31:T413,results = { // mutable nTrials = 0; let totalCardsDrawn = 0; let nTrials = 0; let card = 0; let pip = 0; let cardsDrawn = 0 let outcomes = new Array(52) let cardAvailable = new Array(52*nDecksNum) let i = 0; for (let j = 0; j < outcomes.length; j++ ) { outcomes[j] = {'Cards_Drawn': j, 'Occurances': 0} } let myPips = new Array(13) while (i < nSamples) { i++; myPips.fill(0); cardAvailable.fill(true) cardsDrawn = 0; while ( true ) { card = (Math.floor(Math.random()*52*nDecksNum)); if (cardAvailable[card]) { pip = card % 13; myPips[pip]++; cardsDrawn++; cardAvailable[card] = replaceCards; if (myPips[pip] == 4) { break; } } } nTrials++; totalCardsDrawn += cardsDrawn; outcomes[cardsDrawn].Occurances = outcomes[cardsDrawn].Occurances + 1; } return {data: outcomes, nSamples: nTrials, nDrawn: totalCardsDrawn, aveCardsDrawn: totalCardsDrawn/nTrials } } 32:[] 2f:{"title":"Tickler Puzzle Four of a Kind","cells":[{"id":0,"value":"md`# Tickler Puzzle Four of a Kind`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"md`[RJ's](http://mical.org) Monday Morning Tickler: Four of a Kind. \nImagine we have a deck of 52 standard playing cards.\nQuestion: On average, with a standard deck of cards, how many\ncards do we have to draw to get four of a kind? What if we used two decks (and ignored suits) how many cards on average would we have to draw to get four of a kind? The simulator below will help answer these questions. More simulation trials will give more accurate estimates (but refresh more slowly).\n`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":259,"value":"vegalite({\n data: { values: results.data },\n mark: \"bar\",\n autosize: \"fit\",\n width: width,\n encoding: {\n x: {\n field: \"Cards_Drawn\",\n type: \"ordinal\",\n axis: {\"title\": \"Number of Cards Drawn\"}\n },\n y: {\n field: \"Occurances\"\n }\n }\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":471,"value":"md`| Number of Decks | Number of Trials | Ave | Most Likely | Minimum Drawn | Maximum Drawn\n| :-------------: | :-------------: |:-------------:| :-----:| :-------------: |:-------------:|\n| ${nDecks} | ${results.nSamples} | ${Math.floor(results.aveCardsDrawn*100)/100} | ${mostLikely} | ${minimumDrawn} | ${maximumDrawn}\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":288,"value":"md`Use the slider to change the number of trials in each sumulation.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":299,"value":"viewof nSamples = {\n const form = html``;\n form.i.oninput = () => {\n form.o.value = Math.pow(10,Math.floor(form.i.valueAsNumber));\n form.value = Math.pow(10,Math.floor(form.i.valueAsNumber)) ;\n };\n form.i.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":526,"value":"md`You can change the number of decks of cards used in the simulation`","pinned":false,"hidden":false,"mode":"ojs"},{"id":447,"value":"viewof nDecks = DOM.select(nDecksList)","pinned":false,"hidden":false,"mode":"ojs"},{"id":380,"value":"md`## Computed Raw Data`","pinned":false,"hidden":false,"mode":"ojs"},{"id":167,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":387,"value":"md`## Appendix: Libraries, Utilities and Variables`","pinned":false,"hidden":false,"mode":"ojs"},{"id":254,"value":"vegalite = require(\"@observablehq/vega-lite\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":365,"value":"howManyDecks = replaceCards ? 'an infinite number of decks' : 'a single deck of cards';","pinned":false,"hidden":false,"mode":"ojs"},{"id":421,"value":"strategy = replaceCards ? \"Replacing cards\" : \"Not replacing cards\" ;","pinned":false,"hidden":false,"mode":"ojs"},{"id":401,"value":"replaceCards = nDecks == \"infinite\" ? true : false;","pinned":false,"hidden":false,"mode":"ojs"},{"id":395,"value":"checkbox = ({label = '', value = false} = {}) => {\n let wrapper = html``\n let check = html``\n wrapper.append(check)\n wrapper.append(label || '')\n \n check.checked = value\n \n check.addEventListener('change', (e) => {\n wrapper.value = check.checked\n wrapper.dispatchEvent(new CustomEvent('input'))\n })\n \n // we need to have a starting value\n wrapper.value = check.checked\n \n return wrapper\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":452,"value":"nDecksList = [\"1\", \"2\", \"5\", \"10\", \"100\", \"infinite\"]","pinned":false,"hidden":false,"mode":"ojs"},{"id":517,"value":"nDecks","pinned":true,"hidden":false,"mode":"ojs"},{"id":398,"value":"viewof v3 = checkbox({label: ' Replace card in deck after drawing it', value: false})","pinned":false,"hidden":false,"mode":"ojs"},{"id":483,"value":"mostLikely = {\n let max = 0;\n let num = 0;\n results.data.forEach( function (item, index) {\n if (item.Occurances > max) {\n max = item.Occurances;\n num = index;\n }\n })\n \n return num;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":492,"value":"minimumDrawn = {\n let num = 0;\n results.data.forEach( function (item, index) {\n if (item.Occurances > 0) {\n if (num == 0) {\n num = index;\n }\n }\n }) \n return num;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":501,"value":"maximumDrawn = {\n let num = 0;\n results.data.forEach( function (item, index) {\n if (item.Occurances > 0) {\n num = index;\n }\n }) \n return num;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":519,"value":"nDecksNum = { \n let n = 1;\n if (nDecks != \"infinite\" ) {\n n = parseInt(nDecks,10);\n }\n return n;\n \n}\n","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W32","stdlib":"1","titling":"auto"}