2d:null 2e:["$","title",null,{"children":"Guessing Wordles (96% Success) | Michael Deagen | Observable"}] 33:Te83,# Guessing Wordles (96% Success) *If you haven't yet played [Wordle](https://www.powerlanguage.co.uk/wordle/), stop reading and go play it now!* ## Highlights * A heuristic algorithm based on **word-frequency** significantly outperforms other heuristics in terms of **mean number of guesses** and **overall success rate**. * This heuristic assumes that the true (unknown) set of 2,500 Wordle solutions is **non-random** and **skewed toward commonly occurring 5-letter words**. * The word-frequency heuristic achieves a **96.4% success rate** on a hypothetical set of 2,500 "common" 5-letter words, compared to the 85% success rate of a position + letter heuristic that assumes a random distribution of words. ## Introduction [Another Observable notebook](https://observablehq.com/@iamgrahamallen/wordle-solver-exploration), by [@iamgrahamallen](https://observablehq.com/@iamgrahamallen), explores heuristics and algorithms for solving the recently trending word game [Wordle](https://www.powerlanguage.co.uk/wordle/), and the best-performing heuristic takes into account the frequency of letters at each of the 5 positions in the solution word (referred to here as the *letter + position heuristic*). The [sequel to that notebook](https://observablehq.com/@iamgrahamallen/wordle-solver-exploration-part-2) provides another great analysis of even more heuristics. To solve the challenge is as few steps as possible, the goal is to *maximize the information gained at each step.* A drawback of the letter + position heuristic algorithm is that it can get stuck trying to pick between words with the same heuristic score as the candidate words are narrowed down (the algorithm still has an impressive ~85% success rate by considering letter and position compared to 79% when considering only letter frequency, but a uniform random heuristic is ~83%). In an [interview in the New York Times](https://www.nytimes.com/2022/01/03/technology/wordle-word-game-creator.html), Wordle's creator, Josh Wardle—a former Reddit engineer who created [The Button](https://www.vox.com/2015/4/10/8383165/reddit-button-explained)—mentioned that his partner helped to *narrow down the original list of 12,000 5-letter English words to about 2,500 that she recognized.* This turns out to be an important piece of information that we can try to incorporate into our algorithm. This notebook is purely based on analysis of historic Wordle data. If you want a tool to help you win at Wordle (*highly discouraged because it ruins the fun!*), check out the recent notebooks by [@mbostock](https://observablehq.com/@mbostock/cheat-at-wordle) or [@visnup](https://observablehq.com/@visnup/cheat-at-wordle). ## Methodology Here, we will try to further improve the odds of solving Wordle *in as few steps as possible* by considering **word frequency** (defined as the number of occurrences per million English words). The list of 5-letter words, sorted by frequency, is imported from [this notebook](https://observablehq.com/@mdeagen/datamuse-api-example), which used the [Datamuse API](https://www.datamuse.com/api/) to collect word frequencies. ## Results We explore the hypothesis that *words chosen for Wordle have higher word-frequency scores,* then compare the word-frequency heuristic against the letter + position heuristic by evaluating performance against prior Wordle solutions as well as hypothetical sets of 2,500 words (one random and one with common words). ### *Preliminary Analysis of Past Wordle Solutions* First, we can take a quick glance at [this year's Wordle solutions so far](https://screenrant.com/wordle-answers-updated-word-puzzle-guide/) to see how these words rank in our frequency-sorted collection.34:T436,### *Extrapolating the Evaluation* Assuming 2,500 5-letter Wordle solutions exist, and solutions are not repeated, we can expect ${(2500/365.25).toFixed(2)} years of daily enjoyment of Wordle (until around fall 2028). To compare heuristic algorithms on a larger sample, we will test on two hypothetical word lists of 2,500. One is a **random** selection, and the other contains **common** words to reflect our underlying assumption that frequently-occurring words were preferentially selected to improve game playability. On each hypothetical set of 2,500 words, we will compare the heuristics: **2** sets × **2** heuristics = **4** experiments! 👩‍🔬 For the "common" words, we will use a slice of the frequency-sorted list, taking the 501^st to 3000^th words. The performance of the heuristic diminishes the further down the list you go, but this cut-off is consistent with the ranks of prior Wordle solutions. The arrays below show the common and random word sets used in these experiments, and the full results of each experiment are attached.35:T733,## Discussion The sample size for evaluation is small at this point, but the initial results indicate that the *word-frequency heuristic likely outperforms the letter + position heuristic on actual Wordle solutions.* Essentially, we are discarding the assumption that Wordle solutions are randomly drawn from the full list of 12k words, and that there is a bias toward more-frequent words (to increase game playability). Instead of using win-percentage as the only heuristic, it is also helpful to look at the average number of guesses required to get to the solution. The letter + position heuristic is less deterministic than the word-frequency heuristic due to ties in heuristic scores. For example, the Jan. 2, 2021 Wordle solution (*boost*) ranges from 4 guesses (*sores bousy boast boost*) to a mere 2 guesses (*sores boost*). On a small sample set, this non-deterministic behavior impacts the mean number of guesses and occasionally makes a difference between a win/loss. Another interesting thing to note is how the word-frequency heuristic algorithm has an 84% success rate on the random word set. While the results will vary based on the randomly samples words, it is in between the success rate of the letter + position heuristic on the random words and common words. In any event, these results are comparable with the uniform-random heuristic mentioned by [@iamgrahamallen](https://observablehq.com/@iamgrahamallen/wordle-solver-exploration-part-2). This approach incorporates a lot of external information to reach its success rate, such as the interview in the New York Times suggesting that the words were manually selected. Additionally, the [Datamuse API](https://www.datamuse.com/api/) made it possible to easily collect word frequencies [in a separate notebook](https://observablehq.com/@mdeagen/datamuse-api-example).36:T78b,## Conclusion This notebook would not be possible without helper functions from [@iamgrahamallen](https://observablehq.com/@iamgrahamallen) and of course the Wordle game itself by Josh Wardle. The heuristic assumes that the underlying set of Wordle solutions roughly follows the list of most frequently-occurring 5-letter words in English, and with this heuristic we can get a 96.4% success rate on the algorithm from a test set of common words. Despite the high success rate of this "simple" word-frequency heuristic, I still find [@iamgrahamallen's](https://observablehq.com/@iamgrahamallen/wordle-solver-exploration) letter + position heuristic more satisfying in how it intentionally maximizes information based on the narrowed-down words at each step. I am curious to see how the mean guess rate can be further reduced, perhaps by considering some weighted combination of frequency and another heuristic (such as letter + position). Also, the relatively high performance of the [uniform random heuristic](https://observablehq.com/@iamgrahamallen/wordle-solver-exploration-part-2) is worth further exploration. Perhaps "wasting" the first couple guesses in order to maximize coverage of letters would result in a greater probability of overall success? (Reminiscent of the [Monty Hall problem](https://en.wikipedia.org/wiki/Monty_Hall_problem)...) To import the set of words with frequencies, feel free to include the following code cell in your notebook: ~~~js import {word_array} from '@mdeagen/datamuse-api-example' ~~~ The array is sorted by frequency (descending order) using: ~~~js word_array.map(x => ({word: x.word, freq: Number(x.f)})).sort((a, b) => (a.freq < b.freq) ? 1 : -1) ~~~ I hope this analysis has been helpful and/or interesting. Lots of thanks to the members of the Observable community who have also been drawn to this fun statistical problem, and I look forward to seeing where future analyses go!37:T8c1,VLspec = ({ "$schema": "https://vega.github.io/schema/vega-lite/v5.json", "hconcat": [ { "layer": [ { "height": width*0.3, "width": width*0.4, "transform": [ {"calculate": "datum.count - 0.45", "as": "bar_start"}, {"calculate": "datum.count + 0.45", "as": "bar_end"} ], "mark": {"type": "bar"}, "encoding": { "x": {"field": "bar_start", "type": "quantitative", "title": "Score (Number of Guesses)"}, "x2": {"field": "bar_end"}, "y": {"aggregate": "count", "title": null} } }, { "mark": {"type": "rule", "size": 2, "color": "firebrick"}, "encoding": { "x": {"aggregate": "mean", "field": "count"} } }, { "mark": {"type": "text", "xOffset": width*0.02, "align": "left", "yOffset": -width*0.12, "fontSize": 16, "color": "firebrick"}, "encoding": { "x": {"aggregate": "mean", "field": "count"}, "text": {"aggregate": "mean", "field": "count", "format": ".5r"} } } ] }, { "transform": [ {"calculate": "datum.count <= 6 ? 'WIN' : 'LOSE'", "as": "result"} ], "layer": [ { "height": width*0.3, "width": width*0.3, "mark": "arc", "encoding": { "color": {"field": "result", "type": "nominal", "scale": {"domain": ["WIN", "LOSE"]}, "title": "Outcome"}, "theta": {"aggregate": "count"} } }, { "transform": [ {"joinaggregate": [{"op": "count", "as": "total"}]}, {"filter": "datum.result == 'WIN'"}, {"joinaggregate": [{"op": "count", "as": "successes"}], "groupby": ["result"]}, {"calculate": "datum.successes / datum.total", "as": "successRate"}, {"sample": 1} ], "mark": {"type": "text", "color": "white", "fontSize": 24, "yOffset": width*0.05}, "encoding": { "text": {"field": "successRate", "type": "quantitative", "format": ".4p"} } } ] } ], "config": {"concat": {"spacing": 2}} })38:[{"id":"98840610f1ffe763781db5badc7efd77b7631399854a6df22493fa92b68414c733c99bcb00d9e89df7dfa4083bc49784a37068c60ed5f612a0e5d3e84630dcf2","href":"https://static.observableusercontent.com/files/98840610f1ffe763781db5badc7efd77b7631399854a6df22493fa92b68414c733c99bcb00d9e89df7dfa4083bc49784a37068c60ed5f612a0e5d3e84630dcf2","name":"heuristicTest_Freq_common.json","type":"application/json","lastModified":1641510467383.208,"size":178396},{"id":"7cf42a4fb9c4cfdfc95efd17952f6d2e56751d3c0bbc009aa9323b76faf40753136da6a890309bf230ee243d4a519cf47475219c4f7a263034e468459f3b29e4","href":"https://static.observableusercontent.com/files/7cf42a4fb9c4cfdfc95efd17952f6d2e56751d3c0bbc009aa9323b76faf40753136da6a890309bf230ee243d4a519cf47475219c4f7a263034e468459f3b29e4","name":"heuristicTest_Freq_random.json","type":"application/json","lastModified":1641508354521.781,"size":188984},{"id":"e6f0b2ed4f51849e1be05e394861c6bba079d628200c28b068956460c2abb3c5627dd073d0c96a9be31232ae28778bad35d0cf7ecb200571fe65ebe5ec50dcb4","href":"https://static.observableusercontent.com/files/e6f0b2ed4f51849e1be05e394861c6bba079d628200c28b068956460c2abb3c5627dd073d0c96a9be31232ae28778bad35d0cf7ecb200571fe65ebe5ec50dcb4","name":"heuristicTest_LP_common.json","type":"application/json","lastModified":1641510476187.597,"size":187000},{"id":"dabee7f45bf2c47c2dd65194ddcd74ff066d6c147964cf30da125a3c0ef910502a17d6723e5e721ab859b8579e39555268aa07565212c72ae095c30175d01a9d","href":"https://static.observableusercontent.com/files/dabee7f45bf2c47c2dd65194ddcd74ff066d6c147964cf30da125a3c0ef910502a17d6723e5e721ab859b8579e39555268aa07565212c72ae095c30175d01a9d","name":"heuristicTest_LP_random.json","type":"application/json","lastModified":1641510473057.841,"size":185675}] 31:{"id":"cfedf73b7daa7bb5","slug":"guessing-wordles-96","title":"Guessing Wordles (96% Success)","thumbnail":"e932ba7b8ad1c5701b8903e6008f3dd30e94b9e72337b673fa4f2983baa22596","access_level":"public","create_time":"$D2022-01-05T18:45:26.211Z","update_time":"$D2022-02-09T12:06:28.519Z","view_time":null,"first_public_time":"$D2022-01-06T23:51:55.069Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"5ca8a3812ea4a326","login":"mdeagen","name":"Michael Deagen","avatar_url":"https://avatars-next.observableusercontent.com/0b8e876e2eac1058faa6c1a2624346f3e72350b8a7e6c9acaec6a9ad920b0476","tier":"starter_2024"},"version":891,"publish_version":891,"role":null,"authored":false,"authors":[{"type":"individual","id":"d3611c0325cb99e9","login":"mdeagen","name":"Michael Deagen","avatar_url":"https://avatars-next.observableusercontent.com/0b8e876e2eac1058faa6c1a2624346f3e72350b8a7e6c9acaec6a9ad920b0476","tier":null}],"members":[{"type":"individual","id":"d3611c0325cb99e9","login":"mdeagen","name":"Michael Deagen","avatar_url":"https://avatars-next.observableusercontent.com/0b8e876e2eac1058faa6c1a2624346f3e72350b8a7e6c9acaec6a9ad920b0476","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":3,"collection":null,"type":"notebook","body":{"title":"Guessing Wordles (96% Success)","cells":[{"id":0,"value":"$33","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":47,"value":"answers_2022 = [\"rebus\", \"boost\", \"truss\", \"siege\", \"tiger\", \"banal\", \"slump\", \"crank\", \"gorge\", \"query\", \"drink\", \"favor\", \"abbey\", \"tangy\", \"panic\", \"solar\", \"shire\", \"proxy\", \"point\", \"robot\", \"prick\", \"wince\", \"crimp\", \"knoll\", \"sugar\", \"whack\", \"mount\", \"perky\", \"could\", \"wrung\", \"light\", \"those\", \"moist\", \"shard\", \"pleat\", \"aloft\", \"skill\", \"elder\", \"frame\"]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"Inputs.table(ranks, {width: 350})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":55,"value":"As we might have guessed, these past solutions happen to be ranked highly in terms of frequency, appearing in the top quadrant or so of our frequency-sorted word list.\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":717,"value":"vl.render({spec: VLspec_tick})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":747,"value":"Hover over a red tick mark to view a tooltip with the word as well as its percentile and rank. This distribution looks *non-random* and *skewed toward words with higher frequencies*, central to the assumption of the heuristic algorithm we'll explore.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":257,"value":"### *Comparing Heuristics on Prior Wordle Solutions*\n\nLet's examine the performance of the **letter + position heuristic** algorithm (imported from [@iamgrahamallen's notebook](https://observablehq.com/@iamgrahamallen/wordle-solver-exploration)) against the recent Wordle solutions. This is the previous best algorithm, with an overall success rate of about 85%.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":274,"value":"Inputs.table(simulatePreviousAnswers_LP, {width: {solution: 70, count: 50}})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":309,"value":"printSimulationResults(simulatePreviousAnswers_LP, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":843,"value":"The letter + position heuristic uses random selection when there is a tie for the top score. Click the button below to redo the simulation.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":845,"value":"viewof resetLPButton = Inputs.button(\"Run Simulation Again\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":187,"value":"What happens if we ignore the letter + position information entirely and instead use a **word-frequency heuristic**, where we just select the available word with the highest word-frequency score at each iteration of guesses?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":245,"value":"Inputs.table(simulatePreviousAnswers_Freq, {width: {solution: 70, count: 50}})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":322,"value":"printSimulationResults(simulatePreviousAnswers_Freq, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":531,"value":"The sample set of known Wordle solutions is small (for now), so we will have to create our own hypothetical test sets to compare these heuristic algorithms at scale.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":415,"value":"$34","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":431,"value":"words_common = words_freq.slice(500,3000).map(x => x.word)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":427,"value":"words_random = expt2.map(x => x.solution)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":609,"value":"#### *Experiment 1: Word-Frequency Heuristic [Common Words]*\n\nThis experiment applied the **word-frequency heuristic** to the list of 2,500 **common words**. The results are attached to the notebook and summarized in the Vega-Lite chart below. The vertical red line shows the average (mean) number of guesses.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":595,"value":"plotVegaLite(expt1, \"#1: Word-Frequency Heuristic (Set of Common Words)\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":576,"value":"#### *Experiment 2: Word-Frequency Heuristic [Random Words]*\n\nHere, the **word-frequency heuristic** is applied to the list of 2,500 **random words**.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":654,"value":"plotVegaLite(expt2, \"#2: Word-Frequency Heuristic (Set of Random Words)\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":579,"value":"#### Experiment 3: Letter + Position Heuristic [Common Words]\n\nNow we evaluate the **letter + position heuristic** against the 2,500 **common words**.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":658,"value":"plotVegaLite(expt3, \"#3: Letter + Position Heuristic (Set of Common Words)\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":582,"value":"#### Experiment 4: Letter + Position Heuristic [Random Words]\n\nFinally, the **letter + position heuristic** against the 2,500 **random words**.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":659,"value":"plotVegaLite(expt4, \"#4: Letter + Position Heuristic (Set of Random Words)\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":338,"value":"$35","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":554,"value":"$36","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":37,"value":"---\n\n## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":3,"value":"import {defaultWordsByLetterAndPositionHeuristic, narrowDownWords, wordsByHeuristic, calculateOutcome, evaluateLetterAndPositionHeuristic, words} from '@iamgrahamallen/wordle-solver-exploration'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"import {word_array} from '@mdeagen/datamuse-api-example'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":50,"value":"ranks = answers_2022.map(x => ({word: x, rank: words_freq.findIndex(y => y.word == x)})).map(x => ({...x, percentile: x.rank/words_freq.length*100}))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":716,"value":"VLspec_tick = ({\n \"$schema\": \"https://vega.github.io/schema/vega-lite/v5.json\",\n \"data\": {\"values\": ranks},\n \"layer\": [\n {\n \"params\": [\n {\"name\": \"zoom\", \"select\": \"interval\", \"bind\": \"scales\", \"encodings\": [\"x\"]}\n ],\n \"height\": width*0.15,\n \"mark\": {\"type\": \"bar\", \"color\": \"gray\", \"opacity\": 0.3},\n \"encoding\": {\n \"x\": {\"field\": \"rank\", \"type\": \"quantitative\", \"bin\": {\"extent\": {\"param\": \"zoom\"}}},\n \"y\": {\"aggregate\": \"count\"}\n }\n },\n {\n \"width\": width*0.8,\n \"mark\": {\"type\": \"tick\", \"color\": \"firebrick\", \"thickness\": 2},\n \"encoding\": {\n \"x\": {\"field\": \"rank\", \"type\": \"quantitative\", \"scale\": {\"domain\": [0,12000]}, \"title\": \"← Higher Word-Frequency Scores\"},\n \"tooltip\": [\n {\"field\": \"word\", \"type\": \"nominal\", \"title\": \"Word\"},\n {\"field\": \"rank\", \"type\": \"quantitative\", \"title\": \"Rank\"},\n {\"field\": \"percentile\", \"type\": \"quantitative\", \"title\": \"Percentile\", \"format\": \".5r\"}\n ]\n }\n }\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"words_LP = defaultWordsByLetterAndPositionHeuristic.sort((a, b) => (a.score < b.score) ? 1 : -1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"words_freq = word_array.map(x => ({word: x.word, freq: Number(x.f)})).sort((a, b) => (a.freq < b.freq) ? 1 : -1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":209,"value":"frequencyOnlyHeuristic = (narrowedWords) => {\n return (word) => {\n let x = words_freq.find(y => y.word === word);\n if(x === undefined) {\n return 0\n } else return x.freq\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":238,"value":"simulatePreviousAnswers_Freq = games(answers_2022, words_freq.map(x => x.word), frequencyOnlyHeuristic)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":265,"value":"simulatePreviousAnswers_LP = {\n resetLPButton;\n return games(answers_2022, words_LP.map(x => x.word), evaluateLetterAndPositionHeuristic)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":227,"value":"// adapted from @iamgrahamallen's notebook\n\nfunction simulateGame(goal, defaultWords, heuristic) { \n const calculateOutcomeForGuess = calculateOutcome(goal);\n let narrowedWords = words;\n //let guess = d3.shuffle(defaultWords)[0];\n let guess = defaultWords[0];\n let guesses = [guess];\n\n let i = 0;\n while (guess != goal && i < 100) {\n narrowedWords = narrowDownWords(\n guess,\n calculateOutcomeForGuess(guess),\n narrowedWords\n );\n const wordsToGuess = wordsByHeuristic(narrowedWords, heuristic);\n if (!wordsToGuess.length) {\n console.log([goal, guesses]);\n }\n // It's possible to have multiple of the same score, so in that event, pick one at random\n const topScore = wordsToGuess[0].score;\n const topGuesses = d3.group(wordsToGuess, (d) => d.score).get(topScore);\n guess = topGuesses[d3.randomInt(0, topGuesses.length)()].word;\n i++;\n guesses.push(guess);\n }\n\n if (i > 10) {\n console.log([goal, i]);\n }\n\n return [goal, guesses.join(\" \")];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":235,"value":"games = function(array, words, heuristic) {\n let results = [];\n for (let i = 0; i < array.length; ++i) {\n let x = simulateGame(array[i], words, heuristic);\n let outcome = ({solution: x[0], count: x[1].split(\" \").length, sequence: x[1]})\n results.push(outcome);\n }\n return results;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":291,"value":"getSuccessRatePercent = function(outcomes, precision) {\n return (outcomes.filter(x => x.count <= 6).length / outcomes.length * 100).toFixed(precision)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":299,"value":"getMeanGuesses = function(outcomes, precision) {\n return (outcomes.map(x => x.count).reduce((a,b) => a+b) / outcomes.length).toFixed(precision)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":306,"value":"printSimulationResults = function(outcomes, precision){\n const percentSuccess = getSuccessRatePercent(outcomes, precision);\n const meanGuesses = getMeanGuesses(outcomes, precision);\n return md`The win percentage is **${percentSuccess}%**, reaching the solution with a mean of **${meanGuesses}** guesses.`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":543,"value":"expt1 = await FileAttachment(\"heuristicTest_Freq_common.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":604,"value":"expt2 = await FileAttachment(\"heuristicTest_Freq_random.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":618,"value":"expt3 = await FileAttachment(\"heuristicTest_LP_common.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":620,"value":"expt4 = await FileAttachment(\"heuristicTest_LP_random.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":474,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":591,"value":"plotVegaLite = function(data, title) {\n let x = VLspec;\n x.data = {values: data};\n //x.title = {text: title, fontSize: 20, fontWeight: \"normal\", fontStyle: \"italic\"};\n return vl.render({spec: x})\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":630,"value":"The code below was used to run experiments, using *yield* to print interim results:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":463,"value":"runExperiment = {\n let results = [];\n let wordsToTest = words_random;\n let heuristic = evaluateLetterAndPositionHeuristic;\n let defaultWords = words_LP.map(x => x.word);\n for (let i = 0; i < wordsToTest.length; ++i) {\n let x = simulateGame(wordsToTest[i], defaultWords, heuristic);\n let outcome = ({solution: x[0], count: x[1].split(\" \").length, sequence: x[1]})\n results.push(outcome);\n yield results;\n }\n return results;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W38","stdlib":"1","titling":"auto"}} 32:"$31:body"