Snapshot the bet cost, fee address and pool cap onto the round at open, and cap the pool (B-95, RND-05, RND-06, RND-23, BET-20, BET-21, DAT-26, DAT-27, DAT-61, DAT-62, API-21, API-30, API-31, ADR-10, LIM-16)

Only the duration and the cooldown (and, since B-73, the draw confirmations) were copied onto
the round when it opened. The cost of a bet and the fee address were read live, so an edit from
/admin in the middle of a round gave the players of that round different stakes for the same
chance and redirected the commission of the round in progress.

- `rounds.bet_amount_sats`, `rounds.fee_address` and `rounds.max_round_pool_sats` are copied from
  round_config in the transaction that opens the round (Alembic a7d3e9f15b48: plain add_column,
  existing rounds backfilled with the current configuration, i.e. what they were using; the
  expression indexes untouched). `place_bet` charges the round's cost, `_trigger_payout` pays the
  round's fee address (an empty one on the row still stops the payout, as before),
  `GET /rounds/current` advertises the round's cost while one is active and the configured one
  otherwise. The minimum withdrawal and the fee rate stay live, by design (ADR-20, ADR-10).
- `round_config.max_round_pool_sats` (0 = none, otherwise >= the bet cost and <= 4e15, in
  /admin and PUT/GET /admin/config): a bet is refused with `round_full` (params also carry
  `max_round_pool_sats`) once the sum of the round's participant rows, in-flight ones included,
  has reached the round's cap, before anything moves; the pool can exceed it by one bet at most.
  A cap under the bet cost is a 422 `max_round_pool_below_bet_amount`.
- PUT /admin/config's payability check (RND-40) now also judges a fee-rate change against the
  bet cost the round in progress opened with, which can be lower than the configured one.
- `error.round_full` no longer says "maximum of N players" (it also fires for the pool cap): the
  seven translations are generic.

Ambiguity resolved: the spec said the cap is snapshotted (RND-05, BET-20, ARC) in some places and
"applies immediately, also to the round in progress" in the round_config table of modello-dati;
the snapshot wins, with a column on `rounds` (modello-dati/api/guide-admin brought in line).

Tests changed because the spec changed: the payout fixtures seed the round's own fee address, and
the old "fee address missing" payout test now empties the round's address (clearing it in the
configuration mid-round must not stop the payout). New test_round_snapshot.py: the copy at open,
edits reaching only the next round, every bet of a round paying the same stake whether the cost
is raised or lowered meanwhile, the payout following the round's address (and surviving it being
cleared in the configuration), the cap (exactly at the cap is full, in-flight bets count, no cap,
a mid-round edit of the cap does not apply, the refused player's coins untouched), plus the route,
the admin bounds and the two 422s, the fee-rate check against the round's own cost, and the
migration backfill. Mutation-checked: charging the live cost, paying the live address, not
copying the cap and `>` instead of `>=` each fail tests.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

app/api/routes/admin.py

@@ -15,7 +15,7 @@ from app.db.models import AuditLog, BugReport, PendingTransaction, Round, User
 from app.db.session import get_session
 from app.rounds.config import get_round_config
 from app.rounds.pause import AUTOMATIC_REASONS, OPERATOR_REASON
-from app.rounds.service import payout_config_problem
+from app.rounds.service import get_active_round, payout_config_problem
 from app.wallet.address import is_valid_plm_address
 from app.wallet.hd import derive_user_wif
 from app.wallet.psbt_builder import MAX_FEE_RATE_SAT_VB
@@ -49,6 +49,7 @@ _CONFIG_FIELDS = (
     "draw_animation_seconds",
     "deposit_confirmations",  # B-82 (DAT-62)
     "draw_confirmations",  # B-73 (DAT-62)
+    "max_round_pool_sats",  # B-95 (DAT-62)
 )
 
 
@@ -62,6 +63,7 @@ class RoundConfigResponse(BaseModel):
     draw_animation_seconds: int
     deposit_confirmations: int  # B-82 (DAT-62)
     draw_confirmations: int  # B-73 (DAT-62)
+    max_round_pool_sats: int  # B-95 (DAT-62)
     paused: bool
     paused_reason: str | None = None  # B-78 (DAT-69): why, or None when not paused
 
@@ -85,6 +87,7 @@ class RoundConfigUpdate(BaseModel):
     draw_animation_seconds: int | None = Field(default=None, ge=0, le=600)
     deposit_confirmations: int | None = Field(default=None, ge=1, le=100)  # B-82 (DAT-62)
     draw_confirmations: int | None = Field(default=None, ge=1, le=20)  # B-73 (DAT-62)
+    max_round_pool_sats: int | None = Field(default=None, ge=0, le=4_000_000_000_000_000)  # B-95 (DAT-62)
 
     @field_validator("fee_address")
     @classmethod
@@ -137,7 +140,16 @@ async def update_config(
     # refused before anything is written — the payout reads fee_rate_sat_vb at build time, so
     # a rate raised mid-round could otherwise make the round in progress unpayable.
     if "bet_amount_sats" in changes or "fee_rate_sat_vb" in changes:
-        problem = payout_config_problem(config.bet_amount_sats, config.fee_rate_sat_vb)
+        amounts = {config.bet_amount_sats}
+        if "fee_rate_sat_vb" in changes:
+            # B-95: the round in progress is paid with the bet amount it opened with, which may
+            # differ from the one configured now — a higher fee rate has to leave *it* payable too.
+            active = await get_active_round(session)
+            if active is not None:
+                amounts.add(active.bet_amount_sats)
+        problem = next(
+            (p for p in (payout_config_problem(a, config.fee_rate_sat_vb) for a in sorted(amounts)) if p), None
+        )
         if problem is not None:
             await session.rollback()
             raise http_error(
@@ -148,6 +160,21 @@ async def update_config(
                 reason=problem,
             )
 
+    # B-95 (DAT-62): a cap below the price of one bet would refuse every bet of every round.
+    if (
+        ("max_round_pool_sats" in changes or "bet_amount_sats" in changes)
+        and config.max_round_pool_sats
+        and config.max_round_pool_sats < config.bet_amount_sats
+    ):
+        offending = {"max_round_pool_sats": config.max_round_pool_sats, "bet_amount_sats": config.bet_amount_sats}
+        await session.rollback()
+        raise http_error(
+            422,
+            "max_round_pool_below_bet_amount",
+            "max_round_pool_sats must be 0 (no cap) or at least the bet amount",
+            **offending,
+        )
+
     if changes:
         await write_audit_log(session, "config_updated", changes)
     await session.commit()