Ballpark Figures’ fourth specimen, the hangman sequel. The exact solve is a 2022 result over a fixed 2,315-word answer list, so the perfect tree proves the game is beatable, not how a person should play it. The value is in the human-sized compressions cut from it: a two-word policy (SLANT → PRICE), a gray-count rule of thumb, and the first memorizable strategy that guarantees a win in six (LEDGE PAWNS ROCKY THUMB). Along the way, five words with 25 distinct letters turn out to be worse than four words that keep common repeats.
Source: Ballpark Figures — “I Solved Wordle*” — https://www.youtube.com/watch?v=h-Rusd72W7U (44:04, 2026-10-11; auto-caption transcript)
⚠ Sourcing note. The words come from auto-captions, which mangle them. SALET is captioned “salad”/”salot” and is identified by its description (“a type of medieval helmet”) and its 3.42 average. Where a caption is ambiguous, the caption text is shown rather than a guessed spelling.
Links: Hangman — Solving Both Sides (the parent — same tier-list pipeline, same creator; this page corrects two of its claims), Yahtzee — 259 Trillion → 405 Million, Battleship — 30 Billion Boards, The Hollow Opponent
The exact method is dynamic programming over the color groups (first done by mathematicians in early 2022). It is defined over the curated answer list, not over English. Best opener SALET, 3.42 guesses on average, always winning within five (PARSE is marginally better after a late-2022 list change; list edits move results in the 2nd–3rd decimal).
Chris’s read, recorded as the discussion that matters:
| Strategy | Avg guesses | What a human must hold in memory |
|---|---|---|
| Uniform random from 2,315 | 2,315 (0.26% win) | nothing |
| Random, but take the last remaining word | 6.9 | nothing |
| Random compatible answer | 4.08 (>98%) | perfect clue-matching only |
| SLATE, then compatible | 3.82 (~99%) | 1 word |
| 2-word opener (PARSE CLINT / CRANE SPILT), then compatible | ~3.7 | 2 words, fixed |
| SLANT; if mostly gray → PRICE; then compatible | 3.67 | 2 words + one branch |
| Optimal tree | 3.42 (always ≤5) | ~2,000 cases |
His two building blocks are simplification (one rule covering many situations) and randomness. Randomness is not there to stay unpredictable, since the New York Times editor isn’t trying to trick you. It makes any partial strategy complete and easy to analyze. SLANT/PRICE gets within a quarter of a guess of optimal with two words to learn, and it is his own daily strategy.
The gray-count rule. He groups the 243 possible colorings into 19 classes by how many greens, yellows and grays they show, and reads the optimal tree’s habits off those classes. 0 grays → always guess a compatible word. 1 gray → compatible ~85% of the time. 2 → a toss-up. 3–4 → five new letters to gather information. All grays → compatible, since every new word now carries only fresh letters anyway. From the third guess on, go for the answer. This is the hangman tier list move again: a compression made for people, cut out of the exact tree.
The popular claim is that five words covering 25 distinct letters guarantee a win on guess six. It is wrong twice:
The fix is to stop at four fixed words and leave the last two guesses free: LEDGE PAWNS ROCKY THUMB plus any compatible fifth guess guarantees the sixth is forced. It is the first human-memorizable guaranteed win he could find published. Four words with 19 letters beat five with 25. The guarantee was searched with the last two guesses allowed from a wider ~4,000-word list, so it doesn’t depend on knowing exactly which words are answers. That is the same protection against a wrong word list that the hangman page credits to 3b1b’s entropy bot.
Objective choice shows up again. A two-word opener gives the best average. Three- or four-word openers give the best win probability. “The best strategy” depends on which of the two you are scoring.
To find which guess carries the leverage, he plays optimally except for one random compatible guess and measures the cost at each position. Guesses 4 and 5 cost almost nothing (one word is usually left by then). The opener costs little (about 1,500 openers are within 0.1 guess of SALET). The second guess costs the most. A bad first guess can be repaired, and a bad second guess wastes a turn for good. It is also the hardest guess to play by hand, which is why a fixed second word (PRICE) is such a cheap fix.
ADIEU and AUDIO are below the median opener, which means guessing yesterday’s answer beats them. Three things make an opener bad: low-tier letters, duplicates, and too many vowels. The last one only shows up when you look ahead. You need two or three guesses to gather information, so six vowels (counting Y) have to be spread across them. The pattern holds across word lengths (Hello Wordle): the best opener reaches three vowels exactly when the average drops below 3 guesses (length 7), four at length 9, and repeats vowels at length 10. Consonants carry the information, and vowels can be filled in later (B_F_T → BEFIT is easy, _SO_A_E is hard), which is the same reason some writing systems leave vowels out.
Tier-list transfer, as hangman predicted. He rebuilt the hangman alphabet tier list for Wordle with the same pipeline. I drops (it mostly appears in long words), S drops (no S-plural answers), and L and H rise. The new element is that a duplicate letter is ranked as its own tier entry, and it is always low tier.
Being forced to reuse your hints barely moves the average (SALET 3.42 → 3.51) but destroys guarantees. Only 22% of openers can still guarantee a win within five, about one in seven can’t guarantee six, and TRACE, a top opener, can need 8 guesses. The nine -IGHT answers each need 9 guesses to guarantee a solve, and their near-neighbours need 10. The hardest hard-mode words aren’t the ones with rare letters but the ones too similar to too many others: -IGHT, an O-N-D family, an A-T-C family, and many E-R families (spelled out letter by letter in the captions). The good hard-mode openers avoid overlapping those families.
This is the hangman chooser’s weapon occurring naturally. In hangman the adversary forces a suffix to collapse the game. In hard-mode Wordle, English already contains the families, and the rule that takes away the five-new-letters escape is what turns them into traps.
-ING, or are hard mode’s natural families already that answer? (Bonus video not ingested.)games · game-theory · mathematics · strategy