2e:null 2f:["$","title",null,{"children":"N-door Monty Hall | Tom Larkworthy | Observable"}] 34:T634,viewof game = { const n = Inputs.range([3, 20], { value: 3, step: 1, label: "Number of doors (applies on game cycle)" }); const doors = viewroutine(async function*() { const history = new Map(); while (true) { const nChosen = n.value; let state = { history, doors: Array(nChosen).fill("closed") }; let prize = Math.floor(Math.random() * state.doors.length); let firstPick = yield* pickDoor(state); // Open other doors not the prize and not the one picked let otherDoor = prize; while (otherDoor === firstPick) { otherDoor = Math.floor(Math.random() * state.doors.length); } state.doors = state.doors.map((s, index) => index === otherDoor || index === firstPick ? "closed" : "openingEmpty" ); let secondPick = yield* pickDoor(state); const swapped = secondPick !== firstPick; state.doors = state.doors.map(s => (s === "openingEmpty" ? "empty" : s)); state.doors[secondPick] = secondPick === prize ? "openingPrize" : "openingEmpty"; yield* pickDoor(state); const won = secondPick === prize; const historyKey = JSON.stringify([swapped, nChosen]); if (!history.has(historyKey)) { history.set(historyKey, { n: 0, w: 0 }); } console.log( history, historyKey, history.has(historyKey), history.get(historyKey) ); if (won) history.get(historyKey).w++; history.get(historyKey).n++; } }); return view`

${n} ${doors}

`; }35:T6a5,doorButtons = async ({ doors, history } = {}, notify) => { const imgs = await promiseRecursive( doors.map(door => { if (door === 'closed') return FileAttachment("e0@1.jpg").image(); if (door === 'empty') return FileAttachment("e3@1.jpg").image(); if (door === 'prize') return FileAttachment("b3@1.jpg").image(); }) ); const buttons = doors.map((door, i) => door === 'closed' ? ((imgs[i].onclick = () => notify(i)), imgs[i]) : door === 'openingEmpty' ? viewroutine(openEmptyDoor.bind(null, invalidation)) : door === 'openingPrize' ? viewroutine(openPrizeDoor.bind(null, invalidation)) : imgs[i] ); const processed = [...history.keys()].map(key => { const [swapped, n] = JSON.parse(key); return { n, swapped, win_rate: history.get(key).w / history.get(key).n }; }); return htl.html`

${Plot.plot({ y: { domain: [0, 1] }, color: { domain: [false, true] }, x: { domain: [false, true] }, facet: { data: processed, x: "n" }, height: 200, marks: [ Plot.barY(processed, { x: "swapped", y: "win_rate", fill: 'swapped' }), Plot.ruleY([0]) ] })}

${buttons}

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It is not opened.\nNext, the gameshow host opens a different door NOT containing a prize.\nYou get to pick a door again, should you switch from your original guess?\n\nThis application lets you try different amounts of doors and keeps track of the win ratio and whether you swapped or not for you (using [Plot](https://observablehq.com/@observablehq/plot)).\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":94,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":70,"value":"pickDoor = async function*(doors) {\n let notify;\n const result = new Promise(resolve => (notify = resolve));\n yield doorButtons(doors, notify);\n return await result;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":111,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"async function* openEmptyDoor(finish) {\n yield FileAttachment(\"e0@1.jpg\").image();\n await Promises.delay(200);\n yield FileAttachment(\"e1@1.jpg\").image();\n await Promises.delay(200);\n yield FileAttachment(\"e2@1.jpg\").image();\n await Promises.delay(200);\n yield FileAttachment(\"e3@1.jpg\").image();\n await finish;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"async function* openPrizeDoor(finish) {\n yield FileAttachment(\"b0@1.jpg\").image();\n await Promises.delay(200);\n yield FileAttachment(\"b1@1.jpg\").image();\n await Promises.delay(200);\n yield FileAttachment(\"b2@1.jpg\").image();\n await Promises.delay(200);\n yield FileAttachment(\"b3@1.jpg\").image();\n await finish;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":326,"value":"md`The animations are quicker to load if you run through it once`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":211,"value":"openPrizeDoor()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":213,"value":"openEmptyDoor()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"import { viewroutine, ask } from '@tomlarkworthy/viewroutine'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":86,"value":"import { view } from '@tomlarkworthy/view'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"import { promiseRecursive } from '@tomlarkworthy/utils'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":335,"value":"import { footer } from \"@tomlarkworthy/footer\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":353,"value":"footer","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 33:"$32:body"