31:T726,{ const height = 600; const grayScale = d3.scaleSequential( colorScale.domain(), d3.interpolateGreys ); const scale = { x: d3 .scaleBand([...Array(5).keys()], [margin.left, width - margin.right]) .padding(0.05), y: d3 .scaleBand( data.map((d) => d.letter), [height - margin.bottom, margin.top] ) .padding(0.05), color: (d, i) => { if (order === "Alphabetical order") return colorScale(d); return orderToIndex(order.split(" ")[0]) === i ? colorScale(d) : grayScale(d); } }; const svg = d3 .create("svg") .attr("width", width) .attr("height", height) .attr("viewBox", [0, 0, width, height]); // Draw x-axis svg .append("g") .attr("transform", `translate(0, ${margin.top})`) .call(d3.axisTop(scale.x).tickFormat(numToRank)); // Draw y-axis svg .append("g") .attr("transform", `translate(${margin.left}, 0)`) .call(d3.axisLeft(scale.y)); // Draw heatmap svg .selectAll("g.heatmap") .data(data) .join("g") .attr("transform", (d) => `translate(0, ${scale.y(d.letter)})`) .selectAll("rect") .data((d) => d.position) .join("rect") .attr("x", (d, i) => scale.x(i)) .attr("width", scale.x.bandwidth()) .attr("height", scale.y.bandwidth()) .attr("fill", scale.color) .append("title") .text((d) => `${fmt(d * 100)}%`); svg .append("text") .attr("transform", `translate(${width / 2}, 10)`) .attr("text-anchor", "middle") .attr("style", "font-family:sans-serif;font-size:10px") .text("Letter position"); svg.selectAll("path").remove(); return svg.node(); function orderToIndex(order) { var options = ["First", "Second", "Third", "Fourth", "Last"]; return options.indexOf(order); } }32:T780,md` After solving my first Wordle puzzle in two guesses, I'm now convinced that the best strategy is to get really lucky with your first word. One way to get really lucky is to pick letters with a high probability of being in an answer. A few posts on Wordle strategy across the internet discuss where you should place specific letters, and the visualization above can evaluate these claims. * ### Play *T*, *A*, *O*, *D*, or *W* as your first letter ["How to Win at Wordle," *Forbes*](https://www.forbes.com/sites/erikkain/2022/01/25/how-to-win-at-wordle-tips-and-tricks-to-succeed-at-the-viral-puzzle-game)
When sorting by first letter, most of these letters are suboptimal choices, with the exception of *T* (${calcFreq( "T", 1 )}) and *A* (${calcFreq("A", 1)}). But starting with *O* (${calcFreq( "O", 1 )}) tends to be overvalued. * ### Don't play *S* as your last letter [Nate Silver, Twitter](https://twitter.com/NateSilver538/status/1483101987285700608)
When sorting by last letter, *S* (${calcFreq( "S", 5 )}) is not the most probable ending letter, but it does happen. There are truely worse options. *J*, *Q*, and *V* are in a three-way tie for last place with 0%. * ### Play *E*, *S*, *D* and *T* as your last letter ["How to Win at Wordle," *Forbes*](https://www.forbes.com/sites/erikkain/2022/01/25/how-to-win-at-wordle-tips-and-tricks-to-succeed-at-the-viral-puzzle-game)
Finishing with *E* (${calcFreq("E", 5)}) and *T* (${calcFreq( "T", 5 )}) tend to be good bets, but there are many better options than *D* (${calcFreq( "D", 5 )}). We've already covered words that end with *S* (${calcFreq("S", 5)}). * ### Play *S* as your first letter ["How to crack Wordle," *Polygon*](https://www.polygon.com/gaming/22884031/wordle-game-tips-best-first-guess-5-letter-words)
When sorting by first letter, this is actually good advice, *S* (${calcFreq( "S", 1 )}). `33:T4c6,data = { const min = (future ? wordleDay : 1) - 1; const words = answerWords.map(atob).slice(min); const letters = words .map((word) => Array.from(word).map((l, i) => ({ pos: i, letter: l }))) .reduce((prev, curr) => [...prev, ...curr]); return Array.from( d3.group(letters, (d) => d.letter), ([key, vals]) => { const wordMatches = d3.sum(words.map((word) => word.includes(key))); const posFreq = [...Array(5).keys()] .map((i) => d3.group(vals, (d) => d.pos).get(i) || Array()) .map((arr) => arr.length / letters.length); return { letter: key, position: posFreq }; } ).sort((a, b) => { switch (order) { case "Alphabetical order": return d3.descending(a.letter, b.letter); case "First letter": return d3.ascending(a.position[0], b.position[0]); case "Second letter": return d3.ascending(a.position[1], b.position[1]); case "Third letter": return d3.ascending(a.position[2], b.position[2]); case "Fourth letter": return d3.ascending(a.position[3], b.position[3]); case "Last letter": return d3.ascending(a.position[4], b.position[4]); } }); }34:[{"id":"d5dc01f4c6840919e81d009c863d6489ad829e3a4fad8974fd4c2aa72b4c3e28659cdff7588f051f7ad52f4594b6d5b1b13b8c2ac97725c6688c7d547ea4e8cb","href":"https://static.observableusercontent.com/files/d5dc01f4c6840919e81d009c863d6489ad829e3a4fad8974fd4c2aa72b4c3e28659cdff7588f051f7ad52f4594b6d5b1b13b8c2ac97725c6688c7d547ea4e8cb","name":"wordle.csv","type":"text/csv","lastModified":1645309347388.159,"size":391619}] 2f:{"title":"Letter-Position Frequency in Wordle","cells":[{"id":0,"value":"

Spoiler alert!
This notebook discusses the frequency letters in past Wordle puzzles, but it does not reveal any answers.

\n\n# Letter-Position Frequency in Wordle
\nFrequency of letters by position in ${(future) ? \"future\" : \"past\"} Wordle answers.
\nData: [Wordle source code](https://www.powerlanguage.co.uk/wordle/main.e65ce0a5.js)","pinned":false,"hidden":false,"mode":"md"},{"id":18,"value":"viewof order = Inputs.select(\n [\n \"Alphabetical order\",\n \"First letter\",\n \"Second letter\",\n \"Third letter\",\n \"Fourth letter\",\n \"Last letter\"\n ],\n {\n label: \"Sort by\"\n }\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":12,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":58,"value":"html`

${Legend(colorScale, {\n title: \"Letter frequency\",\n width: width - margin.right - margin.left,\n tickFormat: (t) => `${fmt(t * 100)}%`\n})}

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":68,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":32,"value":"## Danger zone\n\nWhile this notebook only looks at past Wordle answers, checking the Future mode box below will perform the same calculations based on all the words in *future* answers.","pinned":false,"hidden":false,"mode":"md"},{"id":115,"value":"viewof future = Inputs.toggle({ label: \"Future mode\" })","pinned":false,"hidden":false,"mode":"ojs"},{"id":309,"value":"## About this dataset\n\nThe Wordle word list and solutions comes from Wordle's source code, before *The New York Times* purchase. The specific data processing pipeline can be found [on GitHub](https://github.com/swkasica/wordle-words).","pinned":false,"hidden":false,"mode":"md"},{"id":164,"value":"

","pinned":false,"hidden":false,"mode":"html"},{"id":123,"value":"wordleDay = Math.floor(\n (new Date().getTime() - new Date(2021, 5, 19).getTime()) /\n (1000 * 60 * 60 * 24)\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":40,"value":"function numToRank(i) {\n const positions = [\"1st\", \"2nd\", \"3rd\", \"4th\", \"5th\"];\n return positions[i];\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":24,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":86,"value":"frequencies = new Map(\n data.map((d) => [d.letter, new Map(d.position.map((d, i) => [i + 1, d]))])\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":94,"value":"function calcFreq(letter, position) {\n return `${fmt(frequencies.get(letter).get(position) * 100)}%`;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":61,"value":"colorScale = d3.scaleSequential(\n [\n 0,\n d3.max(data, (d) => d.position.reduce((prev, curr) => d3.max([prev, curr])))\n ],\n d3.interpolateBlues\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":79,"value":"answerWords = (await FileAttachment(\"wordle.csv\").csv())\n .filter((d) => d.day)\n .map((d) => btoa(d.word.toUpperCase()))\n// answerWords = (await FileAttachment(\"wordle.js\").text())\n// .split(\"\\n\")[1117]\n// .slice(13)\n// .replace(/\\\"|\\s|\\[|\\]/g, \"\")\n// .toUpperCase()\n// .split(\",\")\n// .map(btoa)","pinned":false,"hidden":false,"mode":"ojs"},{"id":302,"value":"margin = ({ top: 40, left: width / 3, bottom: 0, right: width / 3 })","pinned":false,"hidden":false,"mode":"ojs"},{"id":15,"value":"fmt = d3.format(\"0.2f\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":64,"value":"import { Legend } from \"@d3/color-legend\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}