completely remove the skipping first player logic

crates/g3-core/src/lib.rs

@@ -1297,11 +1297,6 @@ impl<W: UiWriter> Agent<W> {
         self.providers.get(None)
     }
 
-    /// Get a reference to the UI writer
-    pub fn ui_writer(&self) -> &W {
-        &self.ui_writer
-    }
-
     /// Get the current session ID for this agent
     pub fn get_session_id(&self) -> Option<&str> {
         self.session_id.as_deref()