Add Phase 1 MVP: D&D text-adventure server

FastAPI + Postgres backend with fastapi-users auth, games/characters
CRUD, and a WebSocket chat endpoint where an x.ai Grok DM narrates
play, rolls dice, and maintains character sheets via tool calls.
React + Tailwind frontend covers registration/login, game list and
creation, participation-code join flow, character viewer, and a
real-time chat session view. Docker Compose skeleton (Postgres +
backend) included; Caddy/frontend container wiring is deferred to
the deploy milestone.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/app/llm/tools/dice.py

@@ -0,0 +1,50 @@
+import re
+from random import SystemRandom
+
+_rng = SystemRandom()
+
+_NOTATION_RE = re.compile(r"^\s*(\d*)d(\d+)\s*(?:([+-])\s*(\d+))?\s*$", re.IGNORECASE)
+
+TOOL_SCHEMA = {
+    "name": "roll_dice",
+    "description": (
+        "Roll dice using standard D&D notation (e.g. '1d20+5', '2d6', 'd8-1'). "
+        "Always use this tool for any dice roll that affects the game — never invent or guess a result yourself."
+    ),
+    "parameters": {
+        "type": "object",
+        "properties": {
+            "notation": {
+                "type": "string",
+                "description": "Dice notation, e.g. '1d20+5'",
+            },
+            "reason": {
+                "type": "string",
+                "description": "Short reason for the roll, e.g. 'Geschicklichkeitsrettung, Schwierigkeit 13'",
+            },
+        },
+        "required": ["notation"],
+    },
+}
+
+
+def roll(notation: str) -> dict:
+    match = _NOTATION_RE.match(notation)
+    if not match:
+        raise ValueError(f"Invalid dice notation: {notation!r}")
+
+    count_str, sides_str, sign, modifier_str = match.groups()
+    count = int(count_str) if count_str else 1
+    sides = int(sides_str)
+
+    if not (1 <= count <= 100) or not (2 <= sides <= 1000):
+        raise ValueError(f"Dice notation out of allowed range: {notation!r}")
+
+    modifier = int(modifier_str) if modifier_str else 0
+    if sign == "-":
+        modifier = -modifier
+
+    rolls = [_rng.randint(1, sides) for _ in range(count)]
+    total = sum(rolls) + modifier
+
+    return {"notation": notation, "rolls": rolls, "modifier": modifier, "total": total}