diff --git a/.vscode/settings.json b/.vscode/settings.json
index 023a7ca..cc73bfb 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -21,5 +21,6 @@
   },
   "[jsonc]": {
     "editor.defaultFormatter": "biomejs.biome"
-  }
+  },
+  "biome.lspBin": "./node_modules/@biomejs/biome/bin/biome"
 }
diff --git a/apps/web/src/routes/kripke/+page.svelte b/apps/web/src/routes/kripke/+page.svelte
index fea63c1..6b98785 100644
--- a/apps/web/src/routes/kripke/+page.svelte
+++ b/apps/web/src/routes/kripke/+page.svelte
@@ -62,7 +62,7 @@ onMount(() => {
         <li>You can also play <a href="/kripke/random">Random Challenge</a>.</li>
       </ul>
 
-      <Rules />
+      <Rules relationSize={relationSize} />
     </section>
   </div>
 </main>
diff --git a/apps/web/src/routes/kripke/components/game.svelte b/apps/web/src/routes/kripke/components/game.svelte
index 605dd92..7c8dd67 100644
--- a/apps/web/src/routes/kripke/components/game.svelte
+++ b/apps/web/src/routes/kripke/components/game.svelte
@@ -48,7 +48,9 @@ let formula: Formula | undefined = $state(undefined);
 let formulaStr = $derived(
   formula ? prettyPrint(formula, { symbols: latexSymbols }) : "",
 );
-let frame: Frame = $state(getFrame(0));
+let frame: Frame = $state(
+  getFrame(moves.findLast((move) => move.type === "guess")?.frameId ?? 0),
+);
 let frameId = $derived(getId(frame));
 
 let remainingRelations = $derived(relationSize - frame.relations.size);
diff --git a/apps/web/src/routes/kripke/components/rules.svelte b/apps/web/src/routes/kripke/components/rules.svelte
index 3f856d2..75580f8 100644
--- a/apps/web/src/routes/kripke/components/rules.svelte
+++ b/apps/web/src/routes/kripke/components/rules.svelte
@@ -2,8 +2,11 @@
 import Katex from "$lib/components/katex.svelte";
 import LuHeart from "lucide-svelte/icons/heart";
 
+let { relationSize }: { relationSize: number } = $props();
+
 const frame = "\\footnotesize \\mathcal{F} = \\left<W, R\\right>";
-const numberConstraint = "\\footnotesize |W| = 4";
+const worldConstraint = "\\footnotesize |W| = 4";
+const relationConstraint = `\\footnotesize |R| = ${relationSize}`;
 const f = "\\footnotesize \\mathcal{F}";
 const validCount =
   "\\footnotesize \\mathrm{N}(\\varphi) = \\bigl| \\Set{ w \\in W | \\forall \\mathop{\\Vdash}\\, (w \\Vdash \\varphi) } \\bigr|";
@@ -12,11 +15,8 @@ const validCount =
 <h2>Rules</h2>
 <ul>
   <li>
-    A Kripke frame with 4 worlds is generated:
-    <Katex math={frame} />, where <Katex math={numberConstraint} />.
-  </li>
-  <li>
-    The game tells you how many accessibility relations are in the frame <Katex math={f} />, but not the exact shape of it.
+    A <a href="https://en.wikipedia.org/wiki/Kripke_semantics" target="_blank" rel="noopener noreferrer">Kripke frame</a> with 4 worlds and {relationSize} relation(s) is generated:
+    <Katex math={frame} />, where <Katex math={worldConstraint} /> and <Katex math={relationConstraint} />.
   </li>
   <li>
     You have a total of 10 moves <span class="inline-flex items-center max-w-fit">(<LuHeart aria-label="♡" size=12 class="mt-1"/>)</span>.
@@ -32,7 +32,7 @@ const validCount =
       </li>
       <li>
         Guess the Kripke frame.
-        If your frame is equal or isomorphic to the secret frame <Katex math={f} />, you win.
+        If your frame is equal or isomorphic to <Katex math={f} />, you win.
       </li>
     </ul>
   </li>
diff --git a/apps/web/src/routes/kripke/random/[seed]/+page.svelte b/apps/web/src/routes/kripke/random/[seed]/+page.svelte
index fd9b305..f9a8db9 100644
--- a/apps/web/src/routes/kripke/random/[seed]/+page.svelte
+++ b/apps/web/src/routes/kripke/random/[seed]/+page.svelte
@@ -50,13 +50,13 @@ $effect(() => {
     <section class="w-[300px] prose prose-sm">
       <h2>Random Challenge!</h2>
       <ul>
-        <li>The answer of the game is determined by a seed number {@render seedNumber()}, which changes on every reload.</li>
+        <li>The answer of the game is determined by a seed number {@render seedNumber()}.</li>
         <li>You can right-click on the seed number to obtain a permalink to this exact game.</li>
         <li>Unlike Daily Challenge, the progress of the game does not persist.</li>
         <li>You can also play <a href="/kripke">Daily Challenge</a>, if you have not yet.</li>
       </ul>
 
-      <Rules />
+      <Rules relationSize={relationSize} />
     </section>
   </div>
 </main>