On this page · 3 sections
The Rankings#
We ranked all 17,723 answer-form openers by expected total guesses for our strategy. For each opener, we played the same generated follow-up strategy against every modelled answer and averaged the finished game lengths. Those averages are exact for that strategy; they are not proof that no other strategy could do better.
The recorded averages distinguish the top rows, but four-decimal ties do not have a meaningful exact ordinal. Suggestion rows round guesses-left to one decimal while ordering keeps the stored values. 48-32=16 leaves the fewest answers after guess one (~31) yet finishes slightly later in this strategy than 52-34=18 (~33 remaining). What matters is not only the average size of the first split, but how cleanly later guesses can divide each branch.
Any of these openers puts you on pace to finish in about 3 guesses. Once you have your colours, see the best second guess for every common pattern.
How We Rank Openers (and Why Other Guides Disagree)#
If you compare Nerdle strategy guides, you'll find three different ways people pick a "best" starter — and they give different answers:
- Character frequency. Count which digits and operators appear most often (per position) and build an opener from them. Quick to compute, but it ignores how feedback actually narrows the pool — and it tends to recommend cramming in two operators, which our data shows is a mistake.
- One-step information. Score each opener by how much it shrinks (or entropy-splits) the answer pool after guess one. Much better — but still myopic: it optimises turn one and just hopes turns two and three take care of themselves.
- Verified-strategy simulation (what NerdleBuddy uses). For every opener, we play the generated strategy through every modelled answer and average the number of guesses it takes to finish. This measures complete games instead of only the first split. It is exact for this strategy and an upper bound on the unknown theoretical optimum.
The myopia problem is real, and our data shows it cleanly: 48-32=16 is the best opener by the one-step metric — it leaves the fewest answers on average (~31) — but it finishes games at an unrounded 2.9841 guesses, losing to 52-34=18 (~33 answers left, but an unrounded 2.9834 to finish). Both display 3.0 guesses left. A slightly bigger pool that keeps splitting cleanly beats a slightly smaller pool that doesn't.
Why the best openers all look alike: one recipe wins — two-digit minus (or plus) two-digit equals two-digit, with all eight characters distinct: six different digits drawn from the most common ones, the most common operator (subtraction, which appears in 44.1% of answers), and the equals sign in its most common position. Every one of the top 100 openers fits that recipe (78 subtractions, 22 additions, none with a repeated character), and the whole top 100 spans about 0.010 expected guesses — roughly one extra guess per hundred games between #1 and #100. So if the leaderboard reads like the same equation wearing different digits, that's exactly what it is: swapping one common digit for another barely changes how much the guess learns, and any of them is effectively tied in this model.
Two-operator openers like 4*9+2=38 — a frequent recommendation elsewhere — test more symbols but produce blurrier feedback. In the real-rules artefact, the best one averages an unrounded 3.06 expected guesses (3.1 displayed) and sits around 1,500th out of 17,723; no two-operator equation appears in the top 100.
Why subtraction specifically? Single-operator addition and subtraction are mirror images — every a+b=c can be read as c−b=a, so the pool contains exactly 3,330 of each, including 3,240 apiece of the two-digit dd±dd=dd shapes. What breaks the tie is the operator symbol itself: − is the most common operator in the game, appearing in 44.1% of answers (addition manages 38.6%), because more than half of all two-operator answers — 4,480 of 8,607 — use a subtraction to pull a large intermediate value back down into an 8-character result. So a subtraction opener tests the likeliest operator alongside six common digits: a green or purple − confirms the most probable structure, and a black − eliminates the biggest slice of the pool any single operator can eliminate. The full-game computation agrees: 78 of the top 100 openers are subtractions. The best addition opener, 46+32=78, averages 2.989 guesses before display rounding (3.0 guesses left) and sits around 22nd in the four-decimal artefact.
Division openers such as 138/69=2 are a popular recommendation elsewhere, and the logic is sound as far as it goes: division equations are highly constrained (the numbers must divide evenly), so their feedback is informative. But division is also the rarest operator — only 22.7% of answers contain one — so a division opener spends its operator slot on the least likely structure. The real-rules artefact puts the best division opener, 168/7=24, around 860th at an unrounded 3.03 expected guesses, with 138/69=2 around 1,400th at 3.06 — about one extra guess every 14 games against the top subtraction cluster. Perfectly playable; just ranked lower by this model. Approximate ranks are intentional because many equations tie at the artefact's four-decimal precision.
After Your First Guess#
A great opener only pays off if the follow-up earns new information. Test fresh digits and operators, move any purple characters to new positions, and remember that a probe guess that can't win is sometimes the fastest path to the answer. We computed the best second guess for every possible first-guess result.
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