Stage 17 (#9): animated shuffle — tiles hop along a low parabola to new slots

Give each rack slot a stable id permuted with the letters on shuffle, so the keyed
rack reorders (rather than relabelling in place) and Svelte's animate directive fires.
hop flies each tile along a parabola (apogee ~half a tile height) with a duration that
scales with the horizontal distance (arc length): the longest 1<->7 swap takes ~0.5s,
shorter swaps land sooner. Ordinary reflow (place/recall) stays instant via a guard.
e2e locks that a shuffle preserves the rack's tile multiset.

ui/src/game/Game.svelte

@@ -43,6 +43,10 @@
   let zoomed = $state(false);
   let selected = $state<number | null>(null);
   let focus = $state<{ row: number; col: number } | null>(null);
+  // A stable id per rack slot, permuted together with the letters on shuffle, so the rack
+  // tiles fly to their new positions (Rack's hop animation) instead of relabelling in place.
+  let rackIds = $state<number[]>([]);
+  let shuffling = $state(false);
   let panel = $state<'none' | 'chat'>('none');
   let historyOpen = $state(false);
   let blankPrompt = $state<{ rackIndex: number; row: number; col: number } | null>(null);
@@ -81,6 +85,7 @@
       view.game.toMove === view.seat,
   );
   const slots = $derived(rackView(placement));
+  const rackSlots = $derived(slots.map((s) => ({ ...s, id: rackIds[s.index] ?? s.index })));
   const isMyTurn = $derived(!!view && view.game.status === 'active' && view.game.toMove === view.seat);
   const gameOver = $derived(!!view && view.game.status !== 'active');
   const bagEmpty = $derived((view?.bagLen ?? 0) === 0);
@@ -98,6 +103,7 @@
       moves = hist.moves;
       setCachedGame(id, st, hist.moves);
       placement = newPlacement(st.rack);
+      rackIds = st.rack.map((_, i) => i);
       preview = null;
       selected = null;
       dirOverride = undefined;
@@ -122,6 +128,7 @@
       view = cached.view;
       moves = cached.moves;
       placement = newPlacement(cached.view.rack);
+      rackIds = cached.view.rack.map((_, i) => i);
     }
     void load();
   });
@@ -373,12 +380,18 @@
   }
   function shuffle() {
     if (placement.pending.length > 0) return;
-    const r = [...placement.rack];
-    for (let i = r.length - 1; i > 0; i--) {
+    // Shuffle an index permutation, then apply it to both the letters and the slot ids so
+    // each tile keeps its id as it flies to a new position (driving Rack's hop animation).
+    const order = placement.rack.map((_, i) => i);
+    for (let i = order.length - 1; i > 0; i--) {
       const j = Math.floor(Math.random() * (i + 1));
-      [r[i], r[j]] = [r[j], r[i]];
+      [order[i], order[j]] = [order[j], order[i]];
     }
-    placement = newPlacement(r);
+    rackIds = order.map((i) => rackIds[i] ?? i);
+    placement = newPlacement(order.map((i) => placement.rack[i]));
+    selected = null;
+    shuffling = true;
+    setTimeout(() => (shuffling = false), 600);
     // A short "shake": a few quick light taps rather than one.
     for (let i = 0; i < 4; i++) setTimeout(() => telegramHaptic('light'), i * 55);
   }
@@ -589,7 +602,7 @@
          a finished game shows the final rack greyed out and the controls disabled. -->
     <div class="rack-row" class:inert={gameOver}>
       <div class="rack-wrap">
-        <Rack {slots} {variant} {selected} ondown={onRackDown} />
+        <Rack slots={rackSlots} {variant} {selected} {shuffling} ondown={onRackDown} />
       </div>
       {#if !gameOver && placement.pending.length > 0}
         <button class="make" onclick={commit} disabled={busy} aria-label={t('game.makeMove')}>✅</button>

ui/src/game/Rack.svelte

@@ -8,25 +8,48 @@
     slots,
     variant,
     selected,
+    shuffling = false,
     ondown,
   }: {
-    slots: RackSlot[];
+    // Each slot carries a stable id that travels with its tile through a shuffle, so the
+    // keyed list reorders (rather than relabelling in place) and the hop animation fires.
+    slots: (RackSlot & { id: number })[];
     variant: Variant;
     selected: number | null;
+    shuffling?: boolean;
     ondown: (e: PointerEvent, index: number) => void;
   } = $props();
 
   // Used slots are hidden (the rack shifts left, freeing room on the right for the
   // MakeMove control); the slot still exists in the model for per-tile recall.
   const visible = $derived(slots.filter((s) => !s.used));
+
+  // hop flies a tile to its shuffled position along a low parabola (apogee ≈ half a tile
+  // height). The duration scales with the horizontal distance — i.e. the arc length — so
+  // the longest swap (slot 1 ↔ 7) takes ~0.5s and shorter swaps land sooner. It runs only
+  // while a shuffle is in progress; ordinary reflow (placing/recalling a tile) is instant.
+  function hop(node: HTMLElement, { from, to }: { from: DOMRect; to: DOMRect }, active: boolean) {
+    const dx = from.left - to.left;
+    const dy = from.top - to.top;
+    const dist = Math.hypot(dx, dy);
+    if (!active || dist < 2) return { duration: 0 };
+    const span = node.parentElement?.getBoundingClientRect().width || dist;
+    const lift = (to.height || from.height) * 0.5;
+    return {
+      duration: Math.max(160, Math.min(500, (dist / span) * 560)),
+      css: (t: number, u: number) =>
+        `transform: translate(${dx * u}px, ${dy * u - Math.sin(Math.PI * t) * lift}px);`,
+    };
+  }
 </script>
 
 <div class="rack" data-rack>
-  {#each visible as slot (slot.index)}
+  {#each visible as slot (slot.id)}
     <button
       class="tile"
       class:selected={selected === slot.index}
       data-rack-index={slot.index}
+      animate:hop={shuffling}
       onpointerdown={(e) => ondown(e, slot.index)}
     >
       <span class="letter">{slot.letter === BLANK ? '' : slot.letter}</span>