refactor(backend): encapsulate throw lifecycle and clean dead code in game.rs

Add Game::process_throw to centralize throw→simulation→scoring→state flow.

Remove dead room_tx field, simplify add_player, and rename end_ends_or_continue.

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

backend/src/game.rs

@@ -24,7 +24,13 @@ pub struct Game {
     stones_red: u8,
     stones_yellow: u8,
     last_end_scored: Option<(u8, i32, Option<Team>)>,
-    pub room_tx: Option<tokio::sync::broadcast::Sender<ServerMessage>>,
+}
+
+pub struct ThrowOutcome {
+    pub trajectory: Vec<(f32, f32, f32)>,
+    pub end_scored: Option<ServerMessage>,
+    pub state_message: ServerMessage,
+    pub game_over: Option<ServerMessage>,
 }
 
 impl Game {
@@ -42,43 +48,31 @@ impl Game {
             stones_red: STONES_PER_TEAM,
             stones_yellow: STONES_PER_TEAM,
             last_end_scored: None,
-            room_tx: None,
         }
     }
 
     pub fn add_player(&mut self, id: String, preferred: Option<Team>) -> Option<Team> {
-        let team = match preferred {
-            Some(Team::Red) if self.red.is_none() => Some(Team::Red),
-            Some(Team::Yellow) if self.yellow.is_none() => Some(Team::Yellow),
-            Some(_) => {
-                // Preferred is taken; fall back to the other free team.
-                if self.red.is_none() {
-                    Some(Team::Red)
-                } else if self.yellow.is_none() {
-                    Some(Team::Yellow)
-                } else {
-                    None
-                }
-            }
-            None => {
-                // Legacy first-free logic.
-                if self.red.is_none() {
-                    Some(Team::Red)
-                } else if self.yellow.is_none() {
-                    Some(Team::Yellow)
-                } else {
-                    None
-                }
-            }
-        };
+        let team = preferred
+            .filter(|t| self.slot_for(t).is_none())
+            .or_else(|| self.first_open_team())?;
 
-        if let Some(t) = team {
-            let player = Player { id, team: t, connected: true };
-            match t {
-                Team::Red => self.red = Some(player),
-                Team::Yellow => self.yellow = Some(player),
-            }
-            Some(t)
+        let player = Player { id, team, connected: true };
+        *self.slot_for(&team) = Some(player);
+        Some(team)
+    }
+
+    fn slot_for(&mut self, team: &Team) -> &mut Option<Player> {
+        match team {
+            Team::Red => &mut self.red,
+            Team::Yellow => &mut self.yellow,
+        }
+    }
+
+    fn first_open_team(&self) -> Option<Team> {
+        if self.red.is_none() {
+            Some(Team::Red)
+        } else if self.yellow.is_none() {
+            Some(Team::Yellow)
         } else {
             None
         }
@@ -171,6 +165,34 @@ impl Game {
         Ok(path)
     }
 
+    pub fn process_throw(
+        &mut self,
+        player_id: &str,
+        broom_x: f32,
+        broom_y: f32,
+        weight: u8,
+        curl: i8,
+        friction: f32,
+    ) -> Result<ThrowOutcome, String> {
+        let trajectory = self.handle_throw(player_id, broom_x, broom_y, weight, curl, friction)?;
+        self.finish_simulation();
+
+        let end_scored = self.take_last_end_scored();
+        let state_message = self.game_state_message();
+        let game_over = if self.phase == GamePhase::GameComplete {
+            Some(self.game_over_message())
+        } else {
+            None
+        };
+
+        Ok(ThrowOutcome {
+            trajectory,
+            end_scored,
+            state_message,
+            game_over,
+        })
+    }
+
     pub fn finish_simulation(&mut self) {
         if self.phase != GamePhase::Simulating {
             return;
@@ -229,10 +251,10 @@ impl Game {
 
         self.last_end_scored = Some((self.end, points, scoring_team));
         self.phase = GamePhase::EndComplete;
-        self.end_ends_or_continue(points, scoring_team);
+        self.advance_end_or_finish();
     }
 
-    fn end_ends_or_continue(&mut self, _points: i32, _scoring_team: Option<Team>) {
+    fn advance_end_or_finish(&mut self) {
         let tied = self.scores[0] == self.scores[1];
         let after_regulation = self.end >= ENDS;
 
@@ -241,10 +263,6 @@ impl Game {
             return;
         }
 
-        if after_regulation && tied {
-            // Extra end
-        }
-
         self.end += 1;
         self.stones_red = STONES_PER_TEAM;
         self.stones_yellow = STONES_PER_TEAM;
@@ -311,13 +329,11 @@ pub struct Room {
 impl Room {
     pub fn new(id: &str) -> Self {
         let (tx, _) = tokio::sync::broadcast::channel(256);
-        let mut room = Self {
+        Self {
             id: id.to_string(),
             game: Game::new(),
             tx,
-        };
-        room.game.room_tx = Some(room.tx.clone());
-        room
+        }
     }
 }