31:[] 2f:{"title":"7th Continent Goat Chart","cells":[{"id":0,"value":"# 7th Continent Goat Chart\n\n[The 7th Continent][1] uses an action deck to run skill checks. A success is determined by the number of stars present on cards you draw, players choosing how many cards to use each attempt.\n\nLet's investigate how the odds of getting various successes change under different circumstances..\n\n

The goat chart from pg. 13 of the game manual

\n\nSee also: [Calculating the chance table][2] – The 7th Continent Forums.\n\n[1]: https://boardgamegeek.com/boardgame/180263/7th-continent\n[2]: https://the7thcontinent.seriouspoulp.com/en/forum/topic/4130/calculating-the-chance-table/page/1/292390/","pinned":false,"hidden":false,"mode":"md"},{"id":341,"value":"### Odds of a star\nThese are the base odds of getting one or more stars with two explorers, basic skills, and one curse.","pinned":false,"hidden":false,"mode":"md"},{"id":525,"value":"viewof explorers = Inputs.range([1, 4], { step: 1, value: 2, label: 'Explorers' })","pinned":false,"hidden":false,"mode":"ojs"},{"id":242,"value":"table(baseOdds, 'stars', '⭐️')","pinned":false,"hidden":false,"mode":"ojs"},{"id":440,"value":"baseOdds = [...odds(1, 14)]","pinned":true,"hidden":false,"mode":"ojs"},{"id":573,"value":"Curiously, I was never able to exactly duplicate the odds in the published table. For example, 3+ stars using 3 cards is around a 49% chance for me and published as 39%","pinned":false,"hidden":false,"mode":"md"},{"id":489,"value":"This is a Monte Carlo simulation of determining these odds. We run ${simulations.toLocaleString()} iterations, but there could be noise between runs. How much noise? Here's the difference between two runs:","pinned":false,"hidden":false,"mode":"md"},{"id":475,"value":"table(\n difference([...odds(1, 14)], baseOdds),\n 'stars',\n '',\n d3.scaleSequential([-5, 5], d3.interpolatePRGn)\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":23,"value":"function* odds(start, end, sevens) {\n for (let draws = start; draws <= end; draws++) {\n const atLeast = { stars: {}, sevens: {}, curses: {} }\n for (const draw of simulate(draws, simulations))\n for (const [type, count] of Object.entries(sum(draw, sevens)))\n for (let c = count; c > 0; c--)\n (atLeast[type][c] = atLeast[type][c] || []).push(draw)\n for (const counts of Object.values(atLeast))\n for (const [count, outcomes] of Object.entries(counts)) {\n const percent = counts[count] = outcomes.length / simulations * 100\n if (percent < 0.5)\n delete counts[count]\n }\n yield { draws, atLeast }\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":335,"value":"### Odds of drawing a 7\nA 7 is a conditional star. The odds of drawing a 7 are decently high, but you have to be able to convert 7s to stars.","pinned":false,"hidden":false,"mode":"md"},{"id":316,"value":"table(baseOdds, 'sevens', '7️⃣')","pinned":false,"hidden":false,"mode":"ojs"},{"id":510,"value":"Converting 7s can multiply. If you can convert a 7 into one star, the difference in generating stars increases meaningfully. Below is showing the difference from the base odds if you can reliably convert 7s into stars:","pinned":false,"hidden":false,"mode":"md"},{"id":514,"value":"viewof sevenStars = Inputs.range([1, 5], { step: 1, value: 1, label: '7-Star multipliers' })","pinned":false,"hidden":false,"mode":"ojs"},{"id":416,"value":"table(difference(oddsWithSevens, baseOdds), 'stars', '', d3.scaleSequential([-20, 20], d3.interpolatePRGn))","pinned":true,"hidden":false,"mode":"ojs"},{"id":517,"value":"table(oddsWithSevens)","pinned":true,"hidden":false,"mode":"ojs"},{"id":412,"value":"oddsWithSevens = [...odds(1, 14, sevenStars)]","pinned":true,"hidden":false,"mode":"ojs"},{"id":449,"value":"function difference(a, b) {\n const result = a.map(({draws, atLeast}, i) => {\n const diff = {}\n for (const [type, counts] of Object.entries(atLeast)) {\n diff[type] = {}\n for (const [count, value] of Object.entries(counts))\n diff[type][count] = value - (b[i].atLeast[type][count] || 0)\n }\n return {\n draws,\n atLeast: diff\n }\n })\n \n // need to cover the keys in b too\n \n return result\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":332,"value":"### Odds of drawing a curse card\nNear the end game, you'll be worried about drawing a curse card. You probably don't want to be drawing 5 cards in that case.","pinned":false,"hidden":false,"mode":"md"},{"id":323,"value":"table(baseOdds, 'curses', '☠️')","pinned":false,"hidden":false,"mode":"ojs"},{"id":240,"value":"table = (odds, type = 'stars', icon = '', color = d3.scaleSequential([0, 100], d3.interpolateCool)) => html`\n \n ${odds.map(({draws}, i) => html``)}\n ${Object.keys(odds[odds.length - 1].atLeast[type]).map(count => html`\n \n \n ${odds.map(({atLeast}) => {\n const percent = atLeast[type][count]\n if (percent)\n return html``\n else\n return html``\n })}\n \n `)}\n

${icon}	${(i === 0 ? '🔷' : '') + draws}
${count}⁺	\n ${percent.toFixed(0)}\n ■\n

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":355,"value":"Counting half stars is slightly tricky. For an optimal arrangement, \n`min(left, right)` works unless they are all “left & right”, in which case `-1`.","pinned":false,"hidden":false,"mode":"md"},{"id":171,"value":"function sum(draw, sevenMultiplier = 0) {\n const [stars, lefts, rights, curses, sevens] = \n ['star', 'left', 'right', 'curse', 'seven'].map(property => d3.sum(draw, c => c[property] || 0))\n const anyHalves = draw.some(c => c.left != c.right)\n const anyLeftRights = draw.some(c => c.left && c.right)\n \n return {\n stars: stars\n + Math.min(lefts, rights)\n - (anyLeftRights && !anyHalves ? 1 : 0)\n + sevenMultiplier * sevens,\n curses,\n sevens\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":176,"value":"sumTest = [\n {cards: [{ star: 1 }, { star: 2 }], expected: 3},\n {cards: [{ left: 1, right: 1 }], expected: 0},\n {cards: [{ left: 1, right: 1 }, { left: 1, right: 1 }], expected: 1},\n {cards: [{ right: 1 }, { left: 1, right: 1 }, { left: 1 }], expected: 2},\n {cards: [{ right: 1 }, { left: 1, right: 1 }, { left: 1, right: 1}, { left: 1 }], expected: 3},\n {cards: [{ right: 1 }, { left: 1, right: 1 }, { left: 1 }, { left: 1 }, { right: 1 }], expected: 3},\n {cards: [{ right: 1 }, { left: 1, right: 1 }, { left: 1 }, { left: 1 }, { right: 1 }, { right: 1 }], \n expected: 3}\n].map(({cards, expected}) => ({ passed: sum(cards).stars === expected, cards }))\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":365,"value":"Simulate drawing from the action deck. Draw without replacement and reshuffle when you reach the end.","pinned":false,"hidden":false,"mode":"md"},{"id":212,"value":"simulations = 5e3","pinned":false,"hidden":false,"mode":"ojs"},{"id":22,"value":"function* simulate(draws, n) {\n let deck = []\n for (let i = 0; i < n; i++) {\n if (deck.length < draws)\n deck = d3.shuffle([...cards])\n yield deck.splice(0, draws)\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":13,"value":"cards = [...moreExplorers(explorers), ...basicSkills, ...advancedSkills, ...curses]","pinned":true,"hidden":false,"mode":"ojs"},{"id":528,"value":"function* moreExplorers(n) {\n for (let i = 0; i < n; i++)\n yield* explorer\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":7,"value":"explorer = [\n { star: 1, left: 1 },\n { star: 1, right: 1 },\n { seven: 1, left: 1 },\n { left: 1, right: 1 },\n { right: 1 },\n]","pinned":true,"hidden":false,"mode":"ojs"},{"id":8,"value":"basicSkills = [\n ...new Array(7).fill({ star: 1 }),\n ...new Array(2).fill({ star: 2 }),\n ...new Array(1).fill({ star: 3 }),\n ...new Array(8).fill({ star: 1, left: 1 }),\n ...new Array(5).fill({ star: 1, right: 1 }),\n ...new Array(4).fill({ left: 1 }),\n ...new Array(4).fill({ right: 1 }),\n ...new Array(1).fill({ seven: 1, star: 1, right: 1 }),\n ...new Array(1).fill({ seven: 1, left: 1 }),\n ...new Array(2).fill({ seven: 1, right: 1 }),\n] // 35","pinned":true,"hidden":false,"mode":"ojs"},{"id":10,"value":"advancedSkills = [\n]","pinned":true,"hidden":false,"mode":"ojs"},{"id":15,"value":"curses = [\n { curse: 1 }, \n { curse: 1, title: \"Death is lurking!\" },\n { curse: 1, title: \"Death is lurking!\" },\n { curse: 1, title: \"Death is lurking!\" },\n { curse: 1, title: \"Death is lurking!\" },\n]","pinned":true,"hidden":false,"mode":"ojs"},{"id":251,"value":"TODO\n- differences\n- 7 star\n- advanced skills\n- number of curses","pinned":false,"hidden":false,"mode":"md"}],"files":"$W31","stdlib":"1","titling":"auto"}