The Boggle numbers
We rolled a million boards per variant, solved every one of them, and did the exact combinatorics on the rest — the ones no computer could ever list. Twelve chapters on what the dice actually do.
The Board
- 1 How many boards The exact number of distinct Boggle boards, for all three tray sizes — a 25-digit number for Classic, and a 69-digit one for Super Big.
- 2 The average board A million rolled boards per variant: how many words a normal deal hides, what it scores, and — put your own score in — how much of a board that really is.
- 3 The best boards The richest and poorest boards a long hill-climbing search could dig out of the dice, with every word they hold.
The Dice
- 4 The dice The real printed faces, which of them are worth rolling, and the cubes that end up dead wood nobody can use.
- 5 Vowels What the dice deal you, what it pays, and why the answer is not simply "more".
- 6 Board positions Centre cells sit on far more paths than corners. Here is exactly how much more, per tray size.
The Words
- 7 Most common words Which word lengths dominate a deal, and the short vowel-heavy words that head the frequency list — none of them anywhere near a sure thing.
- 8 Words worth learning Frequency times points, ranked — plus the plural tax refund: how often finding a word quietly hands you its plural, and why it isn't more often.
- 9 Longest word The longest dictionary words any legal board of each variant can spell, each with a real board that spells it.
- 10 Boggle vs Scrabble Boggle prices a word by length and Scrabble by letter rarity. Where the two games disagree most, in both directions.
- 11 Unplayable words Not every word the dictionary holds can be traced on any legal board. Which ones can't, and exactly why.
- 12 Exact odds How you analyze boards you could never list, and the closed-form expected count for every word — no sampling.
Every number here is reproducible: the sampling is deterministic from a published seed, and the exact counts are closed-form. Start at how many boards exist and read straight through, or take any chapter on its own.