add real-time game data, prediction history, and fix winning cards chart

- WebSocket connection shows live game state (round #, phase, bets per
  chair, pot) in a persistent bar at the top of predictions page
- Prediction cards now display current bet amounts per chair
- Round results flash HIT/MISS against the Bayesian prediction
- New "Last 20 Predictions vs Actual" table with per-game probabilities,
  predicted vs actual winner, and running accuracy
- Predictions auto-refresh after each round ends
- Fix winning cards chart: use taller container (480px) and dedicated
  scales config for horizontal bar rendering
- Add _last_n_predictions() helper to db.py for detailed per-game
  prediction history with game numbers

app/db.py

@@ -1217,14 +1217,39 @@ def _backtest_theories(winners):
     }
 
 
+def _last_n_predictions(winners, n=20):
+    """Get detailed prediction vs actual for the last N games."""
+    warmup = 30
+    if len(winners) <= warmup:
+        return []
+    start = max(warmup, len(winners) - n)
+    results = []
+    for i in range(start, len(winners)):
+        history = winners[:i]
+        actual = winners[i]
+        m1, _ = _markov_matrix_1(history)
+        m2, _ = _markov_matrix_2(history)
+        pred, _ = _bayesian_prediction(history, m1, m2)
+        predicted = max(CHAIR_LABELS, key=lambda c: pred[c])
+        results.append({
+            "index": i,
+            "predicted": predicted,
+            "actual": actual,
+            "correct": predicted == actual,
+            "probs": {c: round(pred[c], 4) for c in CHAIR_LABELS},
+        })
+    return results
+
+
 @_with_lock
 def get_prediction_analysis() -> dict:
     """Run all prediction/game-theory analysis and return results."""
     client = get_client()
 
-    # Query 1: Full winner sequence
-    result = client.query("SELECT winner FROM games ORDER BY game_no ASC")
-    winners = [config.CHAIRS.get(r[0], "?") for r in result.result_rows]
+    # Query 1: Full winner sequence with game numbers
+    result = client.query("SELECT game_no, winner FROM games ORDER BY game_no ASC")
+    game_nos = [r[0] for r in result.result_rows if config.CHAIRS.get(r[1], "?") in CHAIR_LABELS]
+    winners = [config.CHAIRS.get(r[1], "?") for r in result.result_rows]
     winners = [w for w in winners if w in CHAIR_LABELS]  # filter unknowns
 
     # Query 2: Card data for last 500 games
@@ -1252,6 +1277,13 @@ def get_prediction_analysis() -> dict:
     # Backtesting
     backtest = _backtest_theories(winners)
 
+    # Last 20 prediction vs actual
+    last_20_raw = _last_n_predictions(winners, 20)
+    # Attach game_nos to last_20
+    for entry in last_20_raw:
+        idx = entry["index"]
+        entry["game_no"] = game_nos[idx] if idx < len(game_nos) else 0
+
     # Card analysis
     card_values = _card_value_distribution(cards_data)
     face_cards = _face_card_frequency(cards_data)
@@ -1261,6 +1293,7 @@ def get_prediction_analysis() -> dict:
     return {
         "total_games": len(winners),
         "last_winners": winners[-10:] if len(winners) >= 10 else winners,
+        "last_20_predictions": last_20_raw,
         "prediction": prediction,
         "signals": signals,
         "markov1": {"matrix": markov1, "counts": {k: dict(v) for k, v in markov1_counts.items()}},