Boggle

Lately, I have found myself deeply attracted (addicted?) to Wordtwist, which is basically Boggle with a weirder scoring system. Let's explore methods of scoring well in Wordtwist on a good board (one with many words available).

Firstly, an example board:

b x o p
y e t h
o n a s
k e s w

Let's look at the board and talk about it in general.

Sure, the game tells us that there are many words to be found (a pre-game accessible table tells us, with a bit of computation, that there are 316 words waiting to be found), but where do we start looking?

The 'x' near the top left corner is not badly placed. It contains obvious words (which are rewarded with bonus score thanks to the presence of the "weird" letter 'x') such as exo and oxy. In fact, there are 6 3-letter words containing an 'x' in this board: exo, oxy, hox, pox, yex and tex. It pays to know your 3-letter words (I didn't; oh well).

There are 6 other words containing 'x': poxy, next, nexts, oxen, onyx and ethoxy, which is admittedly hard to find.

The other "weird" letter of this board is 'k'. 'k' contributes to surprisingly many short words to those unfamiliar with Boggle-like games: kas, ska, ken, kent, kon, and whatever not. In fact, for this board, the 'k' words are: kon, kons, ken, kens, kea, keas, oke, okes, nek, hank, sank, keno, kent, kents, tank, wank, yoke, yokes, kente, sanko, shank, snoek (and edible marine fish, what the...), snoke, stank, swank, thank and bethank. Of these, kon, kons, ken, kens, kea, keas, oke, okes and nek are 3-letter words and s-plurals. If one recognises 'nk' as an ending stem, one could in theory locate the words hank, sank, tank, wank, shank, stank, swank and thank with some degree of consistency (a glance would give hank, sank, tank and wank surely, and the rest are not that hard to locate if you're looking for words ending with 'nk').

Next, we might take a look at 3-letter words (with some repetition):

yon yok yex yet yen yea wat was wan wae top toe tho tex ten tea taw tas tan tae sny sha sen sea saw sat san sae pox pot poh pht pho oye oxy opt ony ons one oke ohs oes nye nth noy net nek neb naw nat nas nah nae kon ken kea hox hot hop hoe haw hat has han hae exo eth eta ess eon ens ene eat eas ean bye bey bet ben ate ass ash any ant ane ahs

We theorize that most 3-letter words are of the form . Words that fit this bill are:

yon yok yex yet yen wat was wan top tex ten taw tas tan sen saw sat san pox pot poh noy net nek neb naw nat nas nah kon ken hox hot hop haw hat has han bey bet ben

This kind of breaks my hypothesis to bits, accounting for only half of the words. Yet these 3-letter words are the easiest to find. Relooking at the board:

b x o p
y e t h
o n a s
k e s w

One might have a deeply organised attack on these words which go:

 xop xot xoh pot poh tox top toh hot hop hox bex bet ben bey xeb xet xey xen yet yeb yex yen tex ten tey teb neb ney nex net yon yok noy nok kon koy nat tan tah tas taw hat han has haw nat nah nas naw sas sat sah san saw was wan wat wah

This covers all the 41 words in the reduced list above, and took me slightly above 1 minute to type out in full. Knowing the words well could likely reduce this to about 40 seconds, minus away some consistency due to flawed recognition of words. Also, doing it with a more stable presence of mind will probably help in locating the plurals, such as hats, nats, tans, hans, haws and wans more easily.

The remaining 3-letter words:

yea wae toe tho tea tae sny sha sea sae pht pho oye oxy opt ony ons one oke ohs oes nye nth nae kea hoe hae exo eth eta ess eon ens ene eat eas ean bye ate ass ash any ant ane ahs

6 are plurals of 2-letter words:

ons ohs oes ens eas ahs

The rest are weird; go figure:

yea wae toe tho tea tae sny sha sea sae pht pho oye oxy opt ony one oke nye nth nae kea hoe hae exo eth eta ess eon ene eat ean bye ate ass ash any ant ane

The remaining words according to classification where I can find them:

Seeming plurals/third person present tense of 3-letter words:

yens yeas wats wans waes tens teas taws tans taes seas saws sans pots opts ones nets nats hots haws hats haes eths etas eons enes eats eans bets bens ants anes

Others:

yont yean yeah ybet wate wast wash wase wany want wane toph toey toea thaw than thae tene tass tash tane swat swan stop stey sten staw snye sneb snaw shot shop shoe shaw shat shan sent sene sena seat sean sate sash sant sane pote poet phot phat onto noes ness neat hote hate hast hant haet haen eyne etna esne eath east ease bets beth beta bent bene beat bean atop ants ante aeon

5-letter words (words with apparent 4-letter stems are bolded):

yenta yeast yeans yeahs waste wants waney wanes tophs toeas thaws thans thane tense tenes tease tawse tasse swats swath swash swans stens steno stean staws stane snaws snath snash shote shaws shans sents sente senas seats sants santo sanes potae poets phots phase netop neats neath hoten hawse haste hants hanse haets etnas enate eaten beths betas bents bento benes beats beath beast beany beans beano aeons

6-letter words:

yentas thanes swaths steans steane stanes sneath snaths snaste senate potass potash potaes hasten ethane ensate beaths assent

7-letter words:

washpot waeness teashop steanes sneaths shantey hotness hastens ethanes beneath

Notably, waeness and hotness both have the -ness stem.

Random notes that didn't fit in anywhere else:

b x o p
y e t h
o n a s
k e s w

With the letters n, e (x2), a, t, s (x2), we can form (not exhaustively):

eta, etas, tea, teas, tae, eat, eats, ate, east, sate, sae, eas, tas, sat, ass, tass, neat, neats, tane, stane, stanes, stean, steans, steane, steanes, net, nets, ten, tens, sten, stens, sea, seas, sen, ens, nas, san, sans, sane, ane, ean, eans, tan, tans, nat, nats, sene, ene, tene, tenes, taes, sent, ant, ants, sant, sants,

all of which are rather common words with my 5 favourite letters, 's', 't', 'a', 'n' and 'e'. In fact, a square containing 'teas' has 22 words, which are:

tea, teas, tae, taes, eat, eats, eta, etas, ate, ates, sat, tas, set, tes, est, sea, sae, eas, seat, seta, east and sate.

For 'nats': nat, ant, tan, ans, nas, san, tas, sat, tans, nats, ants, sant
For 'nets': ten, net, sen, ens, set, tes, est, nets, tens, sten, nest, sent
For 'sane': san, nas, ans, sea, eas, sae, ens, sen, ane, ean, nae, sean, sane, anes, eans, sena
For 'tane': tan, nat, ant, tea, tae, eat, eta, ate, ten, net, ane, ean, nae, neat, tane, etna, ante