refactor: backend→lotto 서비스 리네이밍 + lotto.db 레거시 테이블 스키마 제거

- backend/ → lotto/ 디렉토리 이동
- docker-compose: lotto-backend→lotto, lotto-frontend→frontend
- deploy scripts, nginx, agent-office config 네이밍 일괄 반영
- lotto/app/db.py에서 todos·blog_posts CREATE TABLE 제거 (personal로 이관 완료)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

lotto/app/utils.py

@@ -0,0 +1,80 @@
+import random
+from typing import List, Dict, Any, Tuple
+
+
+def weighted_sample_6(weights: Dict[int, float]) -> List[int]:
+    """
+    가중 확률 샘플링으로 중복 없이 6개 번호 추출.
+    weights: {1: w1, 2: w2, ..., 45: w45}
+    """
+    pool = list(range(1, 46))
+    chosen: List[int] = []
+    for _ in range(6):
+        total = sum(weights[n] for n in pool)
+        r = random.random() * total
+        acc = 0.0
+        for n in pool:
+            acc += weights[n]
+            if acc >= r:
+                chosen.append(n)
+                pool.remove(n)
+                break
+    return chosen
+
+def calc_metrics(numbers: List[int]) -> Dict[str, Any]:
+    nums = sorted(numbers)
+    s = sum(nums)
+    odd = sum(1 for x in nums if x % 2 == 1)
+    even = len(nums) - odd
+    mn, mx = nums[0], nums[-1]
+    rng = mx - mn
+
+    # 1-10, 11-20, 21-30, 31-40, 41-45
+    buckets = {
+        "1-10": 0,
+        "11-20": 0,
+        "21-30": 0,
+        "31-40": 0,
+        "41-45": 0,
+    }
+    for x in nums:
+        if 1 <= x <= 10:
+            buckets["1-10"] += 1
+        elif 11 <= x <= 20:
+            buckets["11-20"] += 1
+        elif 21 <= x <= 30:
+            buckets["21-30"] += 1
+        elif 31 <= x <= 40:
+            buckets["31-40"] += 1
+        else:
+            buckets["41-45"] += 1
+
+    return {
+        "sum": s,
+        "odd": odd,
+        "even": even,
+        "min": mn,
+        "max": mx,
+        "range": rng,
+        "buckets": buckets,
+    }
+
+def calc_recent_overlap(numbers: List[int], draws: List[Tuple[int, List[int]]], last_k: int) -> Dict[str, Any]:
+    """
+    draws: [(drw_no, [n1..n6]), ...] 오름차순
+    last_k: 최근 k회 기준 중복
+    """
+    if last_k <= 0:
+        return {"last_k": 0, "repeats": 0, "repeated_numbers": []}
+
+    recent = draws[-last_k:] if len(draws) >= last_k else draws
+    recent_set = set()
+    for _, nums in recent:
+        recent_set.update(nums)
+
+    repeated = sorted(set(numbers) & recent_set)
+    return {
+        "last_k": len(recent),
+        "repeats": len(repeated),
+        "repeated_numbers": repeated,
+    }