diff --git a/docs/specs/game-bot/tasks.md b/docs/specs/game-bot/tasks.md
index 6d688c6..432a5fc 100644
--- a/docs/specs/game-bot/tasks.md
+++ b/docs/specs/game-bot/tasks.md
@@ -12,7 +12,7 @@ Work through the tasks in order; each ends with its tests passing and a commit.
       `onTurnStarted`, bot ids in `GameStore`, `PublicIds` and the connection info; `BotPlayer` and its executor in
       `Backend`, `BOT_SEARCH_THREADS`; `bot` in snapshots and their restore; unit tests.
 - [x] 5. **Saving**: `bot` in `GameRecord`, migration `003_bot`, the repository; integration tests.
-- [ ] 6. **Core**: `channel_new_bot_game`, `BotLevel`, `BOT_LEVELS`, `BOT_OFFER_DELAY_MS`, `isBotId`,
+- [x] 6. **Core**: `channel_new_bot_game`, `BotLevel`, `BOT_LEVELS`, `BOT_OFFER_DELAY_MS`, `isBotId`,
       `getBotLevel`, `getPlayerDisplayName` for bots, texts in English and Turkish; unit tests.
 - [ ] 7. **Web app**: `BotLevelPicker`, the home page button, the lobby offer and `?bot=`, "Play again" after a bot
       game, bot names everywhere players are shown.
diff --git a/packages/core/src/localization/en.ts b/packages/core/src/localization/en.ts
index 58ed73e..22ef873 100644
--- a/packages/core/src/localization/en.ts
+++ b/packages/core/src/localization/en.ts
@@ -106,4 +106,13 @@ export const en = {
     StoreLabel: "{{name}}'s store, {{count}} stones",
     OpenGame: "Open the game",
     Score: "Score",
+    PlayWithBot: "Play with bot",
+    NoOpponentYet: "No opponent yet. Play with the bot?",
+    ChooseBotLevel: "Choose how strong the bot is",
+    Bot: "Bot",
+    BotLevelEasy: "Easy",
+    BotLevelMedium: "Medium",
+    BotLevelHard: "Hard",
+    BotLevelMaster: "Master",
+    PlayAgain: "Play again",
 }
\ No newline at end of file
diff --git a/packages/core/src/localization/tr.ts b/packages/core/src/localization/tr.ts
index 153a1b5..d6c07c0 100644
--- a/packages/core/src/localization/tr.ts
+++ b/packages/core/src/localization/tr.ts
@@ -106,4 +106,13 @@ export const tr = {
     StoreLabel: "{{name}} hazinesi, {{count}} taş",
     OpenGame: "Oyunu aç",
     Score: "Skor",
+    PlayWithBot: "Bota karşı oyna",
+    NoOpponentYet: "Henüz rakip bulunamadı. Bota karşı oynamak ister misin?",
+    ChooseBotLevel: "Botun ne kadar güçlü olacağını seç",
+    Bot: "Bot",
+    BotLevelEasy: "Kolay",
+    BotLevelMedium: "Orta",
+    BotLevelHard: "Zor",
+    BotLevelMaster: "Usta",
+    PlayAgain: "Tekrar oyna",
 };
\ No newline at end of file
diff --git a/packages/core/src/models/Bot.ts b/packages/core/src/models/Bot.ts
new file mode 100644
index 0000000..90254e7
--- /dev/null
+++ b/packages/core/src/models/Bot.ts
@@ -0,0 +1,42 @@
+// Games against the bot (docs/specs/game-bot). The bot plays with the user id `bot:<level>`.
+export type BotLevel = "easy" | "medium" | "hard" | "master";
+
+// Weakest first.
+export const BOT_LEVELS: BotLevel[] = ["easy", "medium", "hard", "master"];
+
+// How long the lobby searches for an opponent before it offers the bot.
+export const BOT_OFFER_DELAY_MS = 10_000;
+
+const BOT_ID_PREFIX = "bot:";
+
+export function isBotId(userId: string | undefined): boolean {
+    return userId?.startsWith(BOT_ID_PREFIX) ?? false;
+}
+
+// The level of a bot id, or undefined if it is not one.
+export function getBotLevel(userId: string | undefined): BotLevel | undefined {
+    if (!userId || !isBotId(userId)) return undefined;
+    const level = userId.slice(BOT_ID_PREFIX.length);
+    return (BOT_LEVELS as string[]).includes(level) ? level as BotLevel : undefined;
+}
+
+export function isBotLevel(value: unknown): value is BotLevel {
+    return typeof value === "string" && (BOT_LEVELS as string[]).includes(value);
+}
+
+// Translation key of a level's name, e.g. BotLevelMedium.
+export function getBotLevelTextKey(level: BotLevel): string {
+    return `BotLevel${level.charAt(0).toUpperCase()}${level.slice(1)}`;
+}
+
+const LAST_BOT_LEVEL_KEY = "botLevel";
+
+// The level chosen last on this device; Medium at first.
+export function getLastBotLevel(storage: { getString(key: string): string | undefined }): BotLevel {
+    const saved = storage.getString(LAST_BOT_LEVEL_KEY);
+    return isBotLevel(saved) ? saved : "medium";
+}
+
+export function setLastBotLevel(storage: { setString(key: string, value: string): void }, level: BotLevel): void {
+    storage.setString(LAST_BOT_LEVEL_KEY, level);
+}
diff --git a/packages/core/src/models/index.ts b/packages/core/src/models/index.ts
index 408e5bb..9745bb5 100644
--- a/packages/core/src/models/index.ts
+++ b/packages/core/src/models/index.ts
@@ -6,3 +6,4 @@ export * from './UserConnectionInfo'
 export * from './AuthUser'
 export * from './GameHistory'
 export * from './GameClock'
+export * from './Bot'
diff --git a/packages/core/src/rtmt/channel_names.ts b/packages/core/src/rtmt/channel_names.ts
index e3b532d..ecb9e34 100644
--- a/packages/core/src/rtmt/channel_names.ts
+++ b/packages/core/src/rtmt/channel_names.ts
@@ -1,5 +1,7 @@
 export const channel_new_game = "new_game"
 export const channel_cancel_new_game = "cancel_new_game"
+// client -> server: { level: BotLevel }, starts a game against the bot; ends a search for an opponent.
+export const channel_new_bot_game = "new_bot_game"
 export const channel_on_game_start = "on_game_start"
 export const channel_game_move = "game_move"
 export const channel_on_game_update = "on_game_update"
diff --git a/packages/core/src/util/PlayerUtil.ts b/packages/core/src/util/PlayerUtil.ts
index 3aafc5d..1c169d6 100644
--- a/packages/core/src/util/PlayerUtil.ts
+++ b/packages/core/src/util/PlayerUtil.ts
@@ -1,11 +1,15 @@
+import { getBotLevel, getBotLevelTextKey } from "../models/Bot";
+
 const GUEST_USERNAME_PREFIX = "guest-";
 
 // Name to show for a player, or undefined if the server sent none (legacy userKey players).
-// Guests show as e.g. "Guest 4F2A" instead of their generated username.
+// Guests show as e.g. "Guest 4F2A" instead of their generated username, the bot as e.g. "Bot · Medium".
 export function getPlayerDisplayName(
-    player: { name?: string, isGuest?: boolean } | undefined,
+    player: { userId?: string, name?: string, isGuest?: boolean } | undefined,
     t: (key: string) => string
 ): string | undefined {
+    const botLevel = getBotLevel(player?.userId);
+    if (botLevel) return `${t("Bot")} · ${t(getBotLevelTextKey(botLevel))}`;
     if (!player?.name) return undefined;
     if (player.isGuest) {
         const suffix = player.name.startsWith(GUEST_USERNAME_PREFIX) ? player.name.slice(GUEST_USERNAME_PREFIX.length) : player.name;
diff --git a/packages/core/tests/models/Bot.test.ts b/packages/core/tests/models/Bot.test.ts
new file mode 100644
index 0000000..e711d97
--- /dev/null
+++ b/packages/core/tests/models/Bot.test.ts
@@ -0,0 +1,55 @@
+import { BOT_LEVELS, getBotLevel, getBotLevelTextKey, getLastBotLevel, isBotId, isBotLevel, setLastBotLevel } from "../../src/models";
+import { en, tr } from "../../src/localization";
+import { getPlayerDisplayName } from "../../src/util";
+
+describe("bot ids", () => {
+    it("recognises bot ids and their levels", () => {
+        expect(isBotId("bot:medium")).toBe(true);
+        expect(isBotId("kc:alice")).toBe(false);
+        expect(isBotId(undefined)).toBe(false);
+        expect(getBotLevel("bot:master")).toBe("master");
+        expect(getBotLevel("bot:impossible")).toBeUndefined();
+        expect(getBotLevel("kc:alice")).toBeUndefined();
+    });
+
+    it("checks levels", () => {
+        expect(isBotLevel("hard")).toBe(true);
+        expect(isBotLevel("impossible")).toBe(false);
+        expect(isBotLevel(3)).toBe(false);
+    });
+
+    it("has a name for every level in both languages", () => {
+        for (const level of BOT_LEVELS) {
+            const key = getBotLevelTextKey(level) as keyof typeof en;
+            expect(en[key]).toBeTruthy();
+            expect(tr[key as keyof typeof tr]).toBeTruthy();
+        }
+    });
+});
+
+describe("last bot level", () => {
+    it("is Medium until one is chosen, then the chosen one", () => {
+        const values = new Map<string, string>();
+        const storage = { getString: (key: string) => values.get(key), setString: (key: string, value: string) => { values.set(key, value); } };
+        expect(getLastBotLevel(storage)).toBe("medium");
+        setLastBotLevel(storage, "master");
+        expect(getLastBotLevel(storage)).toBe("master");
+        values.set("botLevel", "impossible");
+        expect(getLastBotLevel(storage)).toBe("medium");
+    });
+});
+
+describe("getPlayerDisplayName", () => {
+    const t = (key: string) => (tr as Record<string, string>)[key] ?? key;
+
+    it("shows the bot with its level", () => {
+        expect(getPlayerDisplayName({ userId: "bot:medium", name: "Bot", isGuest: false }, t)).toBe("Bot · Orta");
+        expect(getPlayerDisplayName({ userId: "bot:easy" }, t)).toBe("Bot · Kolay");
+    });
+
+    it("still shows people and guests as before", () => {
+        expect(getPlayerDisplayName({ userId: "kc:alice", name: "alice", isGuest: false }, t)).toBe("alice");
+        expect(getPlayerDisplayName({ userId: "kc:g", name: "guest-4f2a9b", isGuest: true }, t)).toBe("Misafir 4F2A");
+        expect(getPlayerDisplayName({ userId: "0b9f6d1e" }, t)).toBeUndefined();
+    });
+});