Boggle Words by Length

How a Boggle board turns into points

A Boggle board is a grid of lettered dice. You find words by chaining dice that touch, and the chain has to be a real word. This site implements four rules, and every word in every list on this page obeys all four.

• Three letters minimum. Two-letter words and single letters score nothing. The shortest thing that counts is three dice.
• Eight-way adjacency. A die may be followed by any of its neighbours: left, right, up, down, or any of the four diagonals. Diagonal chains are legal and are where a lot of the long words hide.
• No die twice. A word cannot step on the same cube more than once, so a word of seven letters needs seven separate dice.
• It has to be a dictionary word. Not a proper noun, not an abbreviation, not two words stuck together. The list has to contain it.

Trace an example. Take a 4×4 board where six letters sit in a staircase: C in the top-left corner, A directly to its right, S diagonally below the A, T directly to the right of the S, L diagonally below the T, and E directly to the right of the L. Every die touches the next one, no die is used twice, and the six dice spell C-A-S-T-L-E — a legal six-letter word worth 3 points. Put an S beside the E and CASTLES gives you a seven-letter word worth 5, if the board has an S in the right place. The rules are entirely mechanical, and you can check any candidate answer by hand in a couple of seconds.

That is the test to use when you are unsure whether a find counts: can you trace the word cube by cube, each cube touching the last, without ever stepping on a cube twice, with at least three cubes in total? If yes, it counts. If no, it does not, no matter how obvious the word looks.

The scoring table, and the cliff at eight letters

Here is the complete scoring table this site's Boggle uses. Three and four letters are worth 1 point each, five letters are worth 2, six are worth 3, seven are worth 5, and anything of eight letters or more is worth 11.

Two features of that table matter. The first is that points are not proportional to length. If they were, seven letters would be worth seven points rather than five, and there would be no reason to prefer one long find over two medium ones. The table is set so that a single long word beats a pile of short ones, which makes the game a search for chains rather than a spray of guesses.

The second is the jump from seven to eight. Seven letters is worth 5; eight letters is worth 11. One more letter more than doubles the value of the find, and that single step is where a score is really won or lost. It also explains why seven-letter words are the sweet spot on a 4×4 board: they are the last length the small grid produces in any quantity, and they are the closest available preparation for the eight-letter cliff.

The bottom row of that table is also the honest limit of what this page can show you. The five lists linked here cover lengths three through seven, which is 74,290 words out of a 267,751-word dictionary. The other 193,337 words are eight letters or longer, and every one of them is worth 11 points. The board explorer above searches the three-to-seven lists; the site's Boggle solver searches the whole dictionary, so it will also find the eight-letter words and the rare nines that are worth the same 11 points each.

Where the points actually come from

The scoring table tells you what a word is worth. It does not tell you what a board produces. To find that out, we rolled 2,000 random boards for each size, using this site's own hard-coded dice sets and its own 267,751-word dictionary, and solved every board with the same adjacency rules the game uses. These are measurements of the boards, not estimates about how people play.

The most useful number in that table is the shape of the distribution, and it is not what beginners expect. Short words dominate. On a 4×4 board, three- and four-letter words make up 72.7% of all the words on the board. On a 5×5 they make up 71.8%.

But when you convert words into points, the picture changes. On a 4×4 board, three-letter words supply 24.6% of the available points, four-letter words 26.3%, five-letter words 25.0%, six-letter words 15.6%, seven-letter words 5.9%, and words of eight letters or more 2.7%. On a 5×5 board the split is 23.8%, 24.6%, 22.8%, 17.4% and 7.2%, with words of eight letters or more supplying just over 4%.

So about three quarters of the available points on a 4×4 board come from words of five letters or fewer, and just over 70% on a 5×5 board, with the glamorous long finds supplying the rest. That is the real shape of Boggle. Players who clear out the short words early and then spend the rest of the clock hunting length get the best of both, and players who do only one of the two leave a lot of points on the table.

One more thing falls out of the measurement, and it is worth stating because it is counter-intuitive. A 5×5 board is not much richer than a 4×4 board: 134.95 words against 126.33, and 200.1 points against 180.5. The bigger grid is worth about 11% more points in total, not the doubling that the extra nine dice might suggest. The reason is in the next section.

The three-minute clock

The clock in this site's game is 180 seconds. It does not start when you find your first word or when you tap the first die. It starts the moment you press Shake & Start, with the board already generated, which means the first second you spend orienting yourself is a second you have already spent.

When the countdown reaches thirty seconds the timer text turns red. Nothing about the board or the scoring changes at that point — it is a warning, not a new phase. Its purpose is to make you stop hunting for an eight-letter word and start banking whatever short words you can still see.

A good use of the three minutes splits roughly into thirds, and the split is a rough guide rather than a rule.

• The first minute is a flood. Sweep the board for three- and four-letter words, which is what 72% of the words on the board are. Submit them as you find them. This is the phase where breadth pays, because a three-letter word is one point for almost no thought.
• The second minute is length. Stop looking for short words and start looking for chains. This is where the six- and seven-letter finds live, and they are worth 3 and 5 points for the same single tap.
• The last minute is extension. Take any word you already have and check whether an unused S, D, R or G is touching its end. A six-letter word plus an S is 5 points instead of 3, for one extra letter. This is the cheapest upgrade in the game and it is worth several points a round, every round.

Because the clock is short, the last third is also the phase where a pre-built list of candidates earns its keep. If you have a list of the words that a particular letter combination can produce, you can check it against the board in seconds rather than searching from scratch. That is what the length lists on this site are for: not for reading end to end, but for pulling up the right one and scanning it against what you can see.

And a reminder about what the clock rewards. This site's game is solo, so nothing is ever cancelled — a word another player has found is still yours. That makes the optimal play strictly simple: take every word you can see, in descending order of value per second spent. There is no bluffing layer, and no reason to hold a long word back in case it is also someone else's.

4×4 versus 5×5

Both board sizes are playable in this site's game, and the difference between them is larger than the extra nine dice suggest. It is not a difference in size. It is a difference in what the dice can even spell.

Start with the dice themselves. The 4×4 board uses a set of 16 dice carrying 96 letter faces between them. All 26 letters of the alphabet appear on those faces, but unevenly: E appears on 11 of the 96 faces and J, K, Q, X and Z appear on exactly one face each. The 5×5 board uses 25 dice carrying 166 letter faces, and those faces cover only 19 different letters. There is no B, no J, no K, no Q, no V, no X and no Z anywhere in the 5×5 set.

That is a substantial difference and it is not cosmetic. On a 5×5 board in this game, no word containing B, J, K, Q, V, X or Z can be found, because there is no die showing those letters in the first place. On a 4×4 board every letter is possible, although five of them are one-face rarities. So the bigger board gives you more cells and more paths, and it simultaneously narrows the alphabet you have to work with.

There is a second, opposite effect. The 4×4 set is 34.38% vowels — 33 of its 96 faces. The 5×5 set is 44.58% vowels — 74 of its 166 faces. The bigger board is considerably more vowel-rich, and vowels are what long words need, because a six- or seven-letter word is two consonant runs with vowels threaded between them.

Those two effects roughly cancel out on the totals and show up in the structure instead. A 5×5 board produces more six-letter words (11.62 against 9.41) and more seven-letter words (2.89 against 2.12) and more eight-letter words (0.64 against 0.39). It produces about the same number of five-letter words (22.81 against 22.54). And it cannot produce a single word with a J in it, which is why the two boards have different vocabularies rather than simply different quantities of the same one.

What a board can physically produce

There is an exact way to bound the number of words a board can contain, and it is worth knowing because it stops people expecting more from a grid than a grid can give. Count the non-repeating chains of touching dice. Each chain spells at most one word, so the number of chains of a given length is a hard ceiling on the number of words of that length.

Look at the ratio column. The 5×5 board has 4.34 times as many seven-dice chains as the 4×4 board, and 6.05 times as many eight-dice chains. The gain grows as the chain gets longer, which is exactly why the bigger board is more useful for long words than the raw dice count suggests. But even 296,360 chains is a ceiling, and in practice the measured average was 2.89 seven-letter words.

What a 4×4 board cannot produce is worth stating just as plainly. A seven-letter word needs seven distinct dice out of sixteen, and a board that repeats a letter heavily cannot produce the 32.81% of seven-letter words that are built from seven different letters. The same logic applies at every length: the number of distinct letters on the board caps the number of distinct-letter words available.

One more asymmetry between the sizes, this one about where the words hide. A corner die has three neighbours, an edge die has five, and an interior die has eight. On a 4×4 board, four of the sixteen dice are corners and eight are edges, so half the board is perimeter. On a 5×5 board, nine of the twenty-five are corners and sixteen are edges, so a quarter of the board is perimeter. Long words laid out along the rim are rarer on the smaller board, which is why a 4×4 game rewards working the edges hard.

Q and U on this site

The classic printed Boggle set has a cube with "Qu" printed on one face, so that single cube supplies both letters. This site's version keeps Q and U as separate tiles. The 4×4 die with the faces H, I, M, N, Q and U gives you a plain Q on one roll and a plain U on another, and they are not interchangeable.

For a QU word, that means the Q die has to be next to a U die, and the U die also has to be part of the chain. On the 4×4 set there is exactly one Q face and three U faces, so a board that rolls a Q without a usable U nearby simply cannot produce a QU word. On the 5×5 set there is no Q face at all.

Does this matter in practice? Only slightly, and it is worth being precise rather than alarmist. Few words need QU, and the ones that do are common enough to know: QUIT, QUIZ, QUIP, QUOTE, QUOTA, QUEST, QUICK, QUIET, QUILT, QUEUE, SQUAD, SQUID, SQUINT, BANQUET, LIQUID, LIQUOR, QUALITY, QUARTER, QUARREL, EQUATOR and SEQUEL. Longer ones exist too — QUESTION, QUANTITY, QUARTERLY — and they are worth 11 points each, because anything of eight letters or more scores the same as a seven-letter word.

It also means a board with a Q is a board to look at carefully rather than a board to write off. The 4×4 set has one Q face, so a Q appearing on your grid is a genuine event, and it is worth checking whether a U sits beside it before you move on.

The five lists, and why they grow the way they do

Here is the whole collection, counted from the word files this site ships.

Together those five lists hold 74,290 words. The distribution across them is lopsided in a way worth understanding: three-letter words are 1.74% of the collection, four-letter words 7.34%, five-letter words 16.80%, six-letter words 29.83% and seven-letter words 44.30%.

The growth from one length to the next is not a constant. Going from three letters to four multiplies the list by 4.22. Four to five multiplies it by 2.29. Five to six by 1.78. Six to seven by 1.49. The reason is combinatorial: the number of ways to arrange letters grows much faster than the number of meaningful arrangements does, so each extra letter adds more possible strings and fewer real words relative to the new total. English is a narrowing funnel at the top, and the seven-letter list is where the narrowing starts to bite.

That has a direct consequence for a board. A 4×4 board can physically hold at most 408 three-dice chains but 68,272 seven-dice chains, so there is a colossal surplus of chains at every length. The constraint is never the grid. It is whether the letters in front of you happen to form a real word, and whether you notice it before the clock runs out.

Words of eight letters and more

The lists on this site stop at seven letters, and it is worth explaining why, because the full dictionary does not stop there. The 267,751-word master dictionary breaks down by length like this: 124 two-letter words, 1,292 of three letters, 5,454 of four, 12,478 of five, 22,157 of six, 32,909 of seven, 40,161 of eight, 40,727 of nine, 35,529 of ten, 27,893 of eleven, 20,297 of twelve, 13,857 of thirteen, 9,116 of fourteen and 5,757 of fifteen.

That means 193,337 words — 72.21% of the whole dictionary — are eight letters or longer, and every one of them is worth 11 points. The nine-letter band is the single largest in the dictionary, with 40,727 words, and the eight-letter band is close behind with 40,161 — both bigger than the entire seven-letter list.

And yet the measured average is 0.39 eight-letter words on a 4×4 board and 0.64 on a 5×5 board. Three quarters of 4×4 boards contain no eight-letter word at all, and two thirds of 5×5 boards contain none either. The largest band in the dictionary is the band you are least likely to touch.

That is the tension the game is built around, and it is why the eight-letter cliff matters so much. The word is there — there are 40,161 of them — but it takes eight specific dice in a specific order, and the board has to cooperate. When it does, that single find is worth more than two seven-letter words, and it costs one submission instead of two. When it does not, the whole band is theoretical. The Boggle solver will tell you which side of that line a given board falls on, and it is the fastest way to see whether an eight-letter word was hiding in front of you.

How to use each list

The lists are most useful when you already know something about the board. A few patterns that work well.

• You can see an E and an S. Open the five-letter list and filter for words that contain both. That is 2,246 of the 12,478, and adding one more letter you can see cuts the set again.
• You have found a six-letter word. Pull up the six-letter list and look for a seven-letter word that starts with what you have. The seven-letter list is the natural next step from there.
• The board is dense with consonants. The three-letter list is the fastest flood. Three-letter words are 1 point each and 35% of the board, so this is where a quiet board gets its score.
• You have a rack of letters, not a board. Use the word finder for anagram and pattern searches across the whole dictionary, and the unscramble tool when you want every arrangement of a set of letters.
• You want the whole board solved. The Boggle solver takes 16 or 25 letters, finds every valid word including the eight-letter ones worth 11 points, and shows the path for each one.

Two other pages are worth knowing about. The Boggle game plays a 4×4 or 5×5 board against a three-minute clock and reveals every word you missed when the timer expires, which is the best way to see the board you were given. And the guide to Boggle on a screen grid covers what changes when the board is a fixed 4×4 arrangement you can read in full before you trace anything — no shake, no tumbled dice, and a different scanning pattern.

Where the words come from, and what the list does not tell you

The five lists on this site are slices of one 267,751-word dictionary. It is a broad dictionary, which means it contains every inflected form, every technical term and every archaic compound in the language. A seven-letter list built from it will contain PIZZAZZ alongside PICTURE, and a four-letter list will contain words no puzzle would ever use.

That is fine for a Boggle reference, because the adjacency rule does most of the filtering for you: a word that needs letters the board does not have is not findable, and the filters on each length page let you remove the letters you can see are already spoken for. It is less well suited to anything that assumes a curated answer list.

The honest summary of how to use any of these pages is this. The lists tell you what could be there. The solver tells you what is there. The game tells you what you missed. Used in that order they are a complete workflow: pick a length, filter by the letters in front of you, and scan the short result against the grid.