Birthday Paradox

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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1, viewport-fit=cover">
<title>Birthday Paradox — sloprun.dev</title>
<style>
/* ── sloprun design tokens (verbatim from demos/tokens.css) ───────────────── */
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/* ── end tokens ───────────────────────────────────────────────────────────── */

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  *, *::before, *::after { transition-duration: .001ms !important; animation-duration: .001ms !important; }
}
</style>
</head>
<body>
<div class="wrap">

  <header>
    <div class="top">
      <div>
        <h1>Birthday Paradox</h1>
        <p class="lede">
          Put <b>23 people</b> in a room and it is a coin flip that two of them share a birthday.
          Nobody believes it. So: fill a room, watch where everyone lands on the calendar, then
          run a thousand rooms and see whether reality agrees with the arithmetic.
        </p>
      </div>
      <div class="status" id="status" data-state="idle"><span class="dot"></span><span id="statusText">READY</span></div>
    </div>
  </header>

  <main class="stage">

    <div class="col">

      <section class="card s-ring" aria-label="One room on the calendar ring">
        <h2><span>One room on the calendar ring</span><b id="ringTag">23 PEOPLE</b></h2>
        <div class="cv cv-ring">
          <canvas id="ring" tabindex="0"
            aria-label="Calendar ring. Each dot is one person placed on their birthday; days shared by two or more people light up. Use the arrow keys to step through the people in the room."></canvas>
          <div class="tip" id="ringTip" hidden aria-hidden="true">
            <div class="n" id="tipName"></div>
            <div class="d" id="tipDate"></div>
          </div>
        </div>
        <p class="readout" id="ringRead"></p>
        <p class="keys"><kbd>&larr;</kbd><kbd>&rarr;</kbd> step through the room &middot; <kbd>Esc</kbd> clear</p>
      </section>

      <section class="card s-curve" aria-label="Probability curve">
        <h2><span>Chance of a shared birthday, 2 to 100 people</span><b id="curveTag" class="amb">n = 23 &rarr; 50.73%</b></h2>
        <div class="cv cv-curve">
          <canvas id="curve" class="pick" tabindex="0" role="slider"
            aria-valuemin="2" aria-valuemax="100" aria-valuenow="23"
            aria-valuetext="23 people, 50.73% chance of a shared birthday"
            aria-label="Group size on the shared-birthday probability curve. Click, drag, or use the arrow keys to change the group size."></canvas>
        </div>
        <div class="legend">
          <span><i></i>theory</span>
          <span><i class="hollow"></i>measured runs</span>
          <span>click or arrow-key the chart to move the group size</span>
        </div>
      </section>

      <section class="card s-rooms" aria-label="A thousand simulated rooms">
        <h2><span>1000 rooms, one square each</span><b id="roomsTag">n = 23</b></h2>
        <div class="cv cv-rooms">
          <canvas id="rooms" role="img" aria-label="A grid of one thousand simulated rooms; a filled square is a room where at least two people shared a birthday."></canvas>
        </div>
        <div class="bar" id="barWrap" role="presentation"><i id="bar"></i></div>
        <div class="legend"><span><i></i>shared birthday</span><span><i class="no"></i>all different</span></div>
        <hr class="divider">
        <div class="stats four">
          <div class="stat"><span class="k">Rooms with a match</span><span class="v" id="sHits">&mdash;</span></div>
          <div class="stat"><span class="k">Measured</span><span class="v" id="sEmp">&mdash;</span></div>
          <div class="stat"><span class="k">Theory</span><span class="v" id="sThe">50.73<span class="u">%</span></span></div>
          <div class="stat"><span class="k">Gap</span><span class="v" id="sGap">&mdash;</span></div>
        </div>
        <div class="pill" id="verdict"><span class="dot"></span><span id="verdictText">Run a thousand rooms to test the number on the left.</span></div>
        <p class="readout" id="totals"></p>
      </section>

    </div>

    <div class="col">

      <section class="card s-odds" aria-label="Probability for this group size">
        <h2><span>The odds right now</span></h2>
        <div class="big" id="bigP">50.73%</div>
        <p class="big-sub">chance that at least two of the <span class="mono" id="subN">23</span> people share a birthday</p>
        <hr class="divider">
        <div class="stats">
          <div class="stat"><span class="k">Pairs in the room</span><span class="v" id="sPairs">253</span></div>
          <div class="stat"><span class="k">Matches your day</span><span class="v" id="sSelf">5.86<span class="u">%</span></span></div>
        </div>
        <hr class="divider">
        <p class="formula" id="formula"></p>
      </section>

      <section class="card s-controls" aria-label="Controls">
        <h2><span>Controls</span></h2>
        <div class="ctl-top">
          <label for="nRange">People in the room</label>
          <span class="val" id="nOut">23</span>
        </div>
        <input type="range" id="nRange" min="2" max="100" step="1" value="23"
               aria-valuetext="23 people, 50.73% chance of a shared birthday">
        <div class="scale" aria-hidden="true">
          <span style="left:calc(8px + (100% - 16px) * 0)">2</span>
          <span class="mark" style="left:calc(8px + (100% - 16px) * .2143)">23</span>
          <span style="left:calc(8px + (100% - 16px) * .5918)">60</span>
          <span style="left:calc(8px + (100% - 16px) * 1)">100</span>
        </div>
        <div class="chips" id="chips" role="group" aria-label="Quick group sizes"></div>
        <div class="row">
          <button type="button" id="btnFill">Fill a new room</button>
          <button type="button" id="btnRun" class="primary">Run 1000 rooms</button>
        </div>
      </section>

      <section class="card s-why" aria-label="Why twenty-three">
        <h2><span>Why 23 is the surprise</span></h2>
        <p class="note">
          Ask around and most people guess <b>about 180</b> &mdash; half of 365. That answers a
          different question: how many strangers you need before one matches <b>your</b> birthday.
          In this room that chance is only <span class="amb" id="nSelf">5.86%</span>.
        </p>
        <p class="note">
          Nobody is the reference point. Every <em>pair</em> counts, and
          <span class="mono" id="nN">23</span> people quietly make <span class="mono" id="nPairs">253</span>
          pairs &mdash; each one its own little chance to collide. That is why the answer is
          <b>23</b> and not 180.
        </p>
        <p class="note" id="nCmp"></p>
        <div class="row"><button type="button" id="btnJump">Set the room to 23</button></div>
      </section>

    </div>
  </main>

  <footer>
    <span>birthday-paradox &middot; sloprun.dev</span>
    <span id="footNote">365 equally likely days &middot; no leap years, no twins</span>
  </footer>
</div>

<p class="sr-only" id="live" aria-live="polite"></p>

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    cells: null,       /* Uint8Array(1000) 0 none 1 match, 2 = not yet drawn */
    shown: 0,
    hits: 0,
    totRooms: 0,
    totHits: 0,
    runN: null,        /* group size the in-flight run is simulating */
    lastRunN: null,    /* group size the numbers on screen belong to */
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    var r = RG.c.getBoundingClientRect();
    var p = nearest(e.clientX - r.left, e.clientY - r.top);
    if (p) { showTip(p); st.cursor = p.i; } else { hideTip(); st.cursor = -1; }
    if (!st.animating) drawRing(1);
    ringReadout();
  }
  RG.c.addEventListener("pointermove", ringPoint);
  /* touch never fires a hover, so a tap has to do the same job */
  RG.c.addEventListener("pointerdown", ringPoint);
  RG.c.addEventListener("pointerleave", function () {
    hideTip(); st.cursor = -1; if (!st.animating) drawRing(1); ringReadout();
  });
  RG.c.addEventListener("keydown", function (e) {
    var k = e.key, moved = true;
    if (k === "ArrowRight" || k === "ArrowDown") st.cursor = (st.cursor + 1) % st.room.length;
    else if (k === "ArrowLeft" || k === "ArrowUp") st.cursor = (st.cursor <= 0 ? st.room.length : st.cursor) - 1;
    else if (k === "Home") st.cursor = 0;
    else if (k === "End") st.cursor = st.room.length - 1;
    else if (k === "Escape") st.cursor = -1;
    else moved = false;
    if (!moved) return;
    e.preventDefault();
    if (st.cursor >= 0) { drawRing(1); showTip(ringGeom.pts[st.cursor]); }
    else { hideTip(); drawRing(1); }
    ringReadout();
    if (st.cursor >= 0) say("Person " + (st.cursor + 1) + ", born " + dateLabel(st.room[st.cursor]));
  });

  /* ═══════════════════════════════════════════════════════════════════════
     CURVE
     ═══════════════════════════════════════════════════════════════════════ */

  var cg = { l: 0, r: 0, t: 0, b: 0 };

  function drawCurve() {
    fit(CU);
    var ctx = CU.ctx, w = CU.w, h = CU.h;
    var L = w < 420 ? 32 : 38, Rp = 12, T = 12, B = 24;
    cg.l = L; cg.r = w - Rp; cg.t = T; cg.b = h - B;
    var pw = cg.r - L, ph = cg.b - T;
    function X(n) { return L + (n - 2) / 98 * pw; }
    function Y(p) { return T + (1 - p) * ph; }

    /* grid */
    ctx.font = "9.5px " + C.mono;
    ctx.textBaseline = "middle"; ctx.textAlign = "right";
    var gl = [0, .25, .5, .75, 1], i;
    for (i = 0; i < gl.length; i++) {
      var y = Y(gl[i]);
      ctx.beginPath(); ctx.moveTo(L, y); ctx.lineTo(cg.r, y);
      ctx.strokeStyle = rgba(C.ink, gl[i] === .5 ? .18 : .09);
      ctx.lineWidth = 1;
      ctx.setLineDash(gl[i] === .5 ? [3, 3] : []);
      ctx.stroke(); ctx.setLineDash([]);
      ctx.fillStyle = rgba(C.muted, .95);
      ctx.fillText((gl[i] * 100) + "%", L - 6, y);
    }
    ctx.textAlign = "center"; ctx.textBaseline = "top";
    var xt = w < 420 ? [2, 23, 50, 75, 100] : [2, 10, 23, 40, 60, 80, 100];
    for (i = 0; i < xt.length; i++) {
      ctx.fillStyle = rgba(C.muted, .95);
      ctx.fillText(String(xt[i]), X(xt[i]), cg.b + 6);
    }

    /* area + curve */
    ctx.beginPath();
    ctx.moveTo(X(2), Y(pShared(2)));
    for (i = 3; i <= 100; i++) ctx.lineTo(X(i), Y(pShared(i)));
    ctx.lineTo(X(100), cg.b); ctx.lineTo(X(2), cg.b); ctx.closePath();
    ctx.fillStyle = rgba(C.accent, .12); ctx.fill();

    ctx.beginPath();
    ctx.moveTo(X(2), Y(pShared(2)));
    for (i = 3; i <= 100; i++) ctx.lineTo(X(i), Y(pShared(i)));
    ctx.strokeStyle = C.accent; ctx.lineWidth = 2; ctx.lineJoin = "round";
    ctx.stroke();

    /* the 23 marker, always visible */
    if (st.n !== 23) {
      var x23 = X(23), y23 = Y(pShared(23));
      ctx.beginPath(); ctx.moveTo(x23, y23); ctx.lineTo(x23, cg.b);
      ctx.strokeStyle = rgba(C.ink, .3); ctx.setLineDash([2, 3]); ctx.lineWidth = 1; ctx.stroke();
      ctx.setLineDash([]);
      ctx.beginPath(); ctx.arc(x23, y23, 3, 0, Math.PI * 2);
      ctx.fillStyle = C.surface; ctx.fill();
      ctx.strokeStyle = rgba(C.ink, .55); ctx.lineWidth = 1.4; ctx.stroke();
      ctx.font = "9.5px " + C.mono; ctx.textAlign = "left"; ctx.textBaseline = "bottom";
      ctx.fillStyle = rgba(C.muted, .95);
      /* clear of the measured-run ring that often sits on this same point */
      if (x23 < cg.r - 76) ctx.fillText("23 · 50.7%", x23 + 12, y23 - 7);
    }

    /* current point */
    var p = pShared(st.n), px = X(st.n), py = Y(p);
    ctx.beginPath(); ctx.moveTo(px, py); ctx.lineTo(px, cg.b);
    ctx.strokeStyle = rgba(C.accent, .55); ctx.lineWidth = 1.5; ctx.setLineDash([3, 3]); ctx.stroke();
    ctx.beginPath(); ctx.moveTo(L, py); ctx.lineTo(px, py); ctx.stroke();
    ctx.setLineDash([]);
    ctx.beginPath(); ctx.arc(px, py, 5.5, 0, Math.PI * 2);
    ctx.fillStyle = C.accent; ctx.fill();
    ctx.strokeStyle = C.surface; ctx.lineWidth = 2; ctx.stroke();

    /* measured runs LAST: a run almost always lands on the group size you are
       looking at, and underneath the current dot it would be invisible. */
    for (i = 0; i < st.runs.length; i++) {
      var rr = st.runs[i];
      ctx.beginPath(); ctx.arc(X(rr.n), Y(rr.rate), 8, 0, Math.PI * 2);
      ctx.strokeStyle = rgba(C.ink, .5); ctx.lineWidth = 1.5; ctx.stroke();
    }

    /* label near the point, kept inside the plot */
    var txt = "n=" + st.n + " · " + pct(p, 1) + "%";
    ctx.font = "600 10.5px " + C.mono;
    var tw = ctx.measureText(txt).width + 12, th = 17;
    var bx = px + 10, by = py - th - 9;
    if (bx + tw > cg.r) bx = px - 10 - tw;
    if (by < T) by = py + 9;
    ctx.fillStyle = C.surface;
    ctx.strokeStyle = rgba(C.accent, .55); ctx.lineWidth = 1;
    if (ctx.roundRect) { ctx.beginPath(); ctx.roundRect(bx, by, tw, th, 5); ctx.fill(); ctx.stroke(); }
    else { ctx.fillRect(bx, by, tw, th); ctx.strokeRect(bx, by, tw, th); }
    ctx.fillStyle = C.accent; ctx.textAlign = "center"; ctx.textBaseline = "middle";
    ctx.fillText(txt, bx + tw / 2, by + th / 2 + .5);
  }

  function curveSetFromX(clientX) {
    var r = CU.c.getBoundingClientRect();
    var x = clientX - r.left;
    var pw = cg.r - cg.l;
    var n = Math.round(2 + (x - cg.l) / pw * 98);
    n = Math.max(2, Math.min(100, n));
    if (n !== st.n) setN(n);
  }
  var dragging = false;
  CU.c.addEventListener("pointerdown", function (e) {
    dragging = true;
    if (CU.c.setPointerCapture) { try { CU.c.setPointerCapture(e.pointerId); } catch (err) {} }
    curveSetFromX(e.clientX);
    /* preventDefault would otherwise swallow the focus, stranding arrow keys */
    e.preventDefault();
    CU.c.focus();
  });
  CU.c.addEventListener("pointermove", function (e) { if (dragging) curveSetFromX(e.clientX); });
  window.addEventListener("pointerup", function () { dragging = false; });
  window.addEventListener("pointercancel", function () { dragging = false; });
  CU.c.addEventListener("keydown", function (e) {
    var k = e.key, n = st.n;
    if (k === "ArrowRight" || k === "ArrowUp") n += (e.shiftKey ? 10 : 1);
    else if (k === "ArrowLeft" || k === "ArrowDown") n -= (e.shiftKey ? 10 : 1);
    else if (k === "Home") n = 2;
    else if (k === "End") n = 100;
    else return;
    e.preventDefault();
    setN(n);
  });

  /* ═══════════════════════════════════════════════════════════════════════
     1000 ROOMS
     ═══════════════════════════════════════════════════════════════════════ */

  var TOTAL = 1000, COLS = 50, ROWS = 20;

  function drawRooms() {
    fit(RM);
    var ctx = RM.ctx, w = RM.w, h = RM.h;
    var gap = w < 420 ? 1 : 1.5;
    var cw = (w - gap * (COLS - 1)) / COLS;
    var ch = (h - gap * (ROWS - 1)) / ROWS;
    var rad = Math.min(2, cw / 3);
    var i, r, c, x, y, v;
    for (i = 0; i < TOTAL; i++) {
      r = Math.floor(i / COLS); c = i % COLS;
      x = c * (cw + gap); y = r * (ch + gap);
      v = st.cells && i < st.shown ? st.cells[i] : 2;
      ctx.fillStyle = v === 1 ? C.accent : (v === 0 ? rgba(C.ink, .13) : rgba(C.ink, .05));
      if (ctx.roundRect) { ctx.beginPath(); ctx.roundRect(x, y, Math.max(1, cw), Math.max(1, ch), rad); ctx.fill(); }
      else ctx.fillRect(x, y, Math.max(1, cw), Math.max(1, ch));
    }
  }

  function simulate(n) {
    var cells = new Uint8Array(TOTAL), hits = 0, i, j, seen, day, hit;
    for (i = 0; i < TOTAL; i++) {
      seen = {}; hit = 0;
      for (j = 0; j < n; j++) {
        day = (Math.random() * DAYS) | 0;
        if (seen[day]) { hit = 1; break; }
        seen[day] = 1;
      }
      cells[i] = hit;
      hits += hit;
    }
    return { cells: cells, hits: hits };
  }

  function setStatus(state, text) {
    $("status").setAttribute("data-state", state);
    $("statusText").textContent = text;
  }

  function runRooms() {
    if (st.running) return;
    st.running = true;
    $("btnRun").disabled = true;
    $("btnFill").disabled = true;
    setStatus("run", "RUNNING 1000 ROOMS");

    /* lock the group size for the whole run: the slider stays live, and every
       number this card reports must belong to the n we actually simulated. */
    var runN = st.n;
    st.runN = runN;
    if (st.lastRunN !== runN) { st.totRooms = 0; st.totHits = 0; }
    st.lastRunN = runN;
    $("roomsTag").textContent = "n = " + runN;

    var res = simulate(runN);
    st.cells = res.cells; st.hits = res.hits; st.shown = 0;
    var instant = reduce && reduce.matches;
    var perFrame = instant ? TOTAL : 40;

    function step() {
      st.shown = Math.min(TOTAL, st.shown + perFrame);
      drawRooms();
      var done = 0, i;
      for (i = 0; i < st.shown; i++) done += st.cells[i];
      $("bar").style.width = (st.shown / TOTAL * 100) + "%";
      $("sHits").innerHTML = done + " <span class='u'>/ " + st.shown + "</span>";
      $("sEmp").innerHTML = pct(done / Math.max(1, st.shown)) + "<span class='u'>%</span>";
      if (st.shown < TOTAL) { requestAnimationFrame(step); return; }
      finishRun();
    }
    if (instant) { step(); } else { requestAnimationFrame(step); }
  }

  function finishRun() {
    var n = st.runN, hits = st.hits;
    var emp = hits / TOTAL, th = pShared(n);
    var gap = (emp - th) * 100;
    var sd = Math.sqrt(th * (1 - th) / TOTAL) * 100;

    st.totRooms += TOTAL; st.totHits += hits;
    st.runs.push({ n: n, rate: emp });
    if (st.runs.length > 60) st.runs.shift();

    $("sHits").innerHTML = hits + " <span class='u'>/ 1000</span>";
    $("sEmp").innerHTML = pct(emp) + "<span class='u'>%</span>";
    $("sThe").innerHTML = pct(th) + "<span class='u'>%</span>";
    $("sGap").innerHTML = (gap >= 0 ? "+" : "−") + Math.abs(gap).toFixed(2) + "<span class='u'>pts</span>";
    $("roomsTag").textContent = "n = " + n;

    /* the 2σ band collapses below 0.1 pt at the ends of the range, so keep
       enough decimals for it to stay a number instead of "±0.0" */
    var band = 2 * sd, bandTxt = band < 0.1 ? band.toFixed(3) : band.toFixed(1);
    if (Math.abs(gap) <= band) {
      st.verdict = { cls: "pill ok", text: "measured " + pct(emp) + "% vs theory " + pct(th) + "% — inside the ±" + bandTxt + " pt noise band. The math holds." };
    } else {
      st.verdict = { cls: "pill", text: "measured " + pct(emp) + "% vs theory " + pct(th) + "% — outside ±" + bandTxt + " pts, which is roughly a 1-in-20 run. Run it again." };
    }

    $("totals").innerHTML = "all runs at n=" + n + ": <b>" + st.totRooms.toLocaleString() + "</b> rooms &middot; <b>"
      + pct(st.totHits / st.totRooms) + "%</b> shared &middot; theory <b>" + pct(th) + "%</b>";

    setStatus("ok", "RAN 1000 ROOMS");
    st.running = false;
    st.runN = null;
    $("btnRun").disabled = false;
    $("btnFill").disabled = false;
    syncRunCard();
    drawCurve();
    say("Ran a thousand rooms of " + n + ". " + hits + " had a shared birthday, " + pct(emp) + " percent, against a theory of " + pct(th) + " percent.");
  }

  /* The four stats, the grid and the verdict all describe ONE run at lastRunN.
     They are never mixed with the live slider value: if the two drift apart the
     card says so instead of pairing a stale measurement with a fresh theory. */
  function syncRunCard() {
    var v = $("verdict"), vt = $("verdictText");
    if (!st.running && st.lastRunN !== null && st.lastRunN !== st.n) {
      v.className = "pill";
      vt.textContent = "these numbers are the run at n = " + st.lastRunN + ". Run 1000 rooms again to test n = " + st.n + ".";
    } else {
      v.className = st.verdict.cls;
      vt.textContent = st.verdict.text;
    }
  }

  /* ═══════════════════════════════════════════════════════════════════════
     WIRING
     ═══════════════════════════════════════════════════════════════════════ */

  function setN(n) {
    n = Math.max(2, Math.min(100, Math.round(n)));
    st.n = n;
    $("nRange").value = String(n);
    resizeRoom(n);
    if (st.cursor < 0) hideTip();
    syncNumbers();
    syncRunCard();
    drawRing(1);
    drawCurve();
    ringReadout();
    updateChips();
  }

  function syncNumbers() {
    var n = st.n, p = pShared(n), ps = pSelf(n);
    $("nOut").textContent = String(n);
    $("nRange").setAttribute("aria-valuetext", n + " people, " + pct(p) + "% chance of a shared birthday");
    $("bigP").textContent = pct(p) + "%";
    $("subN").textContent = String(n);
    $("sPairs").textContent = pairsOf(n).toLocaleString();
    $("sSelf").innerHTML = pct(ps) + "<span class='u'>%</span>";
    $("ringTag").textContent = n + " PEOPLE";
    $("curveTag").innerHTML = "n = " + n + " &rarr; " + pct(p) + "%";
    CU.c.setAttribute("aria-valuenow", String(n));
    CU.c.setAttribute("aria-valuetext", n + " people, " + pct(p) + "% chance of a shared birthday");
    $("nSelf").textContent = pct(ps) + "%";
    $("nN").textContent = String(n);
    $("nPairs").textContent = pairsOf(n).toLocaleString();
    $("btnJump").disabled = (n === 23);
    $("btnJump").textContent = n === 23 ? "You are at 23" : "Set the room to 23";

    var terms = [];
    var i;
    for (i = 1; i < Math.min(n, 5); i++) terms.push("<b>" + (365 - i) + "</b>/365");
    /* only show an ellipsis when terms really were skipped: at n = 6 the last
       factor is the next one along, so print it plainly. */
    var tail = "";
    if (n === 6) tail = " &times; <b>360</b>/365";
    else if (n > 6) tail = " &times; … &times; <b>" + (365 - (n - 1)) + "</b>/365";
    var f = "p = 1 &minus; (" + terms.join(" &times; ") + tail + ")";
    if (n === 2) f = "p = 1 &minus; <b>364</b>/365";
    $("formula").innerHTML = f;

    var cmp;
    if (n < 23) cmp = "At <span class='mono'>" + n + "</span> the room is still under even odds &mdash; push the slider up to <span class='mono'>23</span> and watch it cross 50%.";
    else if (n === 23) cmp = "At <span class='mono'>23</span> it is <span class='mono'>50.73%</span>: closer to a coin flip than any other room size.";
    else if (n < 60) cmp = "At <span class='mono'>" + n + "</span> the odds are already <span class='mono'>" + pct(p, 1) + "%</span> &mdash; a room this size almost always has a pair.";
    /* past ~60 the miss chance rounds to 0.000% — say it as odds instead of a dead zero */
    else cmp = "At <span class='mono'>" + n + "</span> a room with no shared birthday is about <span class='mono'>1 in "
             + Math.round(1 / pNone(n)).toLocaleString() + "</span> &mdash; a freak event.";
    $("nCmp").innerHTML = cmp;
  }

  var CHIPS = [5, 10, 23, 41, 70];
  function buildChips() {
    var box = $("chips"), i;
    for (i = 0; i < CHIPS.length; i++) {
      (function (v) {
        var b = document.createElement("button");
        b.type = "button";
        b.textContent = v + (v === 23 ? " ★" : "");
        b.setAttribute("aria-pressed", "false");
        b.setAttribute("aria-label", v + " people");
        b.addEventListener("click", function () { setN(v); say(v + " people, " + pct(pShared(v)) + " percent chance of a shared birthday."); });
        box.appendChild(b);
      })(CHIPS[i]);
    }
  }
  function updateChips() {
    var bs = $("chips").children, i;
    for (i = 0; i < bs.length; i++) bs[i].setAttribute("aria-pressed", CHIPS[i] === st.n ? "true" : "false");
  }

  function say(m) { live.textContent = m; }

  $("nRange").addEventListener("input", function () { setN(+this.value); });
  $("btnFill").addEventListener("click", function () {
    fillRoom(true);
    var nd = st.dupDays.length;
    say(nd ? ("New room of " + st.n + ". " + (nd === 1 ? "One shared day: " + dateLabel(st.dupDays[0].day) : nd + " shared days") + ".")
           : ("New room of " + st.n + ". No two people share a day."));
  });
  $("btnRun").addEventListener("click", runRooms);
  $("btnJump").addEventListener("click", function () { setN(23); say("Group size set to 23."); $("nRange").focus(); });

  /* theme: platform postMessage, plus standalone prefers-color-scheme */
  function repaint() { readPalette(); drawRing(st.animating ? 0 : 1); drawCurve(); drawRooms(); }
  window.addEventListener("message", function (e) {
    var d = e.data;
    if (d && d.type === "sloprun:theme" && (d.theme === "light" || d.theme === "dark")) {
      root.setAttribute("data-theme", d.theme);
      repaint();
    }
  });
  if (window.matchMedia) {
    var mq = window.matchMedia("(prefers-color-scheme: dark)");
    if (mq.addEventListener) mq.addEventListener("change", repaint);
    else if (mq.addListener) mq.addListener(repaint);
  }

  var rt = null;
  function onResize() {
    if (rt) clearTimeout(rt);
    rt = setTimeout(function () { rt = null; repaint(); }, 80);
  }
  if (window.ResizeObserver) new ResizeObserver(onResize).observe(document.body);
  else window.addEventListener("resize", onResize);

  /* ═══════════════════════════════════════════════════════════════════════
     BOOT — opens with a real room, a marked curve, and a finished run
     ═══════════════════════════════════════════════════════════════════════ */

  readPalette();
  buildChips();
  st.room = newRoom(23, mulberry32(23));   /* one shared day: Dec 26 */
  st.dupDays = findDups(st.room);
  syncNumbers();
  updateChips();
  drawRing(1);
  drawCurve();
  drawRooms();
  ringReadout();
  runRooms();

})();
</script>
</body>
</html>