diff --git a/apps/web/src/routes/kripke/+page.svelte b/apps/web/src/routes/kripke/+page.svelte
index b6af55e..67ed5dd 100644
--- a/apps/web/src/routes/kripke/+page.svelte
+++ b/apps/web/src/routes/kripke/+page.svelte
@@ -1,157 +1,21 @@
 <script lang="ts">
-import Katex from "$lib/components/katex.svelte";
-import {
-  type Formula,
-  type Frame,
-  getFrame,
-  getId,
-  isomorphic,
-  latexSymbols,
-  prettyPrint,
-  validWorlds,
-} from "@cannorin/kripke";
+import { type Formula, getId, isomorphic, validWorlds } from "@cannorin/kripke";
 import LuHeart from "lucide-svelte/icons/heart";
-import LuHeartCrack from "lucide-svelte/icons/heart-crack";
-import FormulaInput from "./formula-input.svelte";
-import FrameInput from "./frame-input.svelte";
+import Game from "./game.svelte";
 import { getDailyFrame } from "./system";
 
-let formula: Formula | undefined = $state(undefined);
-let frame: Frame = $state(getFrame(0));
-let math = $derived.by(() => {
-  if (formula) return prettyPrint(formula, { symbols: latexSymbols });
-  return "\\phantom{p}";
-});
-
 const dailyFrame = getDailyFrame();
 const dailyFrameId = isomorphic[getId(dailyFrame)];
-let remainingRelations = $derived(
-  dailyFrame.relations.size - frame.relations.size,
-);
-
-type Move =
-  | { type: "guess"; frameId: number; correct: boolean }
-  | { type: "check"; formulaStr: string; valid: number };
-
-let moves: Move[] = $state([]);
-let life = $derived(10 - moves.length);
-
-let canGuess = $derived.by(() => {
-  if (remainingRelations !== 0) return false;
-  const frameId = isomorphic[getId(frame)];
-  return !moves.some(
-    (move) => move.type === "guess" && move.frameId === frameId,
-  );
-});
-function guess() {
-  if (!canGuess) return;
-  const frameId = isomorphic[getId(frame)];
-  moves.push({ type: "guess", frameId, correct: frameId === dailyFrameId });
-  moves = [...moves];
-}
-
-let canCheck = $derived.by(() => {
-  if (!formula) return false;
-  const formulaStr = prettyPrint(formula);
-  return !moves.some(
-    (move) => move.type === "check" && move.formulaStr === formulaStr,
-  );
-});
-function check() {
-  if (!canCheck || !formula) return;
-  const formulaStr = prettyPrint(formula);
-  const valid = validWorlds(dailyFrame, formula).length;
-  moves.push({ type: "check", formulaStr, valid });
-  moves = [...moves];
-  formula = undefined;
-}
+const relationSize = dailyFrame.relations.size;
+const guess = (frameId: number) => isomorphic[frameId] === dailyFrameId;
+const check = (formula: Formula) => validWorlds(dailyFrame, formula).length;
 </script>
 
-{#snippet sampleArrow()}
-  <svg width="50" height="10" class="mt-[1px]">
-    <defs>
-      <marker
-        id="arrowhead"
-        viewBox="0 0 10 10"
-        refX="8"
-        refY="5"
-        markerWidth="6"
-        markerHeight="6"
-        orient="auto"
-        markerUnits="strokeWidth"
-      >
-        <path d="M0,0 L0,10 L10,5 z" fill="rgb(var(--foreground))" />
-      </marker>
-    </defs>
-    <path d="M 5 5 L 45 5" stroke="rgb(var(--foreground))" stroke-width="1" marker-end="url(#arrowhead)" />
-  </svg>
-{/snippet}
-
 <main class="flex flex-col min-h-screen max-w-full items-center gap-12 lg:gap-16 py-8">
-
   <h1 class="font-display text-6xl">KRiPkE</h1>
 
   <div class="flex flex-col md:flex-row-reverse gap-x-20 gap-y-8">
-    <div class="w-[300px] flex flex-col gap-4">
-      <div class="flex items-center justify-between">
-        {#each [1,2,3,4,5,6,7,8,9,10] as i}
-          {#if i <= life}
-            <LuHeart class="text-primary" />
-          {:else}
-            <LuHeartCrack class="text-muted" />
-          {/if}
-        {/each}
-      </div>
-
-      <div class="flex flex-col items-center gap-2">
-        <div class="w-[300px] h-[300px] flex flex-col items-center justify-betwenn border rounded border-border">
-          <span class="text-xs text-muted self-start px-2 py-1">id: {isomorphic[getId(frame)]}</span>
-          <FrameInput bind:frame />
-          <span class="text-sm px-2 py-1 self-end flex items-center">
-            {@render sampleArrow()} × {remainingRelations}
-          </span>
-        </div>
-
-        <button
-          onclick={guess}
-          disabled={!canGuess}
-          class={[
-            "rounded w-full p-1 text-background bg-primary font-bold flex items-center justify-center gap-2",
-            !canGuess && "bg-muted cursor-not-allowed"
-          ]}>
-          Guess! <span class="flex items-center font-normal">(<LuHeart size=14 class="mt-1 mr-[1px]"/> 1)</span>
-        </button>
-      </div>
-
-      <div class="flex flex-col items-center gap-2">
-        <Katex math={math} />
-        <FormulaInput bind:formula />
-        <button
-          onclick={check}
-          disabled={!canCheck}
-          class={[
-            "rounded w-full p-1 text-background bg-primary font-bold flex items-center justify-center gap-2",
-            !canCheck && "bg-muted cursor-not-allowed"
-          ]}>
-          Check! <span class="flex items-center font-normal">(<LuHeart size=14 class="mt-1 mr-[1px]"/> 1)</span>
-        </button>
-      </div>
-
-      <div>
-        <ul class="flex flex-col gap-2">
-          {#each moves as move}
-            <li>
-              {#if move.type === "guess"}
-                Guess({move.frameId}) = {move.correct}
-              {/if}
-              {#if move.type === "check"}
-                Valid({move.formulaStr}) = {move.valid}
-              {/if}
-            </li>
-          {/each}
-        </ul>
-      </div>
-    </div>
+    <Game relationSize={relationSize} guess={guess} check={check} />
 
     <div class="w-[300px] prose prose-sm">
       <h2>Rules</h2>
diff --git a/apps/web/src/routes/kripke/formula-input.svelte b/apps/web/src/routes/kripke/formula-input.svelte
index 8732d4f..3431dc9 100644
--- a/apps/web/src/routes/kripke/formula-input.svelte
+++ b/apps/web/src/routes/kripke/formula-input.svelte
@@ -3,8 +3,10 @@ import { type Formula, prettyPrint, tryParse } from "@cannorin/kripke";
 
 let {
   formula = $bindable<Formula | undefined>(undefined),
+  disabled = false,
 }: {
   formula?: Formula | undefined;
+  disabled?: boolean | undefined;
 } = $props();
 
 let input = $state(formula ? prettyPrint(formula) : "");
@@ -26,4 +28,5 @@ $effect(() => {
   class={["rounded border border-foreground ring-0 focus:outline-none focus:ring-0 p-2 w-full", error && "border-primary"]}
   type="text"
   placeholder="Enter modal formula"
+  disabled={disabled}
   bind:value={input} />
diff --git a/apps/web/src/routes/kripke/frame-input.svelte b/apps/web/src/routes/kripke/frame-input.svelte
index e404a23..fa052ed 100644
--- a/apps/web/src/routes/kripke/frame-input.svelte
+++ b/apps/web/src/routes/kripke/frame-input.svelte
@@ -3,7 +3,6 @@ import {
   type Frame,
   type Relation,
   type World,
-  getFrame,
   left,
   reverse,
   right,
@@ -12,9 +11,11 @@ import {
 import { type Vector, add, degree, rotate, sub, theta } from "./vector";
 
 let {
-  frame = $bindable<Frame>(getFrame(0)),
+  frame = $bindable<Frame>({ relations: new Set() }),
+  disabled = false,
 }: {
   frame?: Frame | undefined;
+  disabled?: boolean | undefined;
 } = $props();
 
 let selected: World | null = $state(null);
@@ -114,7 +115,6 @@ function getPath(rel: Relation) {
     fill: rgb(var(--background));
     stroke: rgb(var(--foreground));
     stroke-width: 1;
-    cursor: pointer;
   }
   .node.selected {
     stroke: rgb(var(--primary));
@@ -124,7 +124,6 @@ function getPath(rel: Relation) {
     stroke: rgb(var(--foreground));
     stroke-width: 1;
     fill: none;
-    cursor: pointer;
     marker-end: url(#arrowhead);
   }
 </style>
@@ -151,8 +150,8 @@ function getPath(rel: Relation) {
     {#key rel}
       <path
         d={getPath(rel)}
-        class="edge"
-        onclick={(e) => handleEdgeClick(rel, e)}
+        class={["edge", !disabled && "cursor-pointer"]}
+        onclick={(e) => !disabled && handleEdgeClick(rel, e)}
       />
     {/key}
   {/each}
@@ -164,8 +163,8 @@ function getPath(rel: Relation) {
       cx={x}
       cy={y}
       r={radius.x}
-      class="node {selected === w ? 'selected' : ''}"
-      onclick={(e) => handleNodeClick(w, e)}
+      class={["node", selected === w && "selected", !disabled && "cursor-pointer"]}
+      onclick={(e) => !disabled && handleNodeClick(w, e)}
     />
   {/each}
 </svg>
diff --git a/apps/web/src/routes/kripke/game.svelte b/apps/web/src/routes/kripke/game.svelte
new file mode 100644
index 0000000..6478ece
--- /dev/null
+++ b/apps/web/src/routes/kripke/game.svelte
@@ -0,0 +1,178 @@
+<script lang="ts">
+import Katex from "$lib/components/katex.svelte";
+import {
+  type Formula,
+  type Frame,
+  getFrame,
+  getId,
+  isomorphic,
+  latexSymbols,
+  prettyPrint,
+} from "@cannorin/kripke";
+import LuHeart from "lucide-svelte/icons/heart";
+import LuHeartCrack from "lucide-svelte/icons/heart-crack";
+import FormulaInput from "./formula-input.svelte";
+import FrameInput from "./frame-input.svelte";
+
+export type GameStatus = "win" | "lose" | "playing";
+
+export type Move =
+  | { type: "guess"; frameId: number; correct: boolean }
+  | { type: "check"; formulaStr: string; valid: number };
+
+export type Props = {
+  status?: GameStatus;
+  moves?: Move[];
+  relationSize: number;
+  guess: (frameId: number) => boolean | Promise<boolean>;
+  check: (formula: Formula) => number | Promise<number>;
+};
+
+let {
+  status = $bindable<GameStatus>("playing"),
+  moves = $bindable<Move[]>([]),
+  relationSize,
+  guess: guessImpl,
+  check: checkImpl,
+}: Props = $props();
+
+let formula: Formula | undefined = $state(undefined);
+let frame: Frame = $state(getFrame(0));
+let math = $derived.by(() => {
+  if (formula) return prettyPrint(formula, { symbols: latexSymbols });
+  return "\\phantom{p}";
+});
+
+let remainingRelations = $derived(relationSize - frame.relations.size);
+
+let life = $derived(10 - moves.length);
+
+$effect(() => {
+  if (life <= 0) {
+    status = "lose";
+    return;
+  }
+  if (moves.some((move) => move.type === "guess" && move.correct)) {
+    status = "win";
+    return;
+  }
+});
+
+let canGuess = $derived.by(() => {
+  if (status !== "playing" || remainingRelations !== 0) return false;
+  const frameId = isomorphic[getId(frame)];
+  return !moves.some(
+    (move) => move.type === "guess" && move.frameId === frameId,
+  );
+});
+
+async function guess() {
+  if (!canGuess) return;
+  const frameId = getId(frame);
+  const correct = await guessImpl(frameId);
+  moves.push({ type: "guess", frameId, correct });
+  moves = [...moves];
+}
+
+let canCheck = $derived.by(() => {
+  if (status !== "playing" || life === 1 || !formula) return false;
+  const formulaStr = prettyPrint(formula);
+  return !moves.some(
+    (move) => move.type === "check" && move.formulaStr === formulaStr,
+  );
+});
+
+async function check() {
+  if (!canCheck || !formula) return;
+  const valid = await checkImpl(formula);
+  const formulaStr = prettyPrint(formula, { symbols: latexSymbols });
+  moves.push({ type: "check", formulaStr, valid });
+  moves = [...moves];
+  formula = undefined;
+}
+</script>
+
+{#snippet sampleArrow()}
+  <svg width="50" height="10" class="mt-[2px]">
+    <defs>
+      <marker
+        id="arrowhead"
+        viewBox="0 0 10 10"
+        refX="8"
+        refY="5"
+        markerWidth="6"
+        markerHeight="6"
+        orient="auto"
+        markerUnits="strokeWidth"
+      >
+        <path d="M0,0 L0,10 L10,5 z" fill="rgb(var(--foreground))" />
+      </marker>
+    </defs>
+    <path d="M 5 5 L 45 5" stroke="rgb(var(--foreground))" stroke-width="1" marker-end="url(#arrowhead)" />
+  </svg>
+{/snippet}
+
+<div class="w-[300px] flex flex-col gap-4">
+  <div class="flex items-center justify-between">
+    {#each [1,2,3,4,5,6,7,8,9,10] as i}
+      {#if i <= life}
+        <LuHeart class="text-primary" />
+      {:else}
+        <LuHeartCrack class="text-muted" />
+      {/if}
+    {/each}
+  </div>
+
+  <div class="flex flex-col items-center gap-2">
+    <div class="w-[300px] h-[300px] flex flex-col items-center justify-betwenn border rounded border-border">
+      <span class="text-xs text-muted self-start px-2 py-1">id: {isomorphic[getId(frame)]}</span>
+      <FrameInput bind:frame disabled={status !== "playing"} />
+      <span class="text-sm px-2 py-1 self-end flex items-center">
+        {@render sampleArrow()} × {remainingRelations}
+      </span>
+    </div>
+
+    <button
+      onclick={guess}
+      disabled={!canGuess}
+      class={[
+        "rounded w-full p-1 text-background font-bold flex items-center justify-center gap-2",
+        canGuess ? "bg-primary" : "bg-muted cursor-not-allowed"
+      ]}>
+      Guess! <span class="flex items-center font-normal">(<LuHeart size=14 class="mt-1 mr-[1px]"/> 1)</span>
+    </button>
+  </div>
+
+  <div class="flex flex-col items-center gap-2">
+    <Katex math={math} />
+    <FormulaInput bind:formula disabled={status !== "playing"} />
+    <button
+      onclick={check}
+      disabled={!canCheck}
+      class={[
+        "rounded w-full p-1 text-background font-bold flex items-center justify-center gap-2",
+        canCheck ? "bg-primary" : "bg-muted cursor-not-allowed"
+      ]}>
+      {#if life <= 1}
+        Can't Check <span class="font-normal">(Last Move!)</span>
+      {:else}
+        Check! <span class="flex items-center font-normal">(<LuHeart size=14 class="mt-1 mr-[1px]"/> 1)</span>
+      {/if}
+    </button>
+  </div>
+
+  <div>
+    <ul class="flex flex-col gap-2">
+      {#each moves as move}
+        <li>
+          {#if move.type === "guess"}
+            Guess({move.frameId}) = {move.correct}
+          {/if}
+          {#if move.type === "check"}
+            Valid({move.formulaStr}) = {move.valid}
+          {/if}
+        </li>
+      {/each}
+    </ul>
+  </div>
+</div>