3f:null 40:["$","title",null,{"children":"Wordle | Visnu Pitiyanuvath | Observable"}] 46:T636,eliminationScore = (word) => { const exclude = new Set(gray); // per possible remaining answer return ( d3.sum( answers.map((answer) => { // if it's the answer, it'll eliminate all but itself if (word === answer) return answers.length - 1; // see how green, yellow, and gray change const next = { exclude: new Set(exclude), green: green.slice(), yellow: yellow.slice() }; for (const l of word) if (!answer.includes(l)) next.exclude.add(l); for (const [i, [l, a]] of d3.zip(word, answer).entries()) { if (l === a) next.green[i] = l; else if (!next.exclude.has(l)) next.yellow[i] += l; } // check if the cache already has this configuration if (cache.has(next)) return cache.get(next); // count how many answers would be eliminated const include = new Set( next.yellow.concat(next.green).flatMap((l) => Array.from(l)) ); const match = new RegExp( d3 .zip(next.green, next.yellow) .map(([g, y]) => (g ? g[0] : y ? `[^${y}]` : ".")) .join("") ); const delta = answers.length - d3.count( answers, (w) => w.match(match) && d3.every(include, (l) => w.includes(l)) && d3.every(w, (l) => !exclude.has(l)) ); // update cache cache.set(next, delta); return delta; }) ) / answers.length / answers.length ); }47:[{"id":"01eb5f0244429f06e39622551a4ca965426ba71a3be0fce8c7c0f3a8e374fe8191ffb8d9b058bc18588cbcc9b09f71a411abc1d04c5c4a437591e2ea2102c8d0","href":"https://static.observableusercontent.com/files/01eb5f0244429f06e39622551a4ca965426ba71a3be0fce8c7c0f3a8e374fe8191ffb8d9b058bc18588cbcc9b09f71a411abc1d04c5c4a437591e2ea2102c8d0","name":"words@2.csv","type":"text/csv","lastModified":1645128772612.185,"size":77682},{"id":"fdd12dbd54949a680b3a66517285bf1857cdf723a642c5dafb2a316707fb519758457802abe23bb4c5d3beaa0d6f79e93cb3b47f0deb141a112b717ffe47798c","href":"https://static.observableusercontent.com/files/fdd12dbd54949a680b3a66517285bf1857cdf723a642c5dafb2a316707fb519758457802abe23bb4c5d3beaa0d6f79e93cb3b47f0deb141a112b717ffe47798c","name":"words.csv","type":"text/csv","lastModified":1641429187339.793,"size":77832}] 44:{"id":"0c7272a52417997d","slug":"cheat-at-wordle","title":"Wordle","thumbnail":"0e25993cbfa6d7f7953bb996e6912d2a6447f200a10b3f481d4648d70f97ed22","access_level":"public","create_time":"$D2022-01-05T22:45:59.145Z","update_time":"$D2022-10-28T18:12:18.400Z","view_time":null,"first_public_time":"$D2022-01-06T19:55:54.156Z","has_unpublished_edits":null,"fork":false,"stars":12,"starred":false,"owner":{"type":"team","id":"31b136fdb993b00a","login":"visnup","name":"Visnu Pitiyanuvath","avatar_url":"https://avatars-next.observableusercontent.com/b847c4c49993b1df7599d355f47dc0ad9c2dcf43439ce9e8f3410e6368b3aac9","tier":"pro_2026","bio":"","following":false},"version":972,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"dbf69c13a14d2f62","login":"visnup","name":"Visnu Pitiyanuvath","avatar_url":"https://avatars-next.observableusercontent.com/b847c4c49993b1df7599d355f47dc0ad9c2dcf43439ce9e8f3410e6368b3aac9","tier":null,"bio":"","following":false}],"members":[{"type":"individual","id":"a5fdadb4f37b47fb","login":"sydneypalumbo","name":"Sydney Palumbo","avatar_url":"https://avatars-next.observableusercontent.com/3f2e6c40978504365fadc747404e7639e1fdee225ac480c0adb1ee0e60df0fc0","tier":null,"role":"editor"},{"type":"individual","id":"dbf69c13a14d2f62","login":"visnup","name":"Visnu Pitiyanuvath","avatar_url":"https://avatars-next.observableusercontent.com/b847c4c49993b1df7599d355f47dc0ad9c2dcf43439ce9e8f3410e6368b3aac9","tier":null,"role":"editor"}],"comments":[{"id":"a7c837daca53aff8","reply_to_id":null,"content":"I was minutes away from suggesting an update to this with the NYT words, but then saw you just uploaded the new file!","create_time":"$D2022-02-18T01:37:48.757Z","update_time":null,"resolved":true,"user":{"type":"individual","id":"2a6984a21bf6bf27","login":"rlesser","name":"Robert Lesser","avatar_url":"https://avatars-next.observableusercontent.com/433f8326248db53a8d1ead342dfc4d46c845f915b422b6e7f6690ced0f18abd2","tier":null}},{"id":"ee440ccb2bcf2ad9","reply_to_id":"a7c837daca53aff8","content":"Hah. Yes. And @1 was a broken attempt due to a trailing comma.","create_time":"$D2022-02-18T01:39:51.286Z","update_time":null,"resolved":true,"user":{"type":"individual","id":"dbf69c13a14d2f62","login":"visnup","name":"Visnu Pitiyanuvath","avatar_url":"https://avatars-next.observableusercontent.com/b847c4c49993b1df7599d355f47dc0ad9c2dcf43439ce9e8f3410e6368b3aac9","tier":null}}],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":8,"collection":{"id":"6085998240bbe5d6","slug":"games/2","title":"Games","owner":{"id":"31b136fdb993b00a","login":"visnup","name":"Visnu Pitiyanuvath"}},"type":"notebook","body":{"titling":"auto","title":"Wordle","cells":[{"id":0,"value":"# Wordle\n## Just tell me what to guess already!\n\nInspired by [Mike](/@mbostock/cheat-at-wordle) and [Graham](/@iamgrahamallen/wordle-solver-exploration), a way to “augment” [Wordle](https://www.nytimes.com/games/wordle)-guessing… by just telling you what you should guess next. _Update: latest version is slower, but better._\n\nRecord gray letters as you see them. Record specific yellow and green letters in their corresponding boxes. You can add multiple yellow letters in each positional box, which you definitely want to do.\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":297,"value":"viewof green = reset, input(\n htl.html`green`\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":282,"value":"viewof yellow = reset, input(\n htl.html`yellow`\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"viewof grayInput = reset, Inputs.text({\n label: htl.html`gray`,\n spellcheck: false,\n autocomplete: false\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":326,"value":"match = new RegExp(\n d3\n .zip(green, yellow)\n .map(([g, y]) => (g ? g[0] : y ? `[^${y}]` : \".\"))\n .join(\"\")\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":332,"value":"viewof reset = Inputs.button(\"Reset\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":408,"value":"{\n if (answers.length === 0) return md`## _No answer based on your inputs._ 🤨`;\n if (answers.length <= 2) return md`## Answer: ${answers.join(\" or \")} 💡`;\n const combined = scored.concat(ranked).sort((a, b) => b.score - a.score);\n const top = [...new Set(combined\n .filter((d) => d.score === combined[0].score)\n .map((d) => d.word))];\n return top.length > 1\n ? md`## Guess: ${top.slice(0, -1).join(\", \")}, or ${top[top.length - 1]} 🤔`\n : md`## Guess: ${top} 🤔`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":505,"value":"👆 As we get more information, the next best guesses will update.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":717,"value":"viewof algorithm = Inputs.select(\n [\n { label: \"Eliminates the most (slower, but better)\", value: \"delta\" },\n { label: \"Frequency-based\", value: \"frequency\" }\n ],\n { label: \"Algorithm\", format: (d) => d.label }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"#### Informational guesses\nOr if you think you know better, feel free to pick from these good guesses. ${algorithm.value === \"delta\" ? `The score is interpretable as the average percentage of remaining answers the guess will eliminate.` : \"\"}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":606,"value":"Inputs.table(ranked, { rows: 5 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":84,"value":"ranked = {\n const ranked = words.allowed\n .map((word) => ({ word, score: frequencyScore(word) }))\n .filter(({ score }) => score)\n .sort((a, b) => b.score - a.score);\n const sample = 75_000 / answers.length;\n return algorithm.value === \"frequency\"\n ? ranked\n : ranked\n .map(({ word, score }, i) =>\n i < sample\n ? {\n word,\n score: eliminationScore(word),\n _score: score\n }\n : { word, score: null, _score: score }\n )\n .sort((a, b) => b.score - a.score);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":118,"value":"#### Possible answers\n${answers.length.toLocaleString()} (${((answers.length / words.answers.length) * 100).toFixed(0)}%) left!\nIf you’re feeling lucky, you can start guessing actual answers too. ${algorithm.value === \"delta\" ? `Interestingly, answers as guesses get a score boost in that if it luckily _is_ the answer it eliminates the rest of the possibilities immediately.` : \"\"}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":115,"value":"Inputs.table(scored, { rows: 5 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":445,"value":"scored = {\n const scored = answers\n .map((word) => ({ word, score: frequencyScore(word) }))\n .sort((a, b) => b.score - a.score);\n const sample = 50_000 / answers.length;\n return algorithm.value === \"frequency\"\n ? scored.map(({ word, score }) => ({ word, score: score + 1 })) // break ties in favor of answers when suggesting in frequency mode\n : scored\n .map(({ word, score }, i) =>\n i < sample\n ? {\n word,\n score: eliminationScore(word),\n _score: score\n }\n : { word, score: null, _score: score }\n )\n .sort((a, b) => b.score - a.score);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":474,"value":"Letter frequency distribution for the remaining possible answers.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":22,"value":"Plot.barX(frequencies, {\n x: \"1\",\n y: \"0\",\n fill: ([l]) =>\n green.join(\"\").includes(l)\n ? \"#6baa64\"\n : yellow.join(\"\").includes(l)\n ? \"#c9b458\"\n : \"black\",\n sort: { y: \"x\", reverse: true }\n}).plot({\n y: { label: null },\n x: { label: \"Frequency →\", grid: true },\n color: { type: \"identity\" }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":832,"value":"### Scoring\nHow much new information can we get from a guess?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":771,"value":"__eliminationScore__ looks ahead and simulates the number of answers which would be removed across all remaining answers. Then we can pick the guess that would, on average, remove the most possible answers.\n\nThis is slow, so requires memoizing and slows down the UI too much if we want to be exhaustive (or until I can optimize it more). We run it on a sample of guesses prioritized by frequencyScore below.\n\nIf I did this exhaustively, it’d [average 3.49 guesses per game](https://medium.com/@tglaiel/the-mathematically-optimal-first-guess-in-wordle-cbcb03c19b0a) to win.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":540,"value":"$46","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":616,"value":"cache = answers, new d3.InternMap([], JSON.stringify)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"__frequencyScore__ is based on a frequency heuristic: the more intersection between unknown letters in the remaining possible answers and the guess, the more likely it’ll yield change.\n\nIdeally: An unknown letter is best. A known letter in a different place is ok. A second letter (for letters that occur more than once) is ok too. Frequent letters among remaining possible answers are more important than infrequent.\n\nThis simple version below gets us an average of [about 3.6 guesses per game](/@visnup/wordle-algorithms) to win.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":126,"value":"frequencyScore = (word) =>\n Array.from(new Set(word))\n .map((l) => (include.has(l) ? 0 : frequencies.get(l)) || 0)\n .reduce((sum, s) => sum + s)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"frequencies = d3.rollup(\n answers.flatMap((w) => Array.from(w)),\n (r) => r.length,\n (d) => d\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":900,"value":"The remaining set of possible answers based on the information we have so far:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":49,"value":"answers = {\n const exclude = new Set(gray);\n return words.answers.filter(\n (w) =>\n w.match(match) &&\n d3.every(include, (l) => w.includes(l)) &&\n d3.every(w, (l) => !exclude.has(l))\n );\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":62,"value":"include = new Set(yellow.concat(green).flatMap(l => Array.from(l)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":693,"value":"gray = grayInput.toUpperCase()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":384,"value":"All words come from the Wordle site. The first line in the CSV are possible answers. The second line are other acceptable words (for guessing with), but they’re never chosen as a daily solution.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":171,"value":"words = {\n const text = await FileAttachment(\"words@2.csv\").text();\n const [answers, allowed] = text\n .trim()\n .toUpperCase()\n .split(\"\\n\")\n .map((line) => line.split(\",\"));\n return { answers, allowed: allowed.concat(answers) };\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":939,"value":"Curious about the difference between NY Time’s word list and the original.\n\nRemoved answers: ${new Intl.ListFormat().format(difference.answers)}.\n\nRemoved allowed: ${new Intl.ListFormat().format(difference.allowed)}.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":937,"value":"wordsOld = {\n const text = await FileAttachment(\"words.csv\").text();\n const [answers, allowed] = text\n .trim()\n .toUpperCase()\n .split(\"\\n\")\n .map((line) => line.split(\",\"));\n return { answers, allowed: allowed.concat(answers) };\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":946,"value":"difference = {\n const answers = new Set(words.answers);\n const allowed = new Set(words.allowed);\n return {\n answers: wordsOld.answers.filter((w) => !answers.has(w)),\n allowed: wordsOld.allowed.filter((w) => !allowed.has(w))\n };\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":226,"value":"function input(label) {\n const form = htl.html`\n \n `;\n form.value = new Array(5).fill(\"\");\n\n return form;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":521,"value":"mobile = matchMedia(\"(max-width: 640px)\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":896,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":518,"value":"import {matchMedia} from \"@mootari/match-media\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W47","stdlib":"1"}} 45:"$44:body"