A printed letter looks like it could be any of twenty-seven things, about 4.76 bits of surprise apiece. It isn't. By the time you've read this far, the next letter is often predictable. The gap between those two facts is the most-studied number in the science of language, and you can try Shannon's method yourself, by hand.
Here is a strange way to estimate a language's entropy. Cover up the rest of a sentence and ask someone to guess the next letter. If they're wrong, tell them, and let them guess again, and again, until they hit it. Write down how many guesses each letter took. The pattern of those counts gives a sample with which to explore how much information a letter of English carries, in bits.
That experiment is Claude Shannon's, from a 1951 paper with the flat title Prediction and Entropy of Printed English. Its result is one of the quiet shocks of information theory. A 27-symbol alphabet (the 26 letters plus a space) could in principle carry log₂27 = 4.76 bits per letter; that's the ceiling, the entropy of pure noise where every symbol is equally likely and nothing is predictable. Real English, Shannon found, carries somewhere between 0.6 and 1.3 bits. The other three-plus bits are redundancy: structure so thick that a competent reader can fill the gaps. Shannon estimated English to be roughly 75% redundant; the game illustrates predictability without measuring that percentage.
This page makes you the predictor. You play; your completed letters feed Shannon's formula. The displayed estimates can rise or fall as your sample grows; they do not guarantee an interval containing the entropy of English.
A short passage is hidden below. Guess the next letter: type it, or tap the keys. Wrong guesses are told to you (Shannon's rule), and you keep going until you're right; the number of tries is that letter's guess-rank. The full distribution of guess-ranks matters, not just how often you get the first guess right. Your completed letters feed Shannon's equation (17), after the rank frequencies are sorted in descending order. These illustrative sample estimates can rise or fall as letters are resolved.
Click the text (or the keys) and start guessing. Spacebar guesses a space.
Shannon's own subject, on a 129-letter passage from Raymond Chandler's short story Pickup on Noon Street, guessed right on the first try 89 times, or 69%. The two numbers from your game are illustrative sample estimates. Shannon's lower-bound theorem assumes an ideal predictor and applies to finite-context conditional entropy; it does not guarantee a lower bound on the entropy rate of English. A short human sample adds sampling error too.
Your mind reaches back across whole words and clauses. A machine that knows only letter statistics reaches back a fixed number of letters. Shannon called the entropy using N−1 letters of context FN, and showed it falls as the context grows: F₁ (just letter frequencies) ≈ 4.0 bits, F₂ (one letter of memory) ≈ 3.3, F₃ ≈ 3.1, and onward down. Below, those rungs are recomputed live on an embedded slice of a public-domain novel. The green bounds are saved results: an ideal predictor was run offline on the full novel at memory orders 0/1/2, its guess-ranks fed through equation (17) to enclose the model's conditional entropy. For these models, the whole sandwich slides toward the floor as memory grows. Your illustrative game result is plotted separately at the right; its context length is not measured.
Low entropy means high redundancy: letters you didn't strictly need. One way to feel that structure is to start deleting letters and notice how much you can still read. Drag the slider to blank letters while their positions and spaces remain. This is a qualitative illustration of predictability, not a measurement of redundancy; roughly 75% is Shannon's cited estimate.
The game estimates and the embedded-slice n-gram ladder are computed live in your browser. The committed verifier (research/entropy-of-english/verify.mjs) recomputes the full-corpus ladder and ideal-model bounds offline; this panel displays its saved results. The verified anchors are the ceiling F₀ = log₂27, the falling n-gram ladder, and Shannon's bound machinery checked on real text with an ideal predictor (lower ≤ F ≤ upper for the model's conditional entropy at orders 0/1/2). Shannon's and Cover & King's headline numbers are cited, not re-derived.
“The entropy of English” is not one number. It is bounded, not pinned. Shannon gave a band (0.6–1.3 bits for 100 letters of context); Cover & King's convergent gambling method gave ≈1.3; large language models, which are predictors of enormous order, push the estimate toward ~1 bit — but every one of these is a bound or an estimate on a particular corpus, not a constant of nature. The number drifts with genre, era, and what you count as a symbol.
The n-gram rungs depend on corpus and sample. The plug-in F₃ here is around 2.6 on both the embedded slice and the full ~400,000-symbol book, compared with Shannon's 3.1. It uses three-letter blocks, or two preceding letters of context. Corpus differences and finite-sample bias may contribute to the gap; this calculation does not separate their effects. The page treats these rungs as illustrative and checks the bound theorem on the fitted models.
The lower bound assumes an ideal predictor. Shannon proved Σ i(qᵢ−qᵢ₊₁)log₂i ≤ F for an ideal predictor's finite-context conditional entropy. The game instead uses a short human sample, and sorts its rank frequencies in descending order before applying equation (17). Sorting leaves the upper expression unchanged but can change the lower endpoint. These are illustrative estimates, not raw rank-order bounds or a guaranteed interval for English entropy. Shannon discussed reasons for confidence in his own experimental estimates; that does not establish a guarantee for this game.
Sources, verified against the primary texts: Shannon, C. E. (1951), “Prediction and Entropy of Printed English,” Bell System Technical Journal 30:50–64; eq. (17), the §2 n-gram table (F₀ 4.76, F₁ 4.03, F₂ 3.32, F₃ 3.1), the §6 per-column bounds (100 letters: 0.6–1.3), and the Introduction's “redundancy of roughly 75%.” Cover, T. M. & King, R. C. (1978), “A Convergent Gambling Estimate of the Entropy of English,” IEEE Trans. Inf. Theory 24:413 (≈1.3 bits/symbol). Corpus: Mary Shelley, Frankenstein (Project Gutenberg #84, public domain).
The n-gram ladder recomputes live from the embedded slice; the ideal-model bounds are saved offline results. The offline verifier (checks) recomputes the full-corpus figures. The game code processes guesses in page memory and does not send or persist them. The page loads shared assets, and the serving worker adds a page-count pulse and, when configured, a Cloudflare analytics beacon.
Corrected 2026-10-14: The page said that needing more than one guess less often implies lower entropy. The full guess-rank distribution determines the estimates; a higher first-guess success rate alone does not imply lower entropy (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The page called Shannon's 129-letter sample a novel passage. It is from Raymond Chandler's short story Pickup on Noon Street; 89 of 129 first guesses were correct, about 69% (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The page said the game's two numbers straddle true English entropy. They are illustrative sample estimates; Shannon's lower-bound theorem assumes an ideal predictor and bounds finite-context conditional entropy (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The page said surviving readability measured roughly 75% redundancy. The erasure widget preserves spaces and positions and tests no reconstruction; it is a qualitative illustration. Roughly 75% is Shannon's cited estimate (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The page called the erasure text the novel's opening. It joins the second game passage to normalized title and contents text from Frankenstein (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The page called the game's estimates raw. It sorts guess-rank frequencies in descending order before applying equation (17), which can change the lower endpoint (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The page attributed “redundancy of roughly 75%” to the abstract. The quotation is in the Introduction on page 50 (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The page said nothing was fetched, tracked, or stored. Game guesses are processed in page memory; the page requests shared assets, and the serving worker adds a page-count pulse and, when configured, a Cloudflare analytics beacon (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The page said the entropy band falls from the ceiling with every keystroke. The displayed estimates use completed letters and can rise or fall; a wrong guess alone does not add a completed letter (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The related-layer note said the two pages used the same text. This page uses Frankenstein; The Law Even Monkeys Obey uses Moby-Dick, Pride and Prejudice, and Shakespeare (found by the assay line, 2026-10-14).
Corrected 2026-10-14: The chart placed Shannon's ordinary columns 1–15 at 1–15 letters of context. They represent 0–14 known letters; the separate final test still uses 100 known letters (found by the assay line, 2026-10-14).
Written 2026-06-18. Claims re-read against their sources on 2026-10-14: 142 checked, 123 confirmed, 19 wrong, 0 unverifiable. By the assay line (research/assay-line/cited-1014b/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex.
This was the directed repair pass for you-already-know-the-rest, read at f5e5f84f34, using the cited-1014b triage and the Codex source/checker records. I re-read the evidence for all 19 triage items, repaired 12 WRONG claims and 7 MINOR claims, and added 11 mirrored Corrected lines because X7 and X17 describe the same error. MINOR repairs have no public dated line. The 123 CONFIRMED entries below retain the checker's coverage; where an entry overlaps a repair, its wording is narrowed to the supported claim rather than reconfirming the former overstatement. MINOR counts toward wrong. Existing rendered OG images remain unchanged under the instruction against rendering or re-encoding images. The legacy chart source is corrected; the inspected current PNG is a title card without that chart.
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