2f:T45f,{ return Plot.plot({ color: { legend: true, domain: ["all", ...resultTypes], range: ["black", ...colors] }, x: { grid: true }, y: { axis: true, grid: true, percent: true, label: "Percentile" }, marks: [ Plot.ruleY([0]), Plot.line( data, Plot.normalizeY( Plot.binX( { y: "count", cumulative: 1, thresholds: d3.range(...d3.extent(data, (d) => d.throws)) }, { x: "throws", basis: "max", stroke: "result", tip: true } ) ) ), Plot.line( data, Plot.normalizeY( Plot.binX( { y: "count", cumulative: 1, thresholds: d3.range(...d3.extent(data, (d) => d.throws)) }, { x: "throws", basis: "max", tip: true, strokeDasharray: [5, 5] } ) ) ) ], height: 350 }); }30:T45b,{ return Plot.plot({ color: { legend: true, domain: ["all", ...resultTypes], range: ["black", ...colors] }, x: { grid: true }, y: { axis: true, grid: true, percent: true, label: "Percentile" }, marks: [ Plot.ruleY([0]), Plot.line( data, Plot.normalizeY( Plot.binX( { y: "count", cumulative: 1, thresholds: d3.range(...d3.extent(data, (d) => d.turns)) }, { x: "turns", basis: "max", stroke: "result", tip: true } ) ) ), Plot.line( data, Plot.normalizeY( Plot.binX( { y: "count", cumulative: 1, thresholds: d3.range(...d3.extent(data, (d) => d.turns)) }, { x: "turns", basis: "max", tip: true, strokeDasharray: [5, 5] } ) ) ) ], height: 350 }); }31:T468,{ return Plot.plot({ color: { legend: true, domain: ["all", ...resultTypes], range: ["black", ...colors] }, x: { grid: true }, y: { axis: true, grid: true, percent: true, label: "Percentile" }, marks: [ Plot.ruleY([0]), Plot.line( data, Plot.normalizeY( Plot.binX( { y: "count", cumulative: 1, thresholds: d3.range(...d3.extent(data, (d) => d.darkness)) }, { x: "darkness", stroke: "result", basis: "max", tip: true } ) ) ), Plot.line( data, Plot.normalizeY( Plot.binX( { y: "count", cumulative: 1, thresholds: d3.range(...d3.extent(data, (d) => d.darkness)) }, { x: "darkness", basis: "max", tip: true, strokeDasharray: [5, 5] } ) ) ) ], height: 350 }); }32:T872,function game(d6, throwStrategy = "never") { let destiny = 0; let potatoes = 0; let orcs = 0; let darkness = 0; let turns = 0; let throws = 0; let thrownPotatoes = 0; let rolls = 0; const maxTurns = 1000; function roll() { rolls += 1; return d6(); } function throwPotato() { if (potatoes <= darkness) throw new Error("not enough potatoes"); if (orcs <= 0) throw new Error("no orcs"); orcs -= 1; let amount = 1 + darkness; potatoes -= amount; throws += 1; thrownPotatoes += amount; } while (destiny < 10 && potatoes < 10 && orcs < 10 && turns < maxTurns) { const r1 = roll(); turns += 1; if (r1 === 1 || r1 === 2) { const r2 = roll(); if (r2 === 1) potatoes += 1; else if (r2 === 2) { potatoes += 1; destiny += 1; } else if (r2 === 3) { destiny += 1; orcs += 1; } else if (r2 === 4) { orcs += 1; potatoes = Math.max(0, potatoes - 1); } else if (r2 === 5) potatoes = Math.max(0, potatoes - 1); else potatoes += 2; } else if (r1 === 3 || r1 === 4) { const r2 = roll(); if (r2 === 1) orcs += 1; else if (r2 === 2) { destiny += 1; } else if (r2 === 3) { destiny += 1; orcs += 1; } else if (r2 === 4) { orcs += 2; potatoes = Math.max(0, potatoes - 1); } else if (r2 === 5) destiny += 1; else potatoes += 2; } else { darkness += 1; } if (throwStrategy === "eager") { while (orcs > 0 && potatoes > darkness) throwPotato(); } else if (throwStrategy === "desperate") { while (orcs === 10 && potatoes > darkness) throwPotato(); } else if (throwStrategy === "cheap") { while (orcs > 0 && potatoes > darkness && darkness < 3) throwPotato(); } } return { destiny, potatoes, orcs, darkness, turns, throws, thrownPotatoes, rolls, result: turns >= maxTurns ? "max-turns" : orcs >= 10 ? "orcs" : destiny >= 10 ? "destiny" : potatoes >= 10 ? "potatoes" : null }; }33:[] 2d:{"title":"Game of Potato simulator","cells":[{"id":302,"value":"# Game of Potato simulator\n## Statistics for the Game of Potato by Oliver Darkshire ([@deathbadger](https://x.com/deathbybadger)).","pinned":false,"hidden":false,"mode":"md"},{"id":199,"value":"Based on ${(data.length.toLocaleString())} games where players ${throwStrategy === \"never\" ? \"never throw potatoes\" : throwStrategy === \"eager\" ? \"throw potatoes whenever they can\" : throwStrategy === \"desperate\" ? \"only throw potatoes to save their life\" : throwStrategy === \"cheap\" ? \"throw potatoes whenever thy can take down an orc with at most 3\" : \"do confusing things with potatoes\"}, halflings are eaten by orcs ${pct(stats.orcsPercent)} of the time, whisked away by wizards ${pct(stats.destinyPercent)} of the time, and only get to rest with their potatoes ${pct(stats.potatoesPercent)} of the time.\n\nThe median game length is ${d3.quantile(data, 0.5, d => d.turns)} turns, the median amount of darkness in the world is ${d3.quantile(data, 0.5, d => d.darkness)}, and the median number of potatoes thrown is ${d3.quantile(data, 0.5, d => d.thrownPotatoes)} .","pinned":false,"hidden":false,"mode":"md"},{"id":277,"value":"viewof throwStrategy = Inputs.radio([\"eager\", \"desperate\", \"cheap\", \"never\"], {\n label: \"Throwing strategy\",\n value: \"eager\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":317,"value":"## How does the game usually end?","pinned":false,"hidden":false,"mode":"md"},{"id":17,"value":"Plot.plot({\n y: { tickFormat: \"s\" },\n color: {\n domain: resultTypes,\n range: colors\n },\n marks: [\n Plot.ruleY([0]),\n Plot.barY(\n data.filter(Boolean),\n Plot.groupX({ y: \"count\" }, { x: \"result\", fill: \"result\", tip: true })\n )\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":330,"value":"## How many potatoes are thrown at Orcs?\n\nThis counts the number of orcs defeated, not the number of potatoes thrown. Lines being further to the left represent fewer orcs, and to the right represent more orcs.","pinned":false,"hidden":false,"mode":"md"},{"id":326,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs"},{"id":391,"value":"_Given that any potatoes were thrown_, how does the number of potatoes thrown compare to the number of orcs defeated?","pinned":false,"hidden":false,"mode":"md"},{"id":345,"value":"Plot.plot({\n x: { label: \"Orcs defeated\" },\n y: { label: \"Potatoes thrown\" },\n color: { scheme: \"reds\" },\n marks: [\n Plot.frame(),\n Plot.rect(\n data.filter((d) => d.throws > 0),\n Plot.group(\n { fill: \"count\" },\n {\n x: \"throws\",\n y: \"thrownPotatoes\",\n tip: true,\n interval: 1,\n inset: -1\n }\n )\n ),\n Plot.gridX(),\n Plot.gridY()\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":319,"value":"## How long do games take?\n\nLines being further to the left represent shorter games, and to the right represent longer games.","pinned":false,"hidden":false,"mode":"md"},{"id":161,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":321,"value":"## How dark is the world?\nThis measures how often then 5/6 result comes up on the dice, making the world darker and orcs stronger.","pinned":false,"hidden":false,"mode":"md"},{"id":159,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":249,"value":"---\n

","pinned":false,"hidden":false,"mode":"md"},{"id":11,"value":"data = {\n const d6 = dice(6);\n let results = [];\n while (results.length < 100_000) {\n results.push(game(d6, throwStrategy));\n if (Math.random() < 0.0001) yield results;\n }\n yield results;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":261,"value":"pct = d3.format(\".1%\")","pinned":true,"hidden":false,"mode":"ojs"},{"id":251,"value":"stats = {\n let counts = d3.rollup(\n data,\n (ds) => ds.length,\n (d) => d.result\n );\n let rv = {\n orcs: counts.get(\"orcs\"),\n potatoes: counts.get(\"potatoes\"),\n destiny: counts.get(\"destiny\"),\n medianRolls: d3.quantile(data, 0.5, (d) => d.rolls)\n };\n rv.orcsPercent = rv.orcs / data.length;\n rv.potatoesPercent = rv.potatoes / data.length;\n rv.destinyPercent = rv.destiny / data.length;\n return rv;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":240,"value":"resultTypes = [\"destiny\", \"orcs\", \"potatoes\"]","pinned":false,"hidden":false,"mode":"ojs"},{"id":242,"value":"colors = [\n d3.schemeCategory10[1],\n d3.schemeCategory10[2],\n d3.schemeCategory10[5]\n]","pinned":true,"hidden":false,"mode":"ojs"},{"id":9,"value":"function dice(sides = 6) {\n return () => Math.floor(Math.random() * sides) + 1;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":5,"value":"$32","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W33","stdlib":"1","titling":"auto"}