feat(core,engine): Klondike solver and "Winnable deals only" toggle

Closes Quat investigation #1. Today some Klondike deals are
unwinnable from the start and the player has no signal that the
deal they were given is solvable. A new Settings → Gameplay toggle
"Winnable deals only" (default off) makes the engine retry seeds
at deal-time until the solver returns Winnable, up to a cap.

Solver

solitaire_core::solver is a hand-rolled iterative-DFS solver with
memoisation on a 64-bit canonical state hash. Move enumeration is
priority-ordered: foundation moves first (zero choice when an Ace
or rank-up exists), inter-tableau moves second, waste-to-tableau
third, stock-draw last. The draw is skipped when the cycle counter
shows we've recirculated the entire stock without progress —
Klondike's deterministic stock cycle means further draws can't
unlock anything new.

Two budget knobs (move_budget = 100k, state_budget = 200k by
default) cap pathological cases at Inconclusive; the caller treats
Inconclusive as "winnable" so the player isn't penalised for the
solver giving up. Median solve time is 2 ms; pathological
inconclusives top out near 120 ms.

Switched from recursive to iterative DFS after a real-deal solve
overflowed Rust's default 8 MB thread stack. Behaviour identical;
the change is invisible to callers.

Pure logic — solitaire_core has no Bevy or I/O. Same input always
yields the same SolverResult.

Settings

Settings.winnable_deals_only is a #[serde(default)] bool; legacy
files load to false. SOLVER_DEAL_RETRY_CAP = 50 caps the retry
loop. The Settings → Gameplay toggle reads as "Winnable deals only"
with a "(may take a moment when on)" caption.

Engine integration

handle_new_game's seed-selection path now branches on the toggle.
When on AND mode is Classic AND no specific seed was requested
(daily challenges, replays, and explicit-seed requests bypass the
solver), choose_winnable_seed walks seed N, N+1, N+2, … calling
try_solve until it finds Winnable or Inconclusive. If the cap is
hit without a verdict, the latest tried seed is used so the player
always gets a deal rather than spinning forever.

19 new tests (11 solver, 3 settings, 5 engine including the
choose_winnable_seed unit). Two ignored bench/scan helpers
(solver_bench, find_unwinnable) for ad-hoc profiling.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

solitaire_data/src/settings.rs

@@ -166,6 +166,21 @@ pub struct Settings {
     /// `#[serde(default = "default_time_bonus_multiplier")]`.
     #[serde(default = "default_time_bonus_multiplier")]
     pub time_bonus_multiplier: f32,
+    /// When `true`, the engine rejects new-game deals the
+    /// [`solitaire_core::solver`] cannot prove winnable, retrying
+    /// fresh seeds up to [`SOLVER_DEAL_RETRY_CAP`] attempts before
+    /// giving up and using the last tried seed. Off by default —
+    /// the solver adds a few hundred milliseconds of latency on the
+    /// pathological deals that hit the budget cap, and not every
+    /// player wants to wait. Older `settings.json` files written
+    /// before this field existed deserialize cleanly to `false` via
+    /// `#[serde(default)]`.
+    ///
+    /// Scope: only random-seed Classic-mode deals are filtered.
+    /// Daily challenges, replays, and explicit-seed requests skip the
+    /// solver retry loop — see `solitaire_engine::handle_new_game`.
+    #[serde(default)]
+    pub winnable_deals_only: bool,
 }
 
 fn default_draw_mode() -> DrawMode {
@@ -223,6 +238,17 @@ fn default_time_bonus_multiplier() -> f32 {
     1.0
 }
 
+/// Maximum number of seed retries [`solitaire_engine::handle_new_game`]
+/// is willing to attempt before giving up and accepting the latest
+/// candidate seed when [`Settings::winnable_deals_only`] is on. If
+/// every retry comes back [`SolverResult::Unwinnable`] (which would
+/// be very unusual) we'd rather hand the player a possibly-unwinnable
+/// deal than spin forever on the main thread.
+///
+/// 50 attempts × ~50 ms median per solve = ~2.5 s worst-case stall —
+/// the upper bound on UI freeze when the toggle is on.
+pub const SOLVER_DEAL_RETRY_CAP: u32 = 50;
+
 impl Default for Settings {
     fn default() -> Self {
         Self {
@@ -241,6 +267,7 @@ impl Default for Settings {
             shown_achievement_onboarding: false,
             tooltip_delay_secs: default_tooltip_delay(),
             time_bonus_multiplier: default_time_bonus_multiplier(),
+            winnable_deals_only: false,
         }
     }
 }
@@ -428,6 +455,7 @@ mod tests {
             shown_achievement_onboarding: false,
             tooltip_delay_secs: default_tooltip_delay(),
             time_bonus_multiplier: default_time_bonus_multiplier(),
+            winnable_deals_only: false,
         };
         save_settings_to(&path, &s).expect("save");
         let loaded = load_settings_from(&path);
@@ -835,4 +863,49 @@ mod tests {
             s2.time_bonus_multiplier
         );
     }
+
+    // -----------------------------------------------------------------------
+    // winnable_deals_only — solver-backed deal filter toggle
+    // -----------------------------------------------------------------------
+
+    #[test]
+    fn settings_winnable_deals_only_default_is_false() {
+        // Off by default — the solver adds latency we shouldn't impose
+        // on every player without their consent.
+        assert!(
+            !Settings::default().winnable_deals_only,
+            "default winnable_deals_only must be false"
+        );
+    }
+
+    #[test]
+    fn settings_winnable_deals_only_round_trip() {
+        let path = tmp_path("winnable_deals_only_round_trip");
+        let _ = fs::remove_file(&path);
+        let s = Settings {
+            winnable_deals_only: true,
+            ..Settings::default()
+        };
+        save_settings_to(&path, &s).expect("save");
+        let loaded = load_settings_from(&path);
+        assert!(
+            loaded.winnable_deals_only,
+            "winnable_deals_only must survive serde round-trip"
+        );
+        let _ = fs::remove_file(&path);
+    }
+
+    #[test]
+    fn legacy_settings_without_winnable_deals_only_deserializes_to_false() {
+        // A settings.json written before this field existed must
+        // deserialize cleanly to `false` (the default-off behaviour)
+        // rather than failing the whole load or surprising the player
+        // by switching the toggle on.
+        let json = br#"{ "sfx_volume": 0.7, "first_run_complete": true }"#;
+        let s: Settings = serde_json::from_slice(json).unwrap_or_default();
+        assert!(
+            !s.winnable_deals_only,
+            "legacy settings.json missing winnable_deals_only must deserialize to false"
+        );
+    }
 }