from fastapi import APIRouter, HTTPException
import uuid

games = []  # In-memory storage

router = APIRouter()

@router.post("/basketb")
async def save_game(
    home_team: str,
    away_team: str,
    home_score: int,
    away_score: int
):
    """Save a basketball 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("/basketb")
async def get_games():
    """Fetch all basketball games from the database"""
    return {
        "games": games,
        "method": "GET",
        "_verb": "get"
    }
```

This code defines two routes:

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

The `save_game` function expects the home team, away team, home score, and away score as parameters. It generates a unique `game_id` using `uuid.uuid4()`, creates a dictionary representing the game, and appends it to the `games` list. The response includes a success message and the `game_id`.

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

Note that this implementation uses an in-memory list for storing games, which is not suitable for production use. In a real-world scenario, you would need to integrate with a database like PostgreSQL, MySQL, or MongoDB.