Dice Probability Lab

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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="color-scheme" content="light dark">
<title>Dice Probability Lab</title>
<style>
/* sloprun design tokens — inline this block into every demo (self-contained rule).
   Identity: instrument-panel. Machine facts in mono; human words in sans.
   Green is EARNED: only for "it ran / it worked" states, never decoration. */
:root {
  --bg: #F6F6F3;          /* neutral paper, not cream */
  --surface: #FFFFFF;
  --ink: #1A1D21;
  --muted: #5A6068;
  --line: #E3E2DC;
  --accent: #C05600;      /* phosphor amber, darkened for light bg */
  --accent-soft: #FFF3E6;
  --run: #1A7F37;         /* earned green */
  --run-soft: #E7F4EA;
  --danger: #C93C37;
  --radius: 10px;
  --font-sans: system-ui, -apple-system, "Segoe UI", sans-serif;
  --font-mono: ui-monospace, "SF Mono", "Cascadia Code", Menlo, Consolas, monospace;
}
@media (prefers-color-scheme: dark) {
  :root:not([data-theme="light"]) {
    --bg: #14161A; --surface: #1C1F26; --ink: #E8E6E1; --muted: #9AA0A8;
    --line: #2A2E36; --accent: #FFB454; --accent-soft: #2A2118;
    --run: #3FB950; --run-soft: #16281B; --danger: #F47067;
  }
}
:root[data-theme="dark"] {
  --bg: #14161A; --surface: #1C1F26; --ink: #E8E6E1; --muted: #9AA0A8;
  --line: #2A2E36; --accent: #FFB454; --accent-soft: #2A2118;
  --run: #3FB950; --run-soft: #16281B; --danger: #F47067;
}
body { background: var(--bg); color: var(--ink); font-family: var(--font-sans); }

/* ---------- base ---------- */
*, *::before, *::after { box-sizing: border-box; }
html, body { margin: 0; padding: 0; }
body {
  line-height: 1.5;
  overflow-x: hidden;
  -webkit-text-size-adjust: 100%;
  font-size: 15px;
}
.wrap { max-width: 1120px; margin: 0 auto; padding: 18px 14px 30px; }
h1, h2, h3 { margin: 0; font-weight: 600; letter-spacing: -0.01em; }
.mono { font-family: var(--font-mono); font-variant-numeric: tabular-nums; }
.sr {
  position: absolute; width: 1px; height: 1px; padding: 0; margin: -1px;
  overflow: hidden; clip: rect(0 0 0 0); white-space: nowrap; border: 0;
}
:focus-visible { outline: 2px solid var(--accent); outline-offset: 2px; border-radius: 4px; }

/* ---------- header ---------- */
.head {
  display: flex; flex-wrap: wrap; gap: 12px 16px;
  align-items: flex-start; justify-content: space-between;
  padding-bottom: 14px; margin-bottom: 14px;
  border-bottom: 1px solid var(--line);
}
.head h1 { font-size: 1.32rem; }
.lede { margin: 5px 0 0; color: var(--muted); max-width: 60ch; font-size: 0.95rem; }
.status {
  display: inline-flex; align-items: center; gap: 8px;
  font-family: var(--font-mono); font-size: 0.74rem; letter-spacing: 0.02em;
  padding: 6px 10px; border: 1px solid var(--line); border-radius: 999px;
  background: var(--surface); color: var(--muted); white-space: nowrap; flex-shrink: 0;
}
.status .dot { width: 8px; height: 8px; border-radius: 50%; background: var(--muted); flex: none; }
.status[data-state="run"] .dot { background: var(--accent); animation: pulse 1.1s ease-in-out infinite; }
.status[data-state="run"] { color: var(--accent); border-color: var(--accent); background: var(--accent-soft); }
.status[data-state="ok"] .dot { background: var(--run); }
.status[data-state="ok"] { color: var(--run); border-color: var(--run); background: var(--run-soft); }
@keyframes pulse { 0%,100% { opacity: 1; } 50% { opacity: 0.25; } }

/* ---------- layout ---------- */
.grid { display: grid; gap: 14px; grid-template-columns: 286px minmax(0, 1fr); align-items: start; }
.col { display: grid; gap: 14px; min-width: 0; }
/* the readouts column is tall; keep the controls reachable while reading it */
@media (min-width: 881px) { .controls { position: sticky; top: 14px; } }
@media (max-width: 880px) {
  .grid { grid-template-columns: minmax(0, 1fr); }
}
.panel {
  background: var(--surface); border: 1px solid var(--line);
  border-radius: var(--radius); padding: 14px; min-width: 0;
}
.panel > h2 {
  font-family: var(--font-mono); font-size: 0.7rem; text-transform: uppercase;
  letter-spacing: 0.09em; color: var(--muted); font-weight: 600; margin-bottom: 11px;
}

/* ---------- buttons ---------- */
button {
  font: inherit; color: var(--ink); background: var(--surface);
  border: 1px solid var(--line); border-radius: 7px;
  padding: 7px 11px; min-height: 36px; cursor: pointer;
  font-family: var(--font-mono); font-size: 0.75rem;
  transition: background 0.12s ease, border-color 0.12s ease, color 0.12s ease;
}
button:hover { border-color: var(--accent); color: var(--accent); }
button[aria-pressed="true"] { background: var(--accent-soft); border-color: var(--accent); color: var(--accent); }
.picker { display: grid; grid-template-columns: repeat(6, minmax(0, 1fr)); gap: 6px; }
.picker button { min-width: 0; padding: 7px 2px; font-size: 0.82rem; font-weight: 600; }
.picker-legend, .grp-legend {
  font-family: var(--font-mono); font-size: 0.63rem; text-transform: uppercase;
  letter-spacing: 0.08em; color: var(--muted); display: block; margin-bottom: 6px;
}
.rollrow { display: flex; gap: 6px; margin-bottom: 8px; }
.rollrow button { flex: 1 1 0; }
.rollrow button.primary {
  flex: 1.35 1 0; background: var(--accent-soft); border-color: var(--accent);
  color: var(--accent); font-weight: 600;
}
.rollrow button.primary:hover { background: var(--accent); color: var(--surface); }
.utilrow { display: flex; gap: 6px; }
.utilrow button { flex: 1 1 0; }
.hint { font-family: var(--font-mono); font-size: 0.66rem; color: var(--muted); margin: 10px 0 0; line-height: 1.6; }

/* ---------- dice tray ---------- */
.tray-wrap { display: flex; align-items: center; gap: 14px; flex-wrap: wrap; }
.tray { display: flex; gap: 8px; flex-wrap: wrap; min-width: 0; }
.die {
  /* --dw drives every internal measure: percentage padding would resolve
     against the tray, not the die, and collapse the pips. */
  --dw: clamp(36px, 11vw, 52px);
  width: var(--dw); height: var(--dw);
  border-radius: calc(var(--dw) * 0.22); background: var(--bg); border: 1px solid var(--line);
  display: grid; grid-template-columns: repeat(3, 1fr); grid-template-rows: repeat(3, 1fr);
  padding: calc(var(--dw) * 0.13); gap: calc(var(--dw) * 0.06); flex: none;
}
.die i { border-radius: 50%; background: transparent; display: block; }
.die i.on { background: var(--ink); }
.die.roll { animation: tumble 0.42s cubic-bezier(.36,.07,.19,.97); }
@keyframes tumble {
  0%   { transform: translateY(0) rotate(0deg); }
  25%  { transform: translateY(-13px) rotate(-19deg); }
  55%  { transform: translateY(-5px) rotate(13deg); }
  80%  { transform: translateY(-2px) rotate(-6deg); }
  100% { transform: translateY(0) rotate(0deg); }
}
.sum-badge { display: flex; align-items: baseline; gap: 7px; margin-left: auto; }
.sum-badge .eq { font-family: var(--font-mono); font-size: 1.1rem; color: var(--muted); }
.sum-badge .val {
  font-family: var(--font-mono); font-variant-numeric: tabular-nums;
  font-size: 2.3rem; font-weight: 600; line-height: 1; letter-spacing: -0.03em; color: var(--accent);
}
.sum-badge .lab { font-family: var(--font-mono); font-size: 0.62rem; color: var(--muted); letter-spacing: 0.07em; }

/* ---------- stats ---------- */
.stats {
  display: grid; grid-template-columns: repeat(auto-fit, minmax(132px, 1fr));
  gap: 1px; background: var(--line); border: 1px solid var(--line);
  border-radius: var(--radius); overflow: hidden; margin: 0;
}
.stat { background: var(--surface); padding: 10px 12px; min-width: 0; }
.stat dt {
  font-family: var(--font-mono); font-size: 0.62rem; text-transform: uppercase;
  letter-spacing: 0.07em; color: var(--muted); margin-bottom: 3px;
}
.stat dd {
  margin: 0; font-family: var(--font-mono); font-variant-numeric: tabular-nums;
  font-size: 1.16rem; font-weight: 600; letter-spacing: -0.02em;
}
.stat dd small {
  font-size: 0.62rem; font-weight: 400; color: var(--muted);
  display: block; letter-spacing: 0.03em; margin-top: 2px;
}
.stat dd.good { color: var(--run); }

/* ---------- charts ---------- */
.chart-head { display: flex; flex-wrap: wrap; gap: 8px 14px; align-items: baseline; justify-content: space-between; margin-bottom: 10px; }
.chart-head h2 { font-family: var(--font-mono); font-size: 0.7rem; text-transform: uppercase; letter-spacing: 0.09em; color: var(--muted); font-weight: 600; }
.legend { display: flex; flex-wrap: wrap; gap: 4px 14px; font-family: var(--font-mono); font-size: 0.67rem; color: var(--muted); }
.legend span { display: inline-flex; align-items: center; gap: 6px; }
.swatch { width: 13px; height: 10px; border-radius: 2px; display: inline-block; border: 1px solid transparent; }
.sw-obs { background: var(--accent-soft); border-color: var(--accent); }
.sw-th { height: 0; border: 0; border-top: 2px solid var(--ink); width: 15px; border-radius: 0; }
canvas { display: block; width: 100%; border-radius: 6px; touch-action: pan-y; }
canvas:focus-visible { outline: 2px solid var(--accent); outline-offset: 2px; }
.readout {
  margin-top: 9px; padding: 8px 10px; border: 1px solid var(--line); border-radius: 7px;
  background: var(--bg); font-family: var(--font-mono); font-size: 0.72rem;
  font-variant-numeric: tabular-nums; display: flex; flex-wrap: wrap;
  gap: 3px 14px; min-height: 35px; align-items: center;
}
.readout b { font-weight: 600; color: var(--accent); }
.readout .k { color: var(--muted); }
.insight { margin: 10px 0 0; font-size: 0.87rem; color: var(--muted); }
.insight b { color: var(--ink); font-weight: 600; }

/* ---------- table ---------- */
.tbl-scroll { max-height: 300px; overflow: auto; border: 1px solid var(--line); border-radius: 7px; }
table { border-collapse: collapse; width: 100%; font-family: var(--font-mono); font-variant-numeric: tabular-nums; font-size: 0.73rem; }
thead th {
  position: sticky; top: 0; background: var(--bg); text-align: right;
  font-weight: 600; font-size: 0.62rem; text-transform: uppercase; letter-spacing: 0.07em;
  color: var(--muted); padding: 7px 9px; border-bottom: 1px solid var(--line); white-space: nowrap;
}
thead th:first-child { text-align: left; }
tbody td { padding: 5px 9px; text-align: right; border-bottom: 1px solid var(--line); white-space: nowrap; }
tbody td:first-child { text-align: left; font-weight: 600; }
tbody tr:last-child td { border-bottom: 0; }
tbody tr { cursor: pointer; }
tbody tr:hover td { background: var(--bg); }
tbody tr.sel td { background: var(--accent-soft); }
tbody tr.sel td:first-child { color: var(--accent); }
tbody td.dim { color: var(--muted); }
.gapcell { display: flex; align-items: center; justify-content: flex-end; gap: 7px; }
.gapbar { height: 6px; border-radius: 3px; background: var(--accent); opacity: 0.55; flex: none; }
.gapnum { min-width: 4.4em; display: inline-block; }
.tbl-note { margin: 9px 0 0; font-size: 0.85rem; color: var(--muted); }
.tbl-note b { color: var(--ink); font-weight: 600; font-family: var(--font-mono); }

/* ---------- footer ---------- */
.foot {
  margin-top: 18px; padding-top: 12px; border-top: 1px solid var(--line);
  font-family: var(--font-mono); font-size: 0.7rem; color: var(--muted);
  display: flex; justify-content: space-between; flex-wrap: wrap; gap: 8px;
}

@media (prefers-reduced-motion: reduce) {
  *, *::before, *::after {
    animation-duration: 0.001ms !important; animation-iteration-count: 1 !important;
    transition-duration: 0.001ms !important;
  }
}
@media (max-width: 460px) {
  .wrap { padding: 14px 11px 24px; }
  .head h1 { font-size: 1.14rem; }
  .sum-badge .val { font-size: 1.9rem; }
  .tray { gap: 6px; }
  /* narrow screens: drop the gap sparkbar so the gap number itself still fits */
  table { font-size: 0.7rem; }
  thead th, tbody td { padding-left: 6px; padding-right: 6px; }
  .gapbar { display: none; }
  .gapnum { min-width: 3.9em; }
}
</style>
</head>
<body>
<div class="wrap">

  <header class="head">
    <div>
      <h1>Dice Probability Lab</h1>
      <p class="lede">Roll a handful of dice over and over. The bars are what actually happened; the line is what the math says should happen. Keep rolling and the bars climb onto the line.</p>
    </div>
    <div class="status" id="status" data-state="idle">
      <span class="dot" aria-hidden="true"></span>
      <span id="statusText">250 rolls</span>
    </div>
  </header>

  <main class="grid">

    <section class="panel controls" aria-labelledby="ctlH">
      <h2 id="ctlH">Controls</h2>

      <div style="margin-bottom:14px">
        <span class="picker-legend" id="diceLbl">How many dice</span>
        <div class="picker" role="group" aria-labelledby="diceLbl" id="picker"></div>
      </div>

      <div>
        <span class="grp-legend">Roll them</span>
        <div class="rollrow">
          <button type="button" id="b1" class="primary">roll</button>
          <button type="button" id="b100">&times;100</button>
          <button type="button" id="b1k">&times;1000</button>
        </div>
        <div class="utilrow">
          <button type="button" id="bauto" aria-pressed="false">auto roll</button>
          <button type="button" id="bclear">clear</button>
        </div>
      </div>

      <p class="hint" id="hint">tip: hit &times;1000 a few times and watch<br>the gap collapse. then try 1 die, and 6.</p>
    </section>

    <div class="col">

      <section class="panel" aria-labelledby="trayH">
        <h2 id="trayH">The roll</h2>
        <div class="tray-wrap">
          <div class="tray" id="tray" aria-hidden="true"></div>
          <div class="sum-badge">
            <span class="eq" aria-hidden="true">=</span>
            <div>
              <div class="val" id="sumVal">7</div>
              <div class="lab">SUM</div>
            </div>
          </div>
        </div>
        <p class="sr" id="live" role="status" aria-live="polite"></p>
      </section>

      <dl class="stats">
        <div class="stat"><dt>Rolls</dt><dd id="s-rolls">—</dd></div>
        <div class="stat"><dt>Average sum</dt><dd id="s-mean">—<small id="s-mean-sub">&nbsp;</small></dd></div>
        <div class="stat"><dt>Most common</dt><dd id="s-mode">—<small id="s-mode-sub">&nbsp;</small></dd></div>
        <div class="stat"><dt>Biggest gap</dt><dd id="s-gap">—<small id="s-gap-sub">&nbsp;</small></dd></div>
      </dl>

      <section class="panel" aria-labelledby="chartH">
        <div class="chart-head">
          <h2 id="chartH">Sums · observed vs theory</h2>
          <div class="legend">
            <span><i class="swatch sw-obs" aria-hidden="true"></i>observed</span>
            <span><i class="swatch sw-th" aria-hidden="true"></i>theory</span>
          </div>
        </div>
        <canvas id="chart" tabindex="0" role="img"
                aria-label="Histogram of dice sums with the theoretical distribution drawn over it. Use the left and right arrow keys to read each sum."></canvas>
        <div class="readout mono" id="readout" role="status" aria-live="polite"></div>
        <p class="insight" id="insight"></p>
      </section>

      <section class="panel" aria-labelledby="convH">
        <div class="chart-head">
          <h2 id="convH">Gap shrinking as rolls pile up</h2>
          <div class="legend"><span>log scale &middot; goal &le; 1.00 pp</span></div>
        </div>
        <canvas id="spark" aria-hidden="true"></canvas>
      </section>

      <section class="panel" aria-labelledby="tblH">
        <h2 id="tblH">Expected vs observed</h2>
        <div class="tbl-scroll">
          <table>
            <caption class="sr">Every possible sum with the number of dice combinations that make it, the theoretical share of rolls, the observed share, and the gap between them.</caption>
            <thead>
              <tr>
                <th scope="col">Sum</th>
                <th scope="col">Ways</th>
                <th scope="col">Theory</th>
                <th scope="col">Observed</th>
                <th scope="col">Gap</th>
              </tr>
            </thead>
            <tbody id="tbody"></tbody>
          </table>
        </div>
        <p class="tbl-note" id="tblNote"></p>
      </section>

    </div>
  </main>

  <footer class="foot">
    <span>demo &middot; sloprun.dev</span>
    <span id="footRight">&mdash;</span>
  </footer>
</div>

<script>
(function () {
  "use strict";

  /* ------------------------------------------------------------------
   * State
   * ------------------------------------------------------------------ */
  var MAX_ROLLS = 2000000;
  var GOAL_PP = 1.0;          /* biggest-gap goal, in percentage points */
  var MIN_ROLLS_OK = 2000;    /* don't call it converged on a lucky few */
  var SEED_ROLLS = 250;

  var N = 2;                  /* dice count */
  var bins = 0;               /* number of distinct sums */
  var ways = [];              /* combinations per sum */
  var waysTotal = 0;          /* 6^N */
  var expected = [];          /* theoretical probability per sum */
  var counts = [];            /* observed count per sum */
  var total = 0;              /* rolls so far */
  var lastDice = [];
  var lastSum = 0;

  var history = [];           /* [rolls, gapPP] samples for the sparkline */
  var nextSample = 0;
  var cursor = -1;            /* selected bin index, -1 = none */
  var flashBin = -1;
  var flashTimer = 0;

  var pending = 0, perFrame = 0, auto = false, autoRate = 0, raf = 0;
  var growT = 1, growRaf = 0;
  var spin = null;
  var lastTablePaint = 0;

  var RM = window.matchMedia("(prefers-reduced-motion: reduce)");
  function reduced() { return RM.matches; }

  var $ = function (id) { return document.getElementById(id); };
  var elTray = $("tray"), elSum = $("sumVal"), elLive = $("live");
  var elStatus = $("status"), elStatusText = $("statusText");
  var elChart = $("chart"), elSpark = $("spark");
  var elReadout = $("readout"), elInsight = $("insight");
  var elTbody = $("tbody"), elTblNote = $("tblNote"), elFootRight = $("footRight");
  var diceEls = [];
  var rowEls = [];

  /* ------------------------------------------------------------------
   * Theory: exact distribution of the sum of N six-sided dice
   * ------------------------------------------------------------------ */
  function buildTheory(n) {
    var w = [1], i, f, nw;
    for (var d = 0; d < n; d++) {
      nw = new Array(w.length + 5);
      for (i = 0; i < nw.length; i++) nw[i] = 0;
      for (i = 0; i < w.length; i++) {
        for (f = 0; f < 6; f++) nw[i + f] += w[i];
      }
      w = nw;
    }
    ways = w;
    bins = w.length;
    waysTotal = Math.pow(6, n);
    expected = new Array(bins);
    for (i = 0; i < bins; i++) expected[i] = ways[i] / waysTotal;
  }

  function sumOf(i) { return N + i; }

  /* ------------------------------------------------------------------
   * Rolling
   * ------------------------------------------------------------------ */
  function rollBulk(k) {
    if (k < 1) return;
    var n = N, s = lastSum, i, d, v;
    for (i = 0; i < k; i++) {
      s = 0;
      for (d = 0; d < n; d++) { v = (Math.random() * 6 | 0) + 1; lastDice[d] = v; s += v; }
      counts[s - n]++;
    }
    total += k;
    lastSum = s;
  }

  function randomFaces() {
    var a = [], d;
    for (d = 0; d < N; d++) a.push((Math.random() * 6 | 0) + 1);
    return a;
  }

  /* ------------------------------------------------------------------
   * Stats
   * ------------------------------------------------------------------ */
  function stats() {
    var gap = 0, gapAt = 0, mean = 0, mode = 0, modeC = -1, i, obs, g;
    for (i = 0; i < bins; i++) {
      obs = total ? counts[i] / total : 0;
      g = Math.abs(obs - expected[i]);
      if (g > gap) { gap = g; gapAt = i; }
      mean += counts[i] * sumOf(i);
      if (counts[i] > modeC) { modeC = counts[i]; mode = i; }
    }
    mean = total ? mean / total : 0;
    return {
      gapPP: gap * 100, gapAt: gapAt, mean: mean, mode: mode, modeC: modeC,
      ok: total >= MIN_ROLLS_OK && gap * 100 <= GOAL_PP
    };
  }

  function theoryMode() {
    var best = -1, at = 0, ties = 0, i;
    for (i = 0; i < bins; i++) {
      if (ways[i] > best) { best = ways[i]; at = i; ties = 1; }
      else if (ways[i] === best) ties++;
    }
    return { at: at, ways: best, ties: ties };
  }

  /* ------------------------------------------------------------------
   * Formatting
   * ------------------------------------------------------------------ */
  function num(n) { return n.toLocaleString("en-US"); }
  function pct(p) {
    var v = p * 100;
    if (v > 0 && v < 0.01) return v.toPrecision(2) + "%";   /* 1-in-46,656 is not 0.00% */
    return v.toFixed(2) + "%";
  }
  function signed(d) {                                       /* pp delta, never "−0.00" */
    var a = Math.abs(d);
    return (a < 0.005 ? "" : (d >= 0 ? "+" : "−")) + a.toFixed(2);
  }
  function pp(x) { return x.toFixed(2) + " pp"; }

  /* ------------------------------------------------------------------
   * Canvas helpers
   * ------------------------------------------------------------------ */
  function cssVar(name, fallback) {
    var v = getComputedStyle(document.documentElement).getPropertyValue(name).trim();
    return v || fallback;
  }
  function rgba(hex, a) {
    var h = hex.replace("#", "");
    if (h.length === 3) h = h[0] + h[0] + h[1] + h[1] + h[2] + h[2];
    var n = parseInt(h, 16);
    if (isNaN(n)) return hex;
    return "rgba(" + ((n >> 16) & 255) + "," + ((n >> 8) & 255) + "," + (n & 255) + "," + a + ")";
  }
  function fit(cv, h) {
    var dpr = Math.min(window.devicePixelRatio || 1, 2);
    var w = cv.clientWidth || (cv.parentNode ? cv.parentNode.clientWidth : 320) || 320;
    cv.style.height = h + "px";
    cv.width = Math.max(1, Math.round(w * dpr));
    cv.height = Math.max(1, Math.round(h * dpr));
    var ctx = cv.getContext("2d");
    ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
    ctx.clearRect(0, 0, w, h);
    return { ctx: ctx, w: w, h: h };
  }
  function niceStep(raw) {
    if (raw <= 0) return 1;
    var p = Math.pow(10, Math.floor(Math.log(raw) / Math.LN10));
    var m = raw / p;
    var s = m <= 1 ? 1 : m <= 2 ? 2 : m <= 5 ? 5 : 10;
    return s * p;
  }

  var geom = null; /* chart geometry, kept for pointer hit-testing */

  /* ------------------------------------------------------------------
   * Chart: histogram + theory line
   * ------------------------------------------------------------------ */
  function drawChart() {
    var narrow = window.innerWidth < 560;
    var H = narrow ? 218 : 288;
    var c = fit(elChart, H), ctx = c.ctx, W = c.w;
    if (!bins) return;

    var ink = cssVar("--ink", "#1A1D21"), muted = cssVar("--muted", "#5A6068");
    var line = cssVar("--line", "#E3E2DC"), accent = cssVar("--accent", "#C05600");
    var surface = cssVar("--surface", "#FFFFFF");
    var mono = cssVar("--font-mono", "monospace");

    var padL = narrow ? 34 : 42, padR = 8, padT = 12, padB = 26;
    var pw = Math.max(10, W - padL - padR), ph = Math.max(10, H - padT - padB);

    var maxE = 0, maxO = 0, i;
    for (i = 0; i < bins; i++) {
      if (expected[i] > maxE) maxE = expected[i];
      if (total && counts[i] / total > maxO) maxO = counts[i] / total;
    }
    var yMax = Math.max(maxE, maxO) * 1.18;
    if (yMax <= 0) yMax = 0.2;

    var step = pw / bins;
    var bw = Math.max(2, step * 0.76);
    function X(i) { return padL + (i + 0.5) * step; }
    function Y(p) { return padT + ph - (p / yMax) * ph; }

    /* grid */
    var gs = niceStep(yMax / 4);
    var gdec = gs * 100 < 1 ? 1 : 0;   /* one decimals rule for the whole axis */
    ctx.font = "11px " + mono;
    ctx.textBaseline = "middle";
    ctx.textAlign = "right";
    for (var g = 0; g <= yMax + 1e-9; g += gs) {
      var y = Y(g);
      if (y < padT - 1) break;
      ctx.strokeStyle = rgba(line, 0.95);
      ctx.lineWidth = 1;
      ctx.beginPath();
      ctx.moveTo(padL, Math.round(y) + 0.5);
      ctx.lineTo(padL + pw, Math.round(y) + 0.5);
      ctx.stroke();
      ctx.fillStyle = muted;
      ctx.fillText((g * 100).toFixed(gdec) + "%", padL - 6, y);
    }

    /* cursor band */
    if (cursor >= 0 && cursor < bins) {
      ctx.fillStyle = rgba(ink, 0.06);
      ctx.fillRect(padL + cursor * step, padT, step, ph);
    }

    /* observed bars */
    for (i = 0; i < bins; i++) {
      var p = total ? counts[i] / total : 0;
      var hgt = (p / yMax) * ph * growT;
      if (hgt < 0.6) continue;
      var x = X(i) - bw / 2;
      var y0 = padT + ph - hgt;
      var hot = (i === cursor) || (i === flashBin);
      ctx.fillStyle = rgba(accent, hot ? 0.42 : 0.24);
      ctx.fillRect(x, y0, bw, hgt);
      ctx.strokeStyle = rgba(accent, hot ? 1 : 0.72);
      ctx.lineWidth = hot ? 2 : 1;
      ctx.strokeRect(Math.round(x) + 0.5, Math.round(y0) + 0.5, Math.round(bw) - 1, Math.round(hgt));
    }

    /* theory line */
    ctx.strokeStyle = ink;
    ctx.lineWidth = 2;
    ctx.lineJoin = "round";
    ctx.beginPath();
    for (i = 0; i < bins; i++) {
      var xx = X(i), yy = Y(expected[i]);
      if (i === 0) ctx.moveTo(xx, yy); else ctx.lineTo(xx, yy);
    }
    ctx.stroke();
    for (i = 0; i < bins; i++) {
      ctx.beginPath();
      ctx.arc(X(i), Y(expected[i]), step > 14 ? 3 : 2.2, 0, 6.2832);
      ctx.fillStyle = ink;
      ctx.fill();
      ctx.lineWidth = 1.5;
      ctx.strokeStyle = surface;
      ctx.stroke();
    }

    /* baseline */
    ctx.strokeStyle = rgba(muted, 0.55);
    ctx.lineWidth = 1;
    ctx.beginPath();
    ctx.moveTo(padL, Math.round(padT + ph) + 0.5);
    ctx.lineTo(padL + pw, Math.round(padT + ph) + 0.5);
    ctx.stroke();

    /* x labels */
    var lblStep = bins <= 12 ? 1 : bins <= 20 ? 2 : 3;
    ctx.textAlign = "center";
    ctx.textBaseline = "top";
    ctx.font = "11px " + mono;
    for (i = 0; i < bins; i++) {
      if (i % lblStep !== 0 && i !== cursor) continue;
      ctx.fillStyle = (i === cursor) ? accent : muted;
      ctx.fillText(String(sumOf(i)), X(i), padT + ph + 7);
    }

    geom = { padL: padL, padT: padT, pw: pw, ph: ph, step: step };
  }

  /* ------------------------------------------------------------------
   * Sparkline: biggest gap vs number of rolls (log x)
   * ------------------------------------------------------------------ */
  function drawSpark(st) {
    var H = 76;
    var c = fit(elSpark, H), ctx = c.ctx, W = c.w;
    var ink = cssVar("--ink", "#1A1D21"), muted = cssVar("--muted", "#5A6068");
    var line = cssVar("--line", "#E3E2DC"), accent = cssVar("--accent", "#C05600");
    var run = cssVar("--run", "#1A7F37"), surface = cssVar("--surface", "#FFFFFF");
    var mono = cssVar("--font-mono", "monospace");

    var padL = 40, padR = 8, padT = 10, padB = 16;
    var pw = Math.max(10, W - padL - padR), ph = Math.max(10, H - padT - padB);

    var maxG = GOAL_PP * 1.6, i;
    for (i = 0; i < history.length; i++) if (history[i][1] > maxG) maxG = history[i][1];
    maxG = maxG * 1.1;

    var x0 = Math.log(10) / Math.LN10;
    var x1 = Math.log(Math.max(1000, total)) / Math.LN10;
    function X(n) {
      var lv = Math.log(Math.max(10, n)) / Math.LN10;
      return padL + ((lv - x0) / Math.max(0.001, x1 - x0)) * pw;
    }
    function Y(g) { return padT + ph - (Math.min(g, maxG) / maxG) * ph; }

    /* frame */
    ctx.strokeStyle = rgba(line, 1);
    ctx.lineWidth = 1;
    ctx.beginPath();
    ctx.moveTo(padL, Math.round(padT + ph) + 0.5);
    ctx.lineTo(padL + pw, Math.round(padT + ph) + 0.5);
    ctx.stroke();

    /* goal line */
    var gy = Y(GOAL_PP);
    ctx.save();
    ctx.setLineDash([4, 4]);
    ctx.strokeStyle = rgba(muted, 0.8);
    ctx.beginPath();
    ctx.moveTo(padL, Math.round(gy) + 0.5);
    ctx.lineTo(padL + pw, Math.round(gy) + 0.5);
    ctx.stroke();
    ctx.restore();

    ctx.font = "10px " + mono;
    ctx.fillStyle = muted;
    ctx.textAlign = "right";
    ctx.textBaseline = "middle";
    ctx.fillText("1.0pp", padL - 5, gy);
    ctx.fillText(maxG.toFixed(1), padL - 5, padT + 3);

    /* empty state: an axis with no trace on it reads as broken */
    if (history.length < 2) {
      var msg = total ? "trace starts at 10 rolls" : "no rolls yet — hit roll";
      var cx = padL + pw / 2, cy = padT + ph / 2;
      ctx.font = "11px " + mono;
      ctx.textAlign = "center";
      ctx.textBaseline = "middle";
      var tw = ctx.measureText(msg).width;
      ctx.fillStyle = surface;                     /* knock the goal dashes out behind it */
      ctx.fillRect(cx - tw / 2 - 6, cy - 8, tw + 12, 16);
      ctx.fillStyle = muted;
      ctx.fillText(msg, cx, cy);
    }

    /* series */
    if (history.length > 1) {
      ctx.strokeStyle = accent;
      ctx.lineWidth = 1.75;
      ctx.lineJoin = "round";
      ctx.beginPath();
      for (i = 0; i < history.length; i++) {
        var px = X(history[i][0]), py = Y(history[i][1]);
        if (i === 0) ctx.moveTo(px, py); else ctx.lineTo(px, py);
      }
      ctx.stroke();
      var lx = X(total), ly = Y(st.gapPP);
      ctx.beginPath();
      ctx.arc(lx, ly, 3.4, 0, 6.2832);
      ctx.fillStyle = st.ok ? run : accent;
      ctx.fill();
      ctx.lineWidth = 1.5;
      ctx.strokeStyle = surface;
      ctx.stroke();
    }

    ctx.font = "10px " + mono;
    ctx.fillStyle = muted;
    ctx.textBaseline = "top";
    ctx.textAlign = "left";
    ctx.fillText("10", padL, padT + ph + 3);
    ctx.textAlign = "right";
    ctx.fillText(num(Math.max(1000, total)) + " rolls", padL + pw, padT + ph + 3);
  }

  /* ------------------------------------------------------------------
   * Dice rendering
   * ------------------------------------------------------------------ */
  var PIPS = {
    1: [4], 2: [0, 8], 3: [0, 4, 8],
    4: [0, 2, 6, 8], 5: [0, 2, 4, 6, 8], 6: [0, 2, 3, 5, 6, 8]
  };
  function buildTray() {
    elTray.textContent = "";
    diceEls = [];
    for (var d = 0; d < N; d++) {
      var die = document.createElement("div");
      die.className = "die";
      for (var i = 0; i < 9; i++) die.appendChild(document.createElement("i"));
      elTray.appendChild(die);
      diceEls.push(die);
    }
  }
  function paintFaces(faces) {
    for (var d = 0; d < diceEls.length; d++) {
      var f = faces[d] || 1, cells = diceEls[d].children, on = PIPS[f];
      for (var i = 0; i < 9; i++) cells[i].className = "";
      for (var k = 0; k < on.length; k++) cells[on[k]].className = "on";
    }
  }

  /* ------------------------------------------------------------------
   * Table
   * ------------------------------------------------------------------ */
  function buildTable() {
    elTbody.textContent = "";
    rowEls = [];
    for (var i = 0; i < bins; i++) {
      var tr = document.createElement("tr");
      var cells = [];
      for (var c = 0; c < 5; c++) {
        var td = document.createElement("td");
        if (c === 1) td.className = "dim";
        tr.appendChild(td);
        cells.push(td);
      }
      var wrapc = document.createElement("span");
      wrapc.className = "gapcell";
      var bar = document.createElement("span");
      bar.className = "gapbar";
      var nums = document.createElement("span");
      nums.className = "gapnum";
      wrapc.appendChild(bar);
      wrapc.appendChild(nums);
      cells[4].appendChild(wrapc);
      (function (idx) {
        tr.addEventListener("click", function () { setCursor(idx); });
      })(i);
      elTbody.appendChild(tr);
      rowEls.push({ tr: tr, c: cells, bar: bar, nums: nums });
    }
    var tm = theoryMode();
    if (N === 1) {
      elTblNote.innerHTML = "One die: every face is equally likely, <b>1 way in 6</b> each. The bars should end up flat.";
    } else {
      elTblNote.innerHTML = "<b>" + sumOf(tm.at) + "</b> is the most likely sum because <b>" + num(tm.ways) +
        "</b> of the " + num(waysTotal) + " possible dice combinations add up to it. The extremes have exactly one combination each.";
    }
  }

  function paintTable(st) {
    var maxGapPct = Math.max(st.gapPP, 0.6);
    for (var i = 0; i < bins; i++) {
      var r = rowEls[i];
      var obs = total ? counts[i] / total : 0;
      var d = (obs - expected[i]) * 100;
      r.c[0].textContent = String(sumOf(i));
      r.c[1].textContent = num(ways[i]);
      r.c[2].textContent = pct(expected[i]);
      r.c[3].textContent = total ? pct(obs) : "—";
      r.nums.textContent = total ? signed(d) : "—";
      r.bar.style.width = total ? (Math.abs(d) / maxGapPct * 34).toFixed(1) + "px" : "0px";
      if ((i === cursor) !== r.tr.classList.contains("sel")) r.tr.classList.toggle("sel", i === cursor);
    }
  }

  /* ------------------------------------------------------------------
   * Readout + insight + status
   * ------------------------------------------------------------------ */
  function paintReadout() {
    if (cursor < 0 || cursor >= bins) {
      elReadout.innerHTML = '<span class="k">tap or hover a bar — or press ← → — to inspect any sum</span>';
      return;
    }
    var i = cursor, obs = total ? counts[i] / total : 0;
    var d = (obs - expected[i]) * 100;
    elReadout.innerHTML =
      '<span>sum <b>' + sumOf(i) + '</b></span>' +
      '<span><span class="k">ways</span> ' + num(ways[i]) + '/' + num(waysTotal) + '</span>' +
      '<span><span class="k">theory</span> ' + pct(expected[i]) + '</span>' +
      '<span><span class="k">observed</span> ' + (total ? pct(obs) + ' (' + num(counts[i]) + ')' : '—') + '</span>' +
      '<span><span class="k">gap</span> ' + (total ? signed(d) + ' pp' : '—') + '</span>';
  }

  function paintInsight(st) {
    if (total === 0) {
      elInsight.innerHTML = "No rolls yet — the line is still there, because probability does not need to be measured to exist. Hit <b>roll</b>.";
      return;
    }
    if (st.ok) {
      elInsight.innerHTML = "After <b>" + num(total) + "</b> rolls every bar sits within <b>" + pp(st.gapPP) +
        "</b> of theory. That is the law of large numbers: no single roll is predictable, but the shape of a great many of them is.";
      return;
    }
    if (total < 400) {
      elInsight.innerHTML = "Only <b>" + num(total) + "</b> roll" + (total === 1 ? "" : "s") +
        " so far, so the picture is lumpy — the worst bar is <b>" + pp(st.gapPP) +
        "</b> from the line. Randomness looks messy up close.";
      return;
    }
    elInsight.innerHTML = "<b>" + num(total) + "</b> rolls in, the worst bar is <b>" + pp(st.gapPP) +
      "</b> from the line. Keep going — the error shrinks roughly with the square root of the number of rolls.";
  }

  function paintStatus(st) {
    if (pending > 0 || auto) {
      elStatus.setAttribute("data-state", "run");
      elStatusText.textContent = "rolling · " + num(total);
      return;
    }
    if (st.ok) {
      elStatus.setAttribute("data-state", "ok");
      elStatusText.textContent = "converged · gap " + st.gapPP.toFixed(2) + "pp";
      return;
    }
    elStatus.setAttribute("data-state", "idle");
    elStatusText.textContent = num(total) + " roll" + (total === 1 ? "" : "s");
  }

  /* ------------------------------------------------------------------
   * Refresh everything
   * ------------------------------------------------------------------ */
  function sample(st) {
    if (total < nextSample) return;
    history.push([total, (st || stats()).gapPP]);
    if (history.length > 800) history.splice(0, 400);
    nextSample = Math.max(total + 1, Math.ceil(total * 1.1));
  }

  function refresh(force) {
    var st = stats();
    sample(st);

    paintFaces(lastDice);
    elSum.textContent = total ? String(lastSum) : "—";

    $("s-rolls").textContent = num(total);
    $("s-mean").firstChild.nodeValue = total ? st.mean.toFixed(3) : "—";
    $("s-mean-sub").textContent = "expect " + (3.5 * N).toFixed(2);
    $("s-mode").firstChild.nodeValue = total ? String(sumOf(st.mode)) : "—";
    var tm = theoryMode();
    $("s-mode-sub").textContent = total
      ? num(st.modeC) + " times · " + (tm.ties > 1 ? "all sums tied" : "theory " + sumOf(tm.at))
      : " ";
    var gapEl = $("s-gap");
    gapEl.firstChild.nodeValue = total ? st.gapPP.toFixed(2) + "pp" : "—";
    gapEl.classList.toggle("good", !!st.ok);
    $("s-gap-sub").textContent = st.ok ? "within goal" : "goal ≤ 1.00pp";

    var now = performance.now();
    if (force || now - lastTablePaintSafe() > 90) { paintTable(st); lastTablePaint = now; }

    drawChart();
    drawSpark(st);
    paintReadout();
    paintInsight(st);
    paintStatus(st);

    elFootRight.textContent = N + (N === 1 ? " die" : " dice") + " · " + num(waysTotal) + " combinations · " + bins + " sums";
    return st;
  }
  function lastTablePaintSafe() { return lastTablePaint; }

  /* ------------------------------------------------------------------
   * Animation driver
   * ------------------------------------------------------------------ */
  function ensureRaf() { if (!raf) raf = requestAnimationFrame(tick); }
  function stopRaf() { if (raf) { cancelAnimationFrame(raf); raf = 0; } }

  function tick() {
    raf = 0;
    var did = false;
    if (pending > 0) {
      var k = Math.min(pending, perFrame);
      rollBulk(k);
      pending -= k;
      did = true;
    }
    if (auto && pending <= 0) {
      autoRate = Math.min(900, Math.round(autoRate * 1.09) + 2);
      rollBulk(autoRate);
      did = true;
      if (total >= MAX_ROLLS) setAuto(false);
    }
    if (did) refresh();
    if (pending > 0 || auto) ensureRaf();
    else { refresh(true); announceBulk(); }
  }

  function queueRolls(k) {
    finishSpin(true);
    if (reduced()) {
      rollBulk(k);
      refresh(true);
      announceBulk();
      return;
    }
    pending += k;
    perFrame = Math.max(1, Math.ceil(pending / 34));
    ensureRaf();
  }

  function setAuto(on) {
    auto = !!on;
    $("bauto").setAttribute("aria-pressed", auto ? "true" : "false");
    $("bauto").textContent = auto ? "stop" : "auto roll";
    if (auto) { finishSpin(true); autoRate = 4; ensureRaf(); }
    else { refresh(true); }
  }

  function animateGrow() {
    if (reduced()) { growT = 1; return; }
    if (growRaf) cancelAnimationFrame(growRaf);
    var t0 = performance.now();
    growT = 0;
    (function step(now) {
      var u = Math.min(1, (now - t0) / 420);
      growT = 1 - Math.pow(1 - u, 3);
      drawChart();
      if (u < 1) growRaf = requestAnimationFrame(step);
      else { growRaf = 0; growT = 1; }
    })(t0);
  }

  /* ------------------------------------------------------------------
   * Single animated roll
   * ------------------------------------------------------------------ */
  function finishSpin(silent) {
    if (!spin) return;
    clearInterval(spin.iv);
    clearTimeout(spin.to);
    spin = null;
    for (var i = 0; i < diceEls.length; i++) diceEls[i].classList.remove("roll");
    rollBulk(1);
    refresh(true);
    if (!silent) { flash(); announceRoll(); }
  }

  function rollOnce() {
    if (reduced() || pending > 0 || auto) {
      rollBulk(1);
      refresh(true);
      flash();
      announceRoll();
      return;
    }
    finishSpin(true);
    var o = {};
    spin = o;
    for (var i = 0; i < diceEls.length; i++) {
      var d = diceEls[i];
      d.classList.remove("roll");
      void d.offsetWidth;
      d.style.animationDelay = (i * 28) + "ms";
      d.classList.add("roll");
    }
    elSum.textContent = "·";
    o.iv = setInterval(function () { paintFaces(randomFaces()); }, 62);
    o.to = setTimeout(function () { if (spin === o) finishSpin(false); }, 420);
  }

  function flash() {
    if (reduced()) return;
    flashBin = lastSum - N;
    drawChart();
    clearTimeout(flashTimer);
    flashTimer = setTimeout(function () { flashBin = -1; drawChart(); }, 300);
  }

  var lastAnnounced = -1;
  function announceRoll() {
    elLive.textContent = "Rolled " + lastDice.slice(0, N).join(" and ") + ". Sum " + lastSum + ". " +
      num(total) + " roll" + (total === 1 ? "" : "s") + " total.";
    lastAnnounced = total;
  }
  function announceBulk() {
    /* nothing rolled yet: the clear handler owns the message, and a "biggest gap"
       computed against zero observations is meaningless. */
    if (!total || total === lastAnnounced) return;
    var st = stats();
    elLive.textContent = num(total) + " rolls total. Biggest gap between observed and theory is " + st.gapPP.toFixed(2) + " percentage points" + (st.ok ? ", within the goal." : ".");
    lastAnnounced = total;
  }

  /* ------------------------------------------------------------------
   * Cursor
   * ------------------------------------------------------------------ */
  function setCursor(i) {
    if (i !== null && i >= 0) i = Math.max(0, Math.min(bins - 1, i));
    if (i === cursor) return;
    cursor = i;
    drawChart();
    paintReadout();
    paintTable(stats());
  }

  function pointerBin(ev) {
    if (!geom) return -1;
    var r = elChart.getBoundingClientRect();
    var x = (ev.touches ? ev.touches[0].clientX : ev.clientX) - r.left;
    var i = Math.floor((x - geom.padL) / geom.step);
    if (i < 0 || i >= bins) return -1;
    return i;
  }

  /* ------------------------------------------------------------------
   * Dice count
   * ------------------------------------------------------------------ */
  function setN(n, seed) {
    finishSpin(true);
    setAuto(false);
    pending = 0;
    stopRaf();
    N = n;
    lastDice = new Array(N);
    for (var d = 0; d < N; d++) lastDice[d] = 1;
    buildTheory(N);
    counts = new Array(bins);
    for (var i = 0; i < bins; i++) counts[i] = 0;
    total = 0;
    lastSum = N;
    history = [];
    nextSample = 10;
    cursor = -1;
    flashBin = -1;
    lastAnnounced = -1;
    buildTray();
    buildTable();
    var btns = $("picker").children;
    for (var b = 0; b < btns.length; b++) btns[b].setAttribute("aria-pressed", (b + 1 === n) ? "true" : "false");
    if (seed) {
      while (total < SEED_ROLLS) {
        rollBulk(Math.min(SEED_ROLLS - total, Math.max(1, Math.ceil(total * 0.12))));
        sample();
      }
    }
    refresh(true);
    animateGrow();
  }

  /* ------------------------------------------------------------------
   * Wiring
   * ------------------------------------------------------------------ */
  (function buildPicker() {
    var p = $("picker");
    for (var i = 1; i <= 6; i++) {
      (function (n) {
        var b = document.createElement("button");
        b.type = "button";
        b.textContent = String(n);
        b.setAttribute("aria-pressed", "false");
        b.setAttribute("aria-label", n + (n === 1 ? " die" : " dice"));
        b.addEventListener("click", function () { if (N !== n) setN(n, true); });
        p.appendChild(b);
      })(i);
    }
  })();

  $("b1").addEventListener("click", rollOnce);
  $("b100").addEventListener("click", function () { queueRolls(100); });
  $("b1k").addEventListener("click", function () { queueRolls(1000); });
  $("bauto").addEventListener("click", function () { setAuto(!auto); });
  $("bclear").addEventListener("click", function () {
    finishSpin(true);
    setAuto(false);
    pending = 0;
    stopRaf();
    for (var i = 0; i < bins; i++) counts[i] = 0;
    total = 0;
    history = [];
    nextSample = 10;
    lastAnnounced = -1;
    cursor = -1;
    refresh(true);
    elLive.textContent = "Cleared. 0 rolls.";
  });

  elChart.addEventListener("mousemove", function (e) { setCursor(pointerBin(e)); });
  elChart.addEventListener("mouseleave", function () { setCursor(-1); });
  var onTouch = function (e) {
    var i = pointerBin(e);
    if (i >= 0) setCursor(i);
  };
  elChart.addEventListener("touchstart", onTouch, { passive: true });
  elChart.addEventListener("touchmove", onTouch, { passive: true });
  elChart.addEventListener("keydown", function (e) {
    var k = e.key, base = cursor < 0 ? Math.floor(bins / 2) : cursor;
    if (k === "ArrowLeft") { setCursor(cursor < 0 ? base : Math.max(0, cursor - 1)); e.preventDefault(); }
    else if (k === "ArrowRight") { setCursor(cursor < 0 ? base : cursor + 1); e.preventDefault(); }
    else if (k === "Home") { setCursor(0); e.preventDefault(); }
    else if (k === "End") { setCursor(bins - 1); e.preventDefault(); }
    else if (k === "Escape") { setCursor(-1); }
  });
  elChart.addEventListener("blur", function () { setCursor(-1); });

  /* theme + resize */
  window.addEventListener("message", function (e) {
    var d = e.data;
    if (d && d.type === "sloprun:theme" && (d.theme === "light" || d.theme === "dark")) {
      document.documentElement.setAttribute("data-theme", d.theme);
      drawChart();
      drawSpark(stats());
    }
  });
  var mq = window.matchMedia("(prefers-color-scheme: dark)");
  var onScheme = function () { drawChart(); drawSpark(stats()); };
  if (mq.addEventListener) mq.addEventListener("change", onScheme);
  else if (mq.addListener) mq.addListener(onScheme);

  var rz = 0, lastW = -1;
  function onResize(force) {
    if (rz) return;
    rz = requestAnimationFrame(function () {
      rz = 0;
      var w = elChart.clientWidth;
      if (!force && w === lastW) return;
      lastW = w;
      drawChart();
      drawSpark(stats());
    });
  }
  window.addEventListener("resize", function () { onResize(true); });
  if (window.ResizeObserver) {
    try {
      new ResizeObserver(function () { onResize(false); }).observe(elChart.parentNode);
    } catch (err) { /* older engines: window resize is enough */ }
  }

  /* ------------------------------------------------------------------
   * Boot: never an empty room
   * ------------------------------------------------------------------ */
  setN(2, true);
})();
</script>
</body>
</html>