The four-letter board is the hardest board, and we can prove it

The board called Easy has four-letter words, the smallest answer pool of the three, and the most guesses. It is also, by the only measure we can take honestly, the hardest board in the game. That was not a design choice. It was a result, and it arrived late enough to be annoying.

What we measured

Before the guess limits were set, three solvers were run against every answer in every pool. The one that matters here is the open solver: it may guess any word in the full dictionary, not just words that could still be the answer, which is what a strong human player does. Here is how many guesses it needed.

Read the mean column again. Four letters costs 6.49 guesses. Six letters costs 5.59 — nearly a full guess fewer, on longer words, from a pool nearly twice the size, with repeated letters allowed on top.

The tail is worse than the mean. If every board were given six guesses, the solver would fail 45.9% of four-letter puzzles and only 16.6% of six-letter ones.

Why short words hide more

The answer is in how much a single tally can say. A tally is two numbers that add to at most the length of the word, so a four-letter board has at most fifteen distinct replies available to it. A six-letter board has twenty-eight.

Against our real answer pools, the best opener on each board actually produces 12 distinct tallies on four letters and 20 on six. So every guess on the easy board carries roughly a third less signal than the same guess on the hard one.

There is a second effect stacked on the first. The four-letter dictionary is 3,903 words in a space of four slots — it is dense. Short words crowd together, differing by a single letter, so a tally that eliminates one frequently spares a dozen of its neighbours. Six-letter words are sparse in comparison, and sparse spaces separate cleanly.

So why is it still called Easy?

Because the label is answering a different question than the one we just measured, and players ask the label’s question first.

• It names the word length, and that is what people choose on. Someone picking a board is deciding whether they want to stare at four letters or six. Calling the four-letter board Hard would mislead far more people than it informed.
• The guess limits already absorb the difference. Easy gets 10 guesses where the other two get 8 — set at the solver’s ninetieth percentile plus one, which is why the limits are uneven. In terms of how likely you are to solve it, the boards are close to level. The extra guesses are where the extra difficulty went.
• Easy is also unscored. No points draining while you think, no leaderboard, no clock to beat. It is the board to hand someone who has never played, and nothing about it should be in a hurry.

What this means if you play it

Take the ten guesses seriously. On the regular board, burning a guess on pure reconnaissance is a real cost against eight. On the easy board you have room for two or three probes that are not attempts at the answer, and you will usually need them, because the tally on four letters is a blunt instrument and the only way through is volume.

The opener still matters — RATE is the measured best on four letters — but expect it to leave you 93.44 candidates out of 600. That is not you playing badly. That is the board.

The general lesson

Length is a proxy for difficulty in a game that tells you where the letters are, because a longer word gives a positional grid more slots to colour in — more letters, more information. Take the positions away and the proxy inverts: the longer word gives the tally a wider range of values to take, so the longer word gets easier.

We shipped the labels anyway, and wrote this instead. If you have played a few days on Regular and want the board that will actually beat you, it is not the one marked Hard.

The measured comparison between tallies and coloured tiles goes into where that inversion comes from.