fix(web client): reactive exit sign

clients/web/src/game/components/board.rs

@@ -312,13 +312,8 @@ pub fn Board(
         exit_field_test = |f| matches!(f, 1..=6);
     }
 
-    // Show a clickable exit sign outside the board when bearing off is possible.
+    // Sequences clone for the reactive exit button (show/hide + class + click).
-    let has_exit_move = valid_sequences
+    let seqs_exit = valid_sequences.clone();
-        .iter()
-        .any(|(m1, m2)| m1.get_to() == 0 || m2.get_to() == 0);
-    let show_exit_btn = all_in_exit && is_move_stage && has_exit_move;
-    let seqs_exit_cls = valid_sequences.clone();
-    let seqs_exit_click = valid_sequences.clone();
 
     // `valid_sequences` is cloned per field (the Vec is small; Send-safe unlike Rc).
     let fields_from = |nums: &[u8], is_top_row: bool| -> Vec<AnyView> {
@@ -624,7 +619,24 @@ pub fn Board(
                 </svg>
                 // Exit sign: circle+arrow outside the board, next to the last exit field.
                 // White exits to the right (top-right quarter); Black exits to the left (top-left).
-                {show_exit_btn.then(|| {
+                {move || {
+                    // Recompute on every staged_moves change: the exit button must appear
+                    // even when the initial board has a checker outside the exit zone,
+                    // because the first move can bring all checkers in (e.g. 15→21, 19→exit).
+                    let staged = staged_moves.get();
+                    let show = is_move_stage && match staged.len() {
+                        0 => seqs_exit.iter().any(|(m1, m2)| m1.get_to() == 0 || m2.get_to() == 0),
+                        1 => {
+                            let (f0, t0) = staged[0];
+                            seqs_exit.iter()
+                                .filter(|(m1, _)| m1.get_from() as u8 == f0 && m1.get_to() as u8 == t0)
+                                .any(|(_, m2)| m2.get_to() == 0)
+                        }
+                        _ => false,
+                    };
+                    show.then(|| {
+                        let seqs_exit_cls = seqs_exit.clone();
+                        let seqs_exit_click = seqs_exit.clone();
                         let (pos_style, line_x1, line_x2, head_pts): (&str, &str, &str, &str) =
                             if is_white {
                                 (
@@ -687,7 +699,8 @@ pub fn Board(
                             </div>
                         }
                         .into_any()
-                })}
+                    })
+                }}
             </div>
             <div class="zone-labels-row">
                 <div class="zone-label zone-label-quarter">{label_bl}</div>