Fix 9-hole course handicap formula to use HI÷2 per WHS spec

Dedicated 9-hole courses have 9-hole ratings and pars, so the WHS
formula is: round((HI÷2) × (slope/113) + (rating − par)).
The previous code used the full HI, giving roughly double the correct
result (e.g. 22 instead of 11 on Augwil White Male for HI 18).

The three cases are now handled correctly:
- Dedicated 9-hole course: HI÷2 with 9-hole ratings
- 9 holes on 18-hole course: full HI with 18-hole ratings, result halved
- Full 18 holes: full HI with 18-hole ratings

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

app/routers/games.py

@@ -331,11 +331,15 @@ async def create_game(request: Request, holes_count: int = Form(...),
         playing_handicap = None
         strokes_allocation_json = None
         par_for_formula = course_par_played * 2 if nine_of_eighteen else course_par_played
+        # Dedicated 9-hole courses have 9-hole ratings: WHS uses HI÷2 in the formula.
+        # For 9-of-18 the full HI is used and the result halved instead.
+        nine_hole_dedicated = (holes_count == 9 and not nine_of_eighteen)
         if hc is not None and tee_id and par_for_formula:
             async with db.execute("SELECT slope, rating FROM course_tees WHERE id = ?", (tee_id,)) as c:
                 tee_row = await c.fetchone()
             if tee_row:
-                ph = round(hc * (tee_row["slope"] / 113) + (tee_row["rating"] - par_for_formula))
+                hc_for_formula = hc / 2 if nine_hole_dedicated else hc
+                ph = round(hc_for_formula * (tee_row["slope"] / 113) + (tee_row["rating"] - par_for_formula))
                 playing_handicap = round(ph / 2) if nine_of_eighteen else ph
                 if hole_rank and playing_handicap > 0:
                     base, extra = divmod(playing_handicap, n_si)