31:T42c,

Middara Abraxis Battle Dice

A tool to minimize lost Abraxis points

e.target.className=e.target.className ? "" : "marginal" } style="box-shadow: 0 3px 10px lightgray; margin-bottom: 1em;" src="${await FileAttachment("Abraxis.png").url()}" />

Abraxis Battle Dice is a mini-game that players can take part in during the adventure mode [of Middara].

The game takes place through a series of 5 rounds. The goal of each round is for adventurers to roll their dice and have the symbols on all 4 of their dice match the symbols printed on the bottom of the Abraxis card they are facing as closely as possible.

Each round, adventurers will simultaneously roll all of their dice and must lock in the result of 1 die.

This process continues until at least 1 adventurer has locked in all 4 of their dice.

For each extra or missing symbol on an adventurer's locked in dice, they lose 1 Abraxis point.

32:T4b3,options.length ? htl.html`${options .map((option) => ({ option, nextRemaining: remaining.filter((d) => d.remaining.includes(option)) })) .sort((a, b) => mean(a.nextRemaining) - mean(b.nextRemaining)) .map( ({ option, nextRemaining }) => htl.html.fragment`

${Plot.plot({ marks: [ Plot.rectY( remaining, Plot.binX( { y: "proportion" }, { x: "error", interval: 1, fill: Dice.teal.color, fillOpacity: 0.8 } ) ), Plot.rectY( nextRemaining, Plot.binX( { y: "proportion" }, { x: "error", interval: 1, fill: Dice.orange.color, fillOpacity: 0.5 } ) ), meanMarks(nextRemaining), Plot.ruleY([0]) ], x: { domain: [0, 12] }, y: { domain: [0, 1], type: "sqrt", tickFormat: "%", grid: true, label: null }, height: 100, width: 300, marginBottom: 19.5 })} ${image(option)}

` )}` : htl.html`👆🏼 Choose rolled dice above.`33:[{"id":"d67c1130599b934c8e6c5ad14ef19ad1ddee8af96a231263ad504d4e114853be60c22b1166bf2d2e6239c6a6349c7d04b64039bead6366d2560e93f5951a2aa1","href":"https://static.observableusercontent.com/files/d67c1130599b934c8e6c5ad14ef19ad1ddee8af96a231263ad504d4e114853be60c22b1166bf2d2e6239c6a6349c7d04b64039bead6366d2560e93f5951a2aa1","name":"Abraxis.png","type":"image/png","lastModified":1658507913358.223,"size":5924239}] 2f:{"title":"Middara Abraxis Battle Dice","cells":[{"id":0,"value":"$31","pinned":false,"hidden":false,"mode":"html"},{"id":1190,"value":"### Abraxis card\nOk great, so pick a target outcome based on the scenario’s Abraxis card:","pinned":false,"hidden":false,"mode":"md"},{"id":1035,"value":"viewof target = Inputs.form({\n bursts: Inputs.range([0, 4], {\n label: htl.html` Bursts`,\n value: 1,\n step: 1\n }),\n books: Inputs.range([0, 8], {\n label: htl.html` Books`,\n value: 2,\n step: 1\n }),\n shields: Inputs.range([0, 8], {\n label: htl.html` Shields`,\n value: 3,\n step: 1\n })\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":916,"value":"The mean absolute error for this target is\n${mean(errors).toFixed(3)}. You can think of this as the average number of points lost if you’re locking in dice purely at random. A histogram of all outcomes is shown below.","pinned":false,"hidden":false,"mode":"md"},{"id":612,"value":"Plot.plot({\n marks: [\n Plot.rectY(\n errors,\n Plot.binX(\n { y: \"proportion\" },\n {\n x: \"error\",\n interval: 1,\n fill: \"gray\",\n fillOpacity: 0.8\n }\n )\n ),\n meanMarks(errors),\n Plot.ruleY([0])\n ],\n x: { domain: [0, 12] },\n y: { domain: [0, 1], type: \"sqrt\", grid: true, tickFormat: \"%\", label: null },\n width: 300,\n height: 100,\n marginBottom: 19.5\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":469,"value":"### Rolled\nPick your rolled options, and let’s calculate future odds.","pinned":false,"hidden":false,"mode":"md"},{"id":1527,"value":"viewof roll = Inputs.button(\"Reset\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":167,"value":"viewof options = roll, Inputs.checkbox(\n [...new Set(dice)].flatMap((d) => d.faces),\n { format: image }\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1542,"value":"With each option, the odds will change, hopefully for the better! You can see how the new roll-adjusted odds distributions update the locked-in adjusted odds.\n\nWe want these distributions to move to the left, minimizing the absolute error.","pinned":false,"hidden":false,"mode":"md"},{"id":964,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":1021,"value":"You likely want to lock in the top option with the least mean absolute error, but maybe you’re maximizing the odds of a perfect 0 score?","pinned":false,"hidden":false,"mode":"md"},{"id":473,"value":"### Locked in\nPick what you want to lock in.","pinned":false,"hidden":false,"mode":"md"},{"id":1533,"value":"viewof reset = Inputs.button(\"Reset\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":229,"value":"viewof locked = reset, Inputs.checkbox(\n dice.flatMap((d) => d.faces),\n { format: image }\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":946,"value":"$${locked.length ? `The current error of these locked in dice is ${result.error} with ${4 - locked.length} more to roll.` : \"❓_Since you haven’t locked anything in yet, this is identical to before…_\"}\nThe locked-in adjusted odds distribution now has a mean absolute error of\n${mean(remaining).toFixed(3)}. ","pinned":false,"hidden":false,"mode":"md"},{"id":637,"value":"Plot.plot({\n marks: [\n Plot.rectY(\n errors,\n Plot.binX(\n { y: \"proportion\" },\n {\n x: \"error\",\n interval: 1,\n fill: \"gray\",\n fillOpacity: 0.8\n }\n )\n ),\n Plot.rectY(\n remaining,\n Plot.binX(\n { y: \"proportion\" },\n {\n x: \"error\",\n interval: 1,\n fill: Dice.teal.color,\n fillOpacity: 0.5\n }\n )\n ),\n meanMarks(remaining),\n Plot.ruleY([0])\n ],\n x: { domain: [0, 12] },\n y: { domain: [0, 1], type: \"sqrt\", tickFormat: \"%\", label: null, grid: true },\n marginBottom: 19.5,\n height: 100,\n width: 300\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":627,"value":"result = error(locked)","pinned":false,"hidden":false,"mode":"ojs"},{"id":225,"value":"remaining = {\n const without = (lhs, rhs) => {\n lhs = [...lhs];\n for (const i of rhs) if (lhs.includes(i)) lhs.splice(lhs.indexOf(i), 1);\n return lhs;\n };\n return errors\n .filter(({ faces }) => without(locked, faces).length === 0)\n .map((d) => ({ ...d, remaining: without(d.faces, locked) }));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":598,"value":"---\n### How this works\nIf you’re curious or you think there’s a bug, here’s what’s going on.\n\nGiven a pool of dice (the four dice per player), we generate all of the face permutations possible. For _n_ dice, this will be 6ⁿ outcomes (with a 6-sided die).","pinned":false,"hidden":false,"mode":"md"},{"id":179,"value":"dice = [Dice.white, Dice.white, Dice.purple, Dice.purple]","pinned":true,"hidden":false,"mode":"ojs"},{"id":1346,"value":"An intuitive-_ish_ way to think of generating all the permutations is to count in base-6—each digit represents a face. Here, we’re counting down from the highest number you can represent (7777) to the lowest (2211). Or, in the case of more standard dice, that would be 6666 to 1111.","pinned":false,"hidden":false,"mode":"md"},{"id":603,"value":"{\n await visibility;\n for (const faces of permute(dice)) {\n yield htl.html`${faces.map(image)}`\n await Promises.delay(200);\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":20,"value":"function* permute(dice) {\n const faces = dice[0].faces.length;\n let n = Math.pow(faces, dice.length);\n while (n-- > 0) {\n const indexes = n.toString(faces).padStart(dice.length, \"0\").split(\"\");\n yield d3.zip(dice, indexes).map(([d, f]) => d.faces[f]);\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":610,"value":"For each outcome, sum the symbols and calculate absolute error from the target specified at the beginning of this notebook. These error distributions are used above. Filtered subsets are used when locking in or checking rolled dice.","pinned":false,"hidden":false,"mode":"md"},{"id":9,"value":"errors = d3.map(permute(dice), error)","pinned":true,"hidden":false,"mode":"ojs"},{"id":556,"value":"error = (faces) => {\n const sum = faces.reduce(add, {});\n return {\n faces,\n sum,\n error: Object.entries(target).reduce(\n (d, [k, v]) => d + Math.abs(target[k] - (sum[k] || 0)),\n 0\n )\n };\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":1328,"value":"### Mean absolute error\nThroughout this notebook, we’re using the concept of [mean absolute error](https://en.wikipedia.org/wiki/Mean_absolute_error), “a measure of errors between paired observations expressing the same phenomenon.”","pinned":false,"hidden":false,"mode":"md"},{"id":948,"value":"mean = (errors) => errors.reduce((sum, d) => sum + d.error, 0) / errors.length","pinned":true,"hidden":false,"mode":"ojs"},{"id":864,"value":"meanMarks = (errors) => [\n Plot.ruleX(\n errors,\n Plot.binX(\n { x: \"mean\" },\n {\n x: \"error\",\n thresholds: [],\n strokeWidth: 2,\n strokeDasharray: \"3 2\"\n }\n )\n ),\n Plot.text(\n errors,\n Plot.binX(\n { x: \"mean\", text: \"mean\" },\n {\n x: \"error\",\n text: \"error\",\n thresholds: [],\n frameAnchor: \"top\",\n dy: -10\n }\n )\n )\n]","pinned":true,"hidden":false,"mode":"ojs"},{"id":1097,"value":"### Dice images\nArtisanal, hand-coded dice SVGs.","pinned":false,"hidden":false,"mode":"md"},{"id":262,"value":"htl.html`${image(Dice.purple.faces[5])} ${image(Dice.white.faces[4])}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":265,"value":"image = ({ n, shields, books, bursts, color, stroke } = {}) =>\n htl.svg``","pinned":true,"hidden":false,"mode":"ojs"},{"id":685,"value":"burst = (x, y) =>\n htl.svg\n .fragment``","pinned":true,"hidden":false,"mode":"ojs"},{"id":668,"value":"shield = (x, y) =>\n htl.svg\n .fragment``","pinned":true,"hidden":false,"mode":"ojs"},{"id":675,"value":"book = (x, y) =>\n htl.svg.fragment``","pinned":true,"hidden":false,"mode":"ojs"},{"id":1233,"value":"### Dice\nThe dice are normally used for attacking monsters.","pinned":false,"hidden":false,"mode":"md"},{"id":6,"value":"import { Dice, add } from \"@visnup/middara\"","pinned":true,"hidden":false,"mode":"ojs"},{"id":403,"value":"","pinned":false,"hidden":false,"mode":"html"}],"files":"$W33","stdlib":"1","titling":"auto"}