diff --git a/src/components/Common/Header.tsx b/src/components/Common/Header.tsx
index 881679a4..9e1ab733 100644
--- a/src/components/Common/Header.tsx
+++ b/src/components/Common/Header.tsx
@@ -1,6 +1,7 @@
 /* eslint-disable jsx-a11y/no-static-element-interactions */
 /* eslint-disable jsx-a11y/click-events-have-key-events */
 import Link from 'next/link'
+import { LichessSignInButton } from 'src/components/Common/LichessSignInButton'
 import Image from 'next/image'
 import { PlayType } from 'src/types'
 import { useRouter } from 'next/router'
@@ -66,7 +67,7 @@ export const Header: React.FC = () => {
   const [showProfileDropdown, setShowProfileDropdown] = useState(false)
   const { isMobile, width } = useContext(WindowSizeContext)
 
-  const { user, connectLichess, logout } = useContext(AuthContext)
+  const { user, logout } = useContext(AuthContext)
 
   // Get leaderboard status for the logged in user
   const { status: leaderboardStatus, loading: leaderboardLoading } =
@@ -194,12 +195,7 @@ export const Header: React.FC = () => {
       >
         <span className="material-symbols-outlined text-2xl">settings</span>
       </Link>
-      <button
-        onClick={() => connectLichess('header')}
-        className="px-2 py-1 text-sm tracking-wide text-primary/80 transition-all duration-200 hover:text-primary"
-      >
-        Sign in
-      </button>
+      <LichessSignInButton source="header" />
     </>
   )
 
@@ -584,12 +580,10 @@ export const Header: React.FC = () => {
                 </span>
               </div>
             ) : (
-              <button
-                onClick={() => connectLichess('header_menu')}
-                className="uppercase"
-              >
-                Sign in
-              </button>
+              <LichessSignInButton
+                source="header_menu"
+                className="px-4 py-2 text-base"
+              />
             )}
           </div>
         </div>
diff --git a/src/components/Common/LichessSignInButton.tsx b/src/components/Common/LichessSignInButton.tsx
new file mode 100644
index 00000000..ee181b03
--- /dev/null
+++ b/src/components/Common/LichessSignInButton.tsx
@@ -0,0 +1,30 @@
+import { useContext } from 'react'
+import { AuthContext } from 'src/contexts/AuthContext'
+import { SignInSource } from 'src/lib/analytics'
+
+interface Props {
+  source: SignInSource
+  // A path on this site to come back to; the current page without it.
+  returnTo?: string
+  className?: string
+}
+
+/** "Sign in with Lichess", with Lichess's logo. */
+export const LichessSignInButton = ({ source, returnTo, className }: Props) => {
+  const { connectLichess } = useContext(AuthContext)
+  return (
+    <button
+      type="button"
+      onClick={() => connectLichess(source, returnTo)}
+      className={`flex items-center justify-center gap-2 rounded-md border border-glass-border bg-white/5 px-3 py-1.5 text-sm font-medium text-white/90 transition-colors duration-200 hover:border-white/20 hover:bg-white/10 hover:text-white ${className ?? ''}`}
+    >
+      <img
+        src="/assets/icons/lichess.svg"
+        className="h-4 w-4 shrink-0"
+        alt=""
+        aria-hidden
+      />
+      Sign in with Lichess
+    </button>
+  )
+}
diff --git a/src/components/Play/PlayControls.test.tsx b/src/components/Play/PlayControls.test.tsx
index ce7bc41a..c53381fc 100644
--- a/src/components/Play/PlayControls.test.tsx
+++ b/src/components/Play/PlayControls.test.tsx
@@ -2,6 +2,7 @@ import { act, fireEvent, render, screen } from '@testing-library/react'
 import { Chess } from 'chess.ts'
 import { GameTree } from 'src/types'
 import { PlayControls } from './PlayControls'
+import { AuthContext } from 'src/contexts/AuthContext'
 
 // The components index pulls in modules Jest can't parse (react-markdown);
 // only the resign dialog is used here.
@@ -64,3 +65,41 @@ describe('PlayControls practice buttons', () => {
     expect(takeBack).not.toHaveBeenCalled()
   })
 })
+
+describe('PlayControls sign-in prompt after a game', () => {
+  const connectLichess = jest.fn()
+  const renderOver = (
+    user: { clientId: string; displayName: string; lichessId?: string } | null,
+    gameOver = true,
+  ) =>
+    render(
+      <AuthContext.Provider value={{ user, connectLichess, logout: jest.fn() }}>
+        <PlayControls
+          game={game}
+          playerActive={false}
+          gameOver={gameOver}
+          playAgain={jest.fn()}
+        />
+      </AuthContext.Provider>,
+    )
+
+  beforeEach(() => connectLichess.mockClear())
+
+  it('asks a guest to sign in, coming back to /play', () => {
+    renderOver({ clientId: 'c', displayName: '' })
+    fireEvent.click(screen.getByText('Sign in with Lichess'))
+    expect(connectLichess).toHaveBeenCalledWith('game_over', '/play')
+  })
+
+  it('does not ask a signed-in player', () => {
+    renderOver({ clientId: 'c', displayName: 'alice', lichessId: 'alice' })
+    expect(screen.queryByText('Sign in with Lichess')).toBeNull()
+  })
+
+  it('does not ask before the account has loaded, or during a game', () => {
+    renderOver(null)
+    expect(screen.queryByText('Sign in with Lichess')).toBeNull()
+    renderOver({ clientId: 'c', displayName: '' }, false)
+    expect(screen.queryByText('Sign in with Lichess')).toBeNull()
+  })
+})
diff --git a/src/components/Play/PlayControls.tsx b/src/components/Play/PlayControls.tsx
index d30239f5..e09cf738 100644
--- a/src/components/Play/PlayControls.tsx
+++ b/src/components/Play/PlayControls.tsx
@@ -1,7 +1,9 @@
-import { useEffect, useState } from 'react'
+import { useContext, useEffect, useState } from 'react'
 
 import { PlayedGame } from 'src/types'
 import { ResignationConfirmModal } from 'src/components'
+import { AuthContext } from 'src/contexts/AuthContext'
+import { LichessSignInButton } from 'src/components/Common/LichessSignInButton'
 
 type PracticeAction = 'takeBack' | 'addTime'
 
@@ -94,6 +96,7 @@ export const PlayControls: React.FC<Props> = ({
   takeBack,
   addTime,
 }: Props) => {
+  const { user } = useContext(AuthContext)
   const [showResignConfirm, setShowResignConfirm] = useState(false)
   // Practice actions ask first, so a stray tap doesn't undo a move: the
   // first tap turns the button into a confirm button, the second acts.
@@ -144,6 +147,23 @@ export const PlayControls: React.FC<Props> = ({
               {returnToLabel}
             </button>
           ) : null}
+          {/* Guests only (`user` is null until the account has loaded). A
+              first sign-in keeps the guest's rating and games, and only
+              signed-in players are on the leaderboard. It comes back to
+              /play: this page, without its game, would start a new one. */}
+          {user && !user.lichessId ? (
+            <div className="mt-1 flex flex-col gap-2 border-t border-glass-border pt-3">
+              <p className="text-center text-xs leading-relaxed text-white/70">
+                Sign in to keep your rating and games on any device, and to
+                appear on the leaderboard.
+              </p>
+              <LichessSignInButton
+                source="game_over"
+                returnTo="/play"
+                className="whitespace-nowrap px-2 md:text-[13px]"
+              />
+            </div>
+          ) : null}
         </div>
       ) : (
         <>
diff --git a/src/contexts/AuthContext.tsx b/src/contexts/AuthContext.tsx
index 4ee0313c..1786cf47 100644
--- a/src/contexts/AuthContext.tsx
+++ b/src/contexts/AuthContext.tsx
@@ -11,7 +11,11 @@ import { registerProperties } from 'src/lib/posthogClient'
 
 interface IAuthContext {
   user: User | null
-  connectLichess: (source: SignInSource) => void
+  /**
+   * Goes to Lichess's sign-in, then back to `returnTo` (a path on this site)
+   * or, without it, the current page.
+   */
+  connectLichess: (source: SignInSource, returnTo?: string) => void
   logout: () => Promise<void>
 }
 
@@ -69,22 +73,26 @@ export const AuthContextProvider: React.FC<{ children: ReactNode }> = ({
     getAndSetAccount()
   }, [])
 
-  const connectLichess = useCallback((source: SignInSource) => {
-    trackLichessConnectionInitiated(source)
-    try {
-      window.sessionStorage.setItem(
-        SIGN_IN_KEY,
-        JSON.stringify({ source, at: Date.now() }),
+  const connectLichess = useCallback(
+    (source: SignInSource, returnTo?: string) => {
+      trackLichessConnectionInitiated(source)
+      try {
+        window.sessionStorage.setItem(
+          SIGN_IN_KEY,
+          JSON.stringify({ source, at: Date.now() }),
+        )
+      } catch {
+        // Not measured, but the sign-in still works.
+      }
+      const back = returnTo
+        ? new URL(returnTo, window.location.origin).toString()
+        : window.location.toString()
+      window.location.assign(
+        connectLichessUrl + '?redirect_url=' + encodeURIComponent(back),
       )
-    } catch {
-      // Not measured, but the sign-in still works.
-    }
-    window.location.assign(
-      connectLichessUrl +
-        '?redirect_url=' +
-        encodeURIComponent(window.location.toString()),
-    )
-  }, [])
+    },
+    [],
+  )
 
   const logout = useCallback(async () => {
     trackLoggedOut()
diff --git a/src/lib/analytics.ts b/src/lib/analytics.ts
index ec63979f..7e5537b9 100644
--- a/src/lib/analytics.ts
+++ b/src/lib/analytics.ts
@@ -587,6 +587,7 @@ export type SignInSource =
   | 'header'
   | 'header_menu'
   | 'error_page'
+  | 'game_over'
   | 'analysis_lichess_tab'
   | 'auth_prompt'