44:["$","title",null,{"children":"Poker Distribution | Zach Bogart | Observable"}] 4c:T8b0,const dealer = (() => { const played = []; let timer = null; const perTick = Inputs.range([1, 1000], {label: "Hands per tick", value: 1, step: 1, transform: Math.log}); // Keep nested input events from re-triggering the outer view. perTick.addEventListener("input", (e) => e.stopPropagation()); const cardsDiv = html`

`; const status = html`

`; const live = html``; const root = html`

${live}

${perTick}${cardsDiv}${status}

`; root.value = []; function play(n, source) { for (let i = 0; i < n; i++) { const cards = randomHand(); played.push({id: played.length + 1, source, cards: cards.map((c) => c.rank + c.suit), handType: evaluateHand(cards)}); } } function show(h) { if (!h) return; cardsDiv.replaceChildren(...h.cards.map((c) => html`

${c}

`)); } function commit() { root.value = played.slice(); status.textContent = `${played.length.toLocaleString()} hands played${timer ? " · simulating…" : ""}`; root.dispatchEvent(new Event("input", {bubbles: true})); } function stop() { if (timer) { clearInterval(timer); timer = null; } live.textContent = "Start live simulation"; } live.onclick = () => { if (timer) { stop(); commit(); return; } live.textContent = "Stop live simulation"; timer = setInterval(() => { play(Math.round(perTick.value), "simulation"); show(played.at(-1)); commit(); }, 200); }; invalidation.then(stop); status.textContent = "0 hands played"; return root; })(); const handsPlayed = view(dealer);4d:T6e0,const observedByType = d3.rollup(handsPlayed, (v) => v.length, (d) => d.handType); const expectedCounts = handOrder.map((handType, i) => { const observed = observedByType.get(handType) ?? 0; const expected = Math.floor(handsPlayed.length * handCombos[i] / 2598960); return {handType, observed, expected, difference: observed - expected}; }); const signed = (d) => d === 0 ? "0" : (d > 0 ? "+" : "−") + Math.abs(d).toLocaleString(); const noData = handsPlayed.length === 0; const countsPlot = display(Plot.plot({ title: "Poker hands: observed vs. expected counts", subtitle: noData ? "No hands played yet" : `${handsPlayed.length.toLocaleString()} hands played`, marginLeft: 110, marginRight: 110, x: noData ? {domain: [0, 1], axis: null} : {label: "Hands", grid: true}, y: {domain: handOrder, label: null}, marks: noData ? [Plot.barX(handOrder, {y: (d) => d, x1: 0, x2: 1, fill: "#e5e5e5", inset: 0.5})] : [ Plot.barX(handsPlayed, Plot.groupY({x: "count"}, {y: "handType"})), Plot.text(handsPlayed, Plot.groupY({x: "count", text: "count"}, {y: "handType", dx: 4, textAnchor: "start"})), Plot.tickX(expectedCounts, {y: "handType", x: "expected", stroke: "orange", strokeWidth: 1, tip: true, title: (d) => `${d.handType}\nexpected: ${d.expected.toLocaleString()}\nobserved: ${d.observed.toLocaleString()}\ndifference: ${signed(d.difference)}`}), // Left-aligned column in the right margin, clear of the bars and count labels. Plot.text(expectedCounts, {y: "handType", text: (d) => signed(d.difference), frameAnchor: "right", textAnchor: "start", dx: 56, fontWeight: "bold", fill: (d) => d.difference > 0 ? "darkgreen" : d.difference < 0 ? "crimson" : "gray"}), Plot.ruleX([0]) ] }));4e:[] 48:{"id":"a8e4e62ad72ca901","slug":"poker-distribution","title":"Poker Distribution","thumbnail":"af4f661148ac026fc211cb33338cecad9551a22b5d1ff17296d4ab69a4a067e0","access_level":"public","create_time":"$D2026-10-27T19:00:03.654Z","update_time":"$D2026-10-27T20:47:39.250Z","view_time":null,"first_public_time":"$D2026-10-28T00:05:28.899Z","has_unpublished_edits":null,"fork":true,"stars":0,"starred":false,"owner":{"type":"team","id":"1da899fe83239203","login":"zachbogart","name":"Zach Bogart","avatar_url":"https://avatars-next.observableusercontent.com/90a52c7f25e244d634f67d16c58dea6d577e871986ac93da60522bbd4add497a","tier":"starter_2024","bio":"I'll know it when I see it.","followed_by_you":false,"follows_you":false},"version":281,"publish_version":281,"role":null,"authored":false,"authors":[{"type":"individual","id":"8f3c727b0fd0bd62","login":"zachbogart","name":"Zach Bogart","avatar_url":"https://avatars-next.observableusercontent.com/90a52c7f25e244d634f67d16c58dea6d577e871986ac93da60522bbd4add497a","tier":null,"bio":"I'll know it when I see it.","followed_by_you":false,"follows_you":false}],"members":[{"type":"team","id":"1da899fe83239203","login":"zachbogart","name":"Zach Bogart","avatar_url":"https://avatars-next.observableusercontent.com/90a52c7f25e244d634f67d16c58dea6d577e871986ac93da60522bbd4add497a","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Poker Distribution","cells":[{"id":26,"value":"# Poker Distribution\n\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":38,"value":"const notRoyal = summary[0].firstDealt == \"Not yet\";\nconst emoji = summary[0].firstDealt > royalFlushOdds ? \"🐌\" : \"🐇\"\nconst royalDeals = d3.format(\"~s\")(Math.round(summary[0].firstDealt / 1e4) * 1e4);\nconst royalText = notRoyal ? \"You haven't seen one yet.\" : `🚨 You saw one after ${royalDeals} ${emoji}`;\n\ndisplay(md`${text}\n- ${royalText}`)","pinned":false,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"$4c","pinned":false,"hidden":false,"mode":"js","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"$4d","pinned":false,"hidden":false,"mode":"js","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"const total = handsPlayed.length;\nconst stats = d3.rollup(\n handsPlayed,\n (v) => ({count: v.length, first: d3.min(v, (d) => d.id)}),\n (d) => d.handType\n);\nconst summary = handOrder.map((handType) => {\n const s = stats.get(handType);\n return {\n handType,\n count: s?.count ?? 0,\n share: total ? (s?.count ?? 0) / total : 0,\n firstDealt: s ? `${s.first}` : \"Not yet\"\n };\n});\ndisplay(Inputs.table(summary, {\n format: {share: d3.format(\".3%\"), firstDealt: d => d == \"Not yet\" ? d : d3.format(\",\")(d)},\n header: {handType: \"Hand\", count: \"Count\", share: \"Share\", firstDealt: \"First dealt\"}\n}));","pinned":false,"hidden":false,"mode":"js","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"---\n## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"function evaluateHand(hand) {\n const values = hand.map((c) => ranks.indexOf(c.rank) + 2).sort((a, b) => b - a);\n const counts = Object.values(d3.rollup(values, (v) => v.length, (v) => v).entries\n ? Object.fromEntries(d3.rollup(values, (v) => v.length, (v) => v)) : {}).sort((a, b) => b - a);\n const flush = new Set(hand.map((c) => c.suit)).size === 1;\n const unique = [...new Set(values)];\n const wheel = unique.join() === \"14,5,4,3,2\"; // A-2-3-4-5\n const straight = unique.length === 5 && (values[0] - values[4] === 4 || wheel);\n const high = wheel ? 5 : values[0];\n\n if (straight && flush) return high === 14 ? \"Royal flush\" : \"Straight flush\";\n if (counts[0] === 4) return \"Four of a kind\";\n if (counts[0] === 3 && counts[1] === 2) return \"Full house\";\n if (flush) return \"Flush\";\n if (straight) return \"Straight\";\n if (counts[0] === 3) return \"Three of a kind\";\n if (counts[0] === 2 && counts[1] === 2) return \"Two pair\";\n if (counts[0] === 2) return \"Pair\";\n return \"High card\";\n}","pinned":false,"hidden":false,"mode":"js","author":"agent","summary":"Define evaluateHand and test it","tool":{"id":"toolu_01BgE5G8W7jcrfvy6BQDtBAP","name":"execute"},"providerMetadata":{"anthropic":{"caller":{"type":"direct"}}},"attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"const suits = [\"♠\", \"♥\", \"♦\", \"♣\"];\nconst ranks = [\"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\", \"10\", \"J\", \"Q\", \"K\", \"A\"];\nconst deck = suits.flatMap((suit) => ranks.map((rank) => ({rank, suit})));\n\n// Draws `n` distinct cards using a partial Fisher–Yates shuffle.\nfunction randomHand(n = 5) {\n const cards = deck.slice();\n for (let i = 0; i < n; i++) {\n const j = i + Math.floor(Math.random() * (cards.length - i));\n [cards[i], cards[j]] = [cards[j], cards[i]];\n }\n return cards.slice(0, n);\n}","pinned":false,"hidden":false,"mode":"js","author":"agent","summary":"Define random poker hand function and show an example","tool":{"id":"toolu_01B9Ab8XoERCSTW67UbXnhtA","name":"execute"},"providerMetadata":{"anthropic":{"caller":{"type":"direct"}}},"attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"const handOrder = [\"Royal flush\", \"Straight flush\", \"Four of a kind\", \"Full house\", \"Flush\", \"Straight\", \"Three of a kind\", \"Two pair\", \"Pair\", \"High card\"];\nconst handCombos = [4, 36, 624, 3744, 5108, 10200, 54912, 123552, 1098240, 1302540]; // of 2,598,960 five-card hands","pinned":false,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"const royalFlushOdds = 1 / (handCombos[0] / d3.sum(handCombos));\nconst format = d3.format(\"~s\")(Math.round(royalFlushOdds / 1e4) * 1e4);\nconst text = `Odds are it'll be about ${format} hands before you'll see a royal flush.`;","pinned":false,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4e","stdlib":"2"}} 24:null