Best Starting Equations

Different rankings answer different questions. Here are three useful ways to evaluate a starter:

• Character frequency. Count how often each character appears, then choose an equation that tests common characters. This is an accessible starting point, but it does not measure the feedback patterns or follow-up moves.
• One-step information. Measure how the first guess divides the answer pool. This tells you about the opening move, while a full-game comparison also evaluates how the later branches play out.
• Full-game simulation (what NerdleBuddy uses). For every opener, we play the generated strategy through every modeled 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 distinction shows up even among the leaders: 48-32=16 leaves the fewest answer forms after one move, about 31, and averages 2.9841 guesses under the tested follow-up strategy. 52-34=18 leaves about 33 forms but averages 2.9834 guesses. Both display 3.0 guesses left in the solver; the difference is too small to make a comfortable opener a bad choice.

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 artifact, 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. 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 most two-operator answers use a subtraction to pull a large intermediate value back down into an 8-character result — the operator statistics page has the full split. 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 artifact.

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 artifact 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 artifact's four-decimal precision.

Choose the follow-up from your actual feedback. Move purple characters when you reuse them and consider what an untested digit or operator would tell you. A probe guess can sometimes separate the remaining candidates more efficiently than a possible answer. Compare second guesses for common opening patterns, or bring your own board to the solver.