diff --git a/tests/e2e/test_availability_solver.py b/tests/e2e/test_availability_solver.py
new file mode 100644
index 00000000..fa3aef11
--- /dev/null
+++ b/tests/e2e/test_availability_solver.py
@@ -0,0 +1,71 @@
+"""Overnight B6 e2e — the solver must not assign a volunteer on time-off.
+
+Regression guard for an existing correctness property that had unit
+coverage but no end-to-end enforcement: a volunteer whose time-off
+covers the only event date must be left unassigned (the role stays
+open) rather than double-booked.
+"""
+
+from __future__ import annotations
+
+import pytest
+
+from tests.e2e._helpers import accept_invitation, invite_token, no_js_errors, rid, signup_admin
+
+pytestmark = pytest.mark.e2e
+
+
+def test_timeoff_blocks_solver_assignment(live_server, new_context, page, db_path):
+    base = live_server
+    vol_email = f"vol+{rid()}@hope.e2e"
+
+    signup_admin(page, base)
+
+    page.goto(f"{base}/a/people")
+    page.click("button:has-text('Invite person')")
+    page.fill("#inv_name", "Dana Vol")
+    page.fill("#inv_email", vol_email)
+    page.select_option("#inv_role", "volunteer")
+    page.click("button:has-text('Send invite')")
+    page.wait_for_selector("#invite-result:has-text('Invitation sent')")
+    vol_page = accept_invitation(new_context(), base, invite_token(db_path, vol_email))
+
+    # Volunteer books time-off covering the event date.
+    vol_page.goto(f"{base}/v/availability")
+    vol_page.wait_for_selector("#start_date")
+    vol_page.fill("#start_date", "2026-06-07")
+    vol_page.fill("#end_date", "2026-06-07")
+    vol_page.fill("#reason", "Vacation")
+    vol_page.click("button:has-text('Add time-off')")
+    vol_page.wait_for_selector("#timeoff-list:has-text('Vacation')")
+
+    # Admin creates the only event on that exact date, one open role.
+    page.goto(f"{base}/a/events")
+    page.click("button:has-text('New event')")
+    page.wait_for_selector("#ev_type", state="visible")
+    page.fill("#ev_type", "Sunday 10am Service")
+    page.fill("#ev_date", "2026-06-07")
+    page.fill("#ev_start", "10:00")
+    page.fill("#ev_end", "11:30")
+    page.fill("input[name=role_name]", "volunteer")
+    page.fill("input[name=role_count]", "1")
+    page.click("button:has-text('Create event')")
+    page.wait_for_selector("#events-list:has-text('Sunday 10am Service')")
+
+    # Solve, then publish.
+    page.goto(f"{base}/a/solver")
+    page.fill("#from_date", "2026-05-19")
+    page.fill("#to_date", "2026-06-30")
+    page.click("button:has-text('Run solver')")
+    page.wait_for_selector("#solver-result:has-text('Review solution')")
+    page.click("a:has-text('Review solution')")
+    page.wait_for_url("**/a/solution/**")
+    page.wait_for_selector("#publish-state")
+    page.click("button:has-text('Publish this solution')")
+    page.wait_for_selector("#publish-state:has-text('Unpublish')")
+
+    # The on-time-off volunteer was NOT scheduled.
+    vol_page.goto(f"{base}/v/schedule")
+    vol_page.wait_for_selector("text=No assignments yet")
+
+    no_js_errors(vol_page)