin, yep, yon, yea


3-letter words that end with vowels, sorted from common to rare:

Words that end in A:
via, ova, yea, boa, pea, tea, bra, sea, spa, ska, era, goa, baa, eta

Words that end in E:
axe, the, bye, cue, ice, hue, she, pie, vie, eve, ace, awe, foe, eye, age, dye, bee, owe, hoe, rye, due, ape, woe, die, sue, aye, toe, tie, ewe, ore, rue, use, ate, lye, are, doe, ale, ode, pee, wee, see, ire, fie, uke, tee, eke, lee, ere

Words that end in I:
chi, ski, koi, phi, poi, obi, psi

Words that end in O:
zoo, who, ego, ago, boo, goo, moo, two, woo, too, coo, ado, pro, loo, bro, fro, rho, tao

Words that end in U:
you, flu, emu, gnu, tau

Words that end in Y:
joy, jay, why, key, guy, boy, buy, coy, way, toy, fly, cry, day, gay, sky, hay, bay, ivy, pay, shy, may, soy, hey, fry, lay, dry, say, ray, try, ply, sly, spy, icy, pry, nay, thy, fey, any, sty, ley


It's interesting to look at how different words fare. Auks and asps are nearly forgotten, but foxes and owls are quite popular. Greek letters (eta, phi, psi, rho, tau) and abbreviations for musical instruments (sax, uke) and for formal wear (tux) do not see much grid time. I am glad to see that everybody loves joy.

If you want to learn useful new words to add to your active Bananagrams vocabulary, the ends of those lists might be a good place to start.

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Further reading:

• What to do when you have too many vowels
• Innergrams and what they can tell us about word favoritism
  - a different look at words that might be in your word blind spot

Follow-up on Bananagrams at PAX East 2011 and Bananagrams doubles

Since this year's PAX East Omegathon paired up players into teams, the Bananagrams round was played in doubles mode. The picture below (from the official Bananagrams Twitter feed), shows a winning grid from the first round of the Bananagrams part of the Omegathon.



I attempted to read off the words from the grid and got:

   H A     P
  NOON B ZOO
   R DEER  IDES
  AS         A
   EEL    FIAT
     E  Z U  E
     A  O E  N
     D COIL
   TEETH
   A R U
   K   MUTER
   EON   I
    N   ME
   PEST
      I
     YET

A few comments on this picture: The grid incorporates a lot of the short words that I find myself using including EEL, EON, YET, and ZOO (two ZOOs, actually). CHUM also seems like a useful word to have in one's Bananagrams vocabulary. And observe the left and right branches of the grid and the way that the players have positioned themselves. If both players are right-handed, it seems to make sense for the player on the right to move closer to the table, so he can more easily reach the upper-right corner of the board with his right hand and still easily cover the lower-right corner of the board. You can see a similar posture adopted in photos of other teams.





It appears that the player on the left sometimes also turns toward the center; this is probably the best strategy, as it will allow the left hand to contribute more.

I've wanted to experiment with Bananagrams doubles for a while now. Knowing that it has been successfully played in the Omegathon gives me confidence that Bananagrams can work well as a team game.

UPDATE: Some video from the Omegathon Bananagrams round is now up

Defensive strategies for Appletters

Since Appletters involves building a zigzagging snake-like line of words, where new words can only be built off the beginning or end of the snake, the options for play can be sometimes highly constrained. Devious players can use this to their advantage.

For instance, you can position words such that you are able to form words from a position that others are unlikely to be able to. As in the example below, where the presence of the word SLIP forces new words starting from the V to be built only to the left, making the V tricky to deal with.

   SPORK
 V L
 I I
 MOP

Among the very few words that end with V are rev and shiv.

    SPORK
REV L
  I I
  MOP

Similarly, there are few words that start with X. Examples include xenon (the atomic element), xi (the Greek letter), xebec (a kind of three-masted Mediterranean ship), xylem (the part of a plant that transports water - like a plant's circulatory system), and xeric (super dry, desert-like).

I think that the only people who will be able to generate words that end in a J or Q are people who have deliberately memorized such words for such purpose as they all look like questionable Scrabble jibberish to me. By properly constructing the snake, one or both ends can almost be completely cut off using this tactic.

There's also what I call the Ouroboros stratagem.

Suppose you have manipulated the situation so the snake looks like this:

    SPORK
REV L   N
E I I   I
L MOP   V
I       E
C       S

A really fiendishly clever thing to do is to build a word that joins up the beginnings and end of the snake, like so:

    SPORK
REV L   N
E I I   I
L MOP   V
I       E
CALENDARS

If it is allowed (and I can find nothing in the instructions that forbids it), finding a way to make the Appletters snake into a closed loop pretty definitively ends the game. In my book, whoever pulls off such a stunt should instantly win, as when you sink the eight-ball on the break in pool.

On the effect of body orientation on anagramming speed

When we are standing up, gravity pulls blood down which is detected by "baroreceptors" in the circulatory system. The circulatory system compensates by increasing the heard rate, so that blood pressure in the upper body is maintained. When the baroreceptors register such a blood pressure drop, the locus coeruleus neurons become more active. The locus coeruleus responds to stress by increasing release of norepinephrine (a.k.a., noradrenaline). This has a number of effects, including increasing heart rate and blood flow and boosting motivation, thinking, and alertness. But researchers have found that increases in norepinephrine coincide with a slight slowing of certain kinds of thinking.

The thesis is that "insight problems", the kind where your brain kind of wanders and does background processing, and then suddenly presents a solution in an "A-ha!" moment, happen faster when you have lower norepinephrine levels. A simple "A-ha"-type problem to test, and one which is very popular in psychological research, is anagramming.

In one experiment [M.P. Walker, C. Liston, J.A. Hobson, R. Stickgold, "Cognitive flexibility across the sleep-wake cycle: REM-sleep enhancement of anagram problem solving", Cognitive Brain Research, Volume 14, p.317-324 (2002)], researchers woke people up at different stages of sleep and asked them to solve anagrams. They found that subjects who had just been in REM sleep were better at anagramming than subjects who had been in some other sleep stage. And REM sleep has a lower locus coeruleus activity level.

In another experiment, [D. M. Lipnicki and D. G. Byrne, Cognitive Brain Research, Volume 24, p.719-722 (2005)], researchers had subjects solve 5-letter anagrams (like unscrambling DEFSU to get FUSED) and perform arithmetic problems (73 - 58 + 19 - 26 = ?), while standing up and then while lying down. When standing up, average anagramming time was 29.4s +/- 6.3s. When lying down, average anagramming time was 26.3s +/- 5.4s. The difference in anagramming times (3.1 seconds) is smaller than the standard deviation of the data, but the statistical analysis suggests that the error bars are not that important, allowing us to conclude that the average person in the study anagrammed 10% faster while lying down.

A similar test found that standing is correlated with people solving simple arithmetic problems a few percent faster, but it's such a small difference that it doesn't seem statistically significant.

Summarizing: When you stand up, your body tends to become more alert and less relaxed, and you may anagram slightly slower as a consequence.

Caveats: This study was performed on randomly selected subjects with no proclivity for word games. When given 32 5-letter anagrams to solve, and 45 seconds to solve each in, the average number of solutions was 8 or 9 (whether sitting or standing). A typical Bananagrams player would do significantly better, I would be willing to bet.

I wonder if the cause and effect might flow the other way: if lower blood pressure allows one to anagram faster, can focusing on anagramming cause blood pressure to be temporarily lowered? Or will it just cause one to lie down?

Anagramming is only one of the skills used in playing word games, of course. The kind of concentration necessary to play Bananagrams fast most likely requires the mind to not be in a relaxed state. (And what I'd really like to see is a study on playing Bananagrams itself). Still, whenever the professional Bananagrams league launches, one of the first drugs they should consider regulating is beta-andrenoceptor antagonist propranolol.

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Further reading:

D. M. Lipnicki and D. G. Byrne, "Thinking on your back: Solving anagrams faster when supine than when standing", Cognitive Brain Research, Volume 24, p.719-722 (2005).

If you have access to it through your library, you can get the paper from here.

Tactics to help you win at Bananagrams

Through playing many, many games of Bananagrams, I have learned a few lessons about how to approach the game:

• Concentrate on making words out of the hardest letters first to get them out of the way.
  
  
• Try to make one long word at the beginning and build off of it. In general, the longer your words are, the more places there will be to build new words.
  
  
• Particularly at the beginning, when you flip over all your letters, try to assess the balance between consonants and vowels. If it is off, you can try to make vowel-heavy or consonant-heavy words [See what to do when you have too many consonants and what to do when you have too many vowels.]. It's far better to do this from the outset, than to have a mostly-finished grid and realize that you need to go back and remodel the whole thing.
  
  
• Try to structure your grid in a more open way.
  
  Good:

     CHILL      
         I 
         POST

  Not-as-good:

     CHILL
         I
      STOP

  The former is far easier to build new words off of:
  

     A
     CHILL W
     U   I A  
     T   POST
     E      O

  We could even quantify the difference between the two approaches. In the first case, words can be build up or down (or both) from 5 letters (C,H,I,S,T) and just in one direction from 2 more (the L and the O). In the second case, there are 8 letters that one can build off of in only one direction. The number of words you can make with the H in any position (HUE, OCHRE, EACH) versus just making words that start or end with a given letter, is definitely bigger than a factor of 2... I'm going to conservatively estimate it to be 3 times larger. Then the flexibility scores of the two grids above would be 3*5+2=17 and 8*1=8. And the advantage of choosing an open structure only grows as the grid becomes larger. It's often the difference between smoothly adding letters to your grid and having to completely rearrange things.
  
  
• When you are in the peeling phase, keep in mind one or two words that you can steal letters from and positions where you can easily add tiles to make new words. Or words that you can easily anagram (with the newly peeled letter) to make a new word.
  Suppose you have the grid below and you peel an A.

       TRY
       I
       E
     FORKS

  From FORKS, you can take the S and combine it with the A to from SAY:

         S
         A
       TRY
       I
       E
     FORK

  Now that I'm thinking about FORK and SAY, I note that the K from FORK could be substituted for the more-easily-used A in SAY to form SKY. So if the next letter I peeled was R, I could quickly make that switch, freeing up the A to build the word FAR:

         S
         K
       TRY
       I
       E
     FOR
     A
     R

  At this stage, I might wind up extending FOR to FORT or FORD or FOUR or FORE or anagramming it to ROOF, depending on what letter become available. It would be nice to build SKY into RISKY. And FAR looks like an appealing place for making FARM, FAIR, or FARE.
  

The speed of Bananagrams is such that you will not be able to consider every possible move, but having just a few rules of thumb to keep you from getting boxed in can allow you to still play fast while increasing your chances of winning.

Palindromes you are most likely to be able to make in Appletters

Since making palindromes earns players bonus points in the Applescore game (as described in this previous post on Appletters), I've compiled a list of the palindromes you are most likely to be able to make during the game (really short ones or ones that use common letters).

Off the top of my head, using only the minimal length examples:

bib, bob
dad, deed, did, dud
eke, ere, eve, ewe, eye
gag, gig
kook
mom
noon, nun
pap, pep, pip, pop, pup
radar
sees
tat, tit, tot
wow

And, of course, there is one Scrabble-legal letter combination that is two letters long and a palindrome: AA. A'a (pronounced /ah ah/) is a type of lava, which is thicker and more viscous than other types. It is characterized by flowing in a sporadic fashion and leaving a rough surface when it cools.

And if it's not already been suggested, then I propose a variation of Appletters called Palindrominoes: The word snake is formed as in regular Appleletters, but if you can form a palindrome where the base letter (the "head" of the snake, I suppose) is inside the palindrome, then you are permitted to position letters both above and below the end-tile, as shown in the example below:

  e   
  VIGOR 
  e   I
      N  
      KITE

Then you can give the snake multiple heads, like a hydra or a planarian or something. A little extra chaos to spice up your Appletters game.

What to do when you have too many vowels (other than panic)

This is the natural complement to the post about what to do when you have too many consonants. As mentioned before, if you dump one of your vowels, assuming that you are picking from the 144-letter Bananagrams distribution, you have an 8% chance of getting three vowels back. In my experience, if you have one extra vowel tile, and you just can't rearrange the grid to fit it in somewhere, even exchanging it for two vowels and a consonant tends to be easier to deal with. Of course, you could wind up with some consonants that are tricky to use (which may be why I rarely dump letters.. I also enjoy rearranging the grid).

Whatever approach you choose, you definitely want to know some words with a large percentage of vowels. There are some nice all-vowel words out there like aye, eye, and you. Here is a sampling of some longer vowel-heavy words:

eunoia (83% vowels)
eerie, adieu, audio, bayou (80%)
year, ooze, area, iota, auto (75%)
sequoia (71%)

"Eunoia" and "sequoia" are also distinctive for being two of the shortest word containing all five vowels. "Eunoia" may get you in trouble if you try to use it since it's an obscure word. [I am partial to it because it is a brain word. It comes from a Greek word meaning "beautiful/favorable thinking". The "beautiful thinking" interpretation led to the obscure English usage of "eunoia" - a state of normal mental health. A stricter reading suggests that the Greek word referred to thinking that was favorable to someone (like one's spouse). The "blissful and benevolent state of mind" interpretation, though questionable, is the nicest.]

If you are interested in obscure words on the extremes of human language, check out the All-Vowel Words and All-Consonant Words dictionaries. They start with tame words like "eau" and "brr" and then spin off into highly arcane references (at times approaching Borges-level bizarreness). They come packaged together in a book called "Wye's Dictionary of Improbable Words", downloadable from Lulu for ~$14.

Pangrams and what to do when you have too many consonants

Pangrams are sentences that use every letter in the alphabet at least once. Just a few examples:

• Nth quark biz gyps cwm fjeld vox. (which sounds like the shortest science fiction story ever)
• Vext cwm fly zing jabs Kurd qoph.
  which I like for the description:
  "An annoyed fly in a valley, humming shrilly, pokes at the nineteenth letter of the Hebrew alphabet that was drawn by a Kurd." (though I prefer the variation: Zing! Vext cwm fly jabs Kurd qoph.)
• Squdgy fez, blank jimp crwth vox! (Translation: An imperative sentence, commanding one's squashed-down brimless hat to mute the skimpy voice of a Celtic violin. I like this one particularly, as it was made by my current hero, Claude Shannon, whom I will write about eventually, elsewhere.)

There are many more 26-letter pangrams. By adding two letters, one can make parsable pangrammatic sentences like:

• Waltz, bad nymph, for quick jigs vex!

As pointed out by Robert Munafo: "The fact that so many optimal pangrams exist in English results mainly from its highly complex and flexible grammar, and the borrowing of so many words from other languages."

In particular, all of the 26-letter pangrams above use Welsh words (which have made their way into the English language), since in Welsh, the letter W is a semivowel. These words are a great way of dealing with a consonant-heavy round of Bananagrams. Check them out:

• cwm (pronounced /koom/) - a Welsh word meaning circular or bowl-like valley, often formed by a glacier.
• crwth (/krooth/) - an archaic Welsh stringed instrument - like a boxy violin (Parenthetically, writing this definition has inspired me to make up my own (suboptimal) pangram: The King of Quips seized the crwth (like a boxy violin) to jam.)

Another one is bwlch which means mountain-pass, and is kind of fun to say. "I pity the /boolch/!".

Some other good words for getting rid of consonants:

• hymns
• fjords
• rhythms
• strengths (the longest dictionary word with only one vowel)

The other option when you have too many consonants is, of course, to dump one of them, in hopes of getting some vowels. There are 63 vowels in a Bananagrams set (counting Y as a vowel), so if you pick 3 tiles from a random pool (starting with all 144 tiles), the probability of getting all consonants would be 81/144*80/143*79/142 which is about 18%. (The probability of getting all vowels is 8%.) [The odds could be computed more efficiently if you took into account all the tiles already turned over. This could be useful near the end of the game, but would seem to require superhuman ability to catalog all the displayed tiles. It seems more plausible in the final move of a Scrabble game.]

So, about 80% of the time you'd probably come out ahead (with one or more extra vowels) though possibly with much rearranging to do to use your new tiles. The other 20% of the time you'd just have more consonants and be even more stuck! This is one reason that I generally only dump at the beginning of a game or else when absolutely necessary.

Q-without-U words

My one concession to the Scrabble-memorizer approach is to know some of the Q-without-U words, as they are so useful in Bananagrams. Also, I do not like to invoke the DUMP rule.

A faqir is another spelling for "fakir", which is like a Hindu monk or ascetic. Tell your friends that it is the name for those guys who sleep on a bed of nails.

A qaid is an Arab chief. The Arabic language is big on the Q-without-U, as we will see.

A qanat is a system for distributing water in arid climates, developed by the ancient Persians, but still in used today. It's basically an underground tunnel, channeling water from some source along a path, and then there are wells drilled down at different positions along its trajectory. It has its own Wikipedia page! If you have more than one, you have qanats.

A qat is an evergreen shrub found in East Africa and Arabia, used as a narcotic (similar in effect and intensity to ecstasy). Possibly one of the shortest words for a drug. (Individual letters and acronyms don't count! Show me the vowels!) You can also make references to "shrubbery" to diffuse any qat-related tension.

A qintar is the Albanian penny. Probably you will never use this one, when you can just make qat.

Qoph is the 19th letter of the Hebrew alphabet. It looks like this:

It is mainly useful when making minimal pangrams: "Vext cwm fly zing jabs Kurd qoph".

Further reading: You may also enjoy:

• What to do when you have too many vowels


• Pangrams and what to do when you have too many consonants