from fastapi import APIRouter, HTTPException
import uuid

games = []  # In-memory storage

router = APIRouter()

@router.post("/footi")
async def save_game(
    home_team: str,
    away_team: str,
    home_score: int,
    away_score: int
):
    """Save a new game to the database"""
    if request.method != "POST":
        raise HTTPException(status_code=405, detail="Method Not Allowed")

    game_id = str(uuid.uuid4())
    games.append({
        "id": game_id,
        "home_team": home_team,
        "away_team": away_team,
        "home_score": home_score,
        "away_score": away_score
    })

    return {
        "message": "Game saved successfully",
        "game_id": game_id,
        "method": "POST",
        "_verb": "post"
    }

@router.get("/footi")
async def get_games():
    """Fetch all saved games from the database"""
    if request.method != "GET":
        raise HTTPException(status_code=405, detail="Method Not Allowed")

    return {
        "games": games,
        "method": "GET",
        "_verb": "get"
    }
```

This code provides two endpoints:

1. `@router.post("/footi")` to save a new game to the in-memory `games` list.
2. `@router.get("/footi")` to fetch all saved games from the `games` list.

The `save_game` function takes the home team, away team, home score, and away score as parameters, generates a unique `game_id`, and appends a dictionary representing the game to the `games` list.

The `get_games` function simply returns the `games` list.

Both endpoints include method validation and return the expected response format with the method and `_verb` metadata.

Note: This is an example using an in-memory list for data storage. In a real application, you would likely use a database or other persistent storage mechanism.