Auto-generate nicknames for invitees joining via link

Invitees no longer need to enter a nickname - they automatically
join with a random name like "Swift Tiger" or "Happy Falcon".
Game creators still enter their nickname manually.

main.go

@@ -106,16 +106,35 @@ func main() {
 			c.Sync()
 		})
 
-		// If nickname exists in session and game exists, join immediately
-		if gameExists && sessionNickname != "" && gi.GetPlayerColor(playerID) == 0 {
-			player := &game.Player{
-				ID:       playerID,
-				Nickname: sessionNickname,
+		// Auto-join logic
+		if gameExists && gi.GetPlayerColor(playerID) == 0 {
+			g := gi.GetGame()
+			// Invitee: game is waiting for second player - auto-generate nickname and join
+			if g.Status == game.StatusWaitingForPlayer {
+				name := sessionNickname
+				if name == "" {
+					name = game.GenerateNickname()
+					c.Session().Set("nickname", name)
+				}
+				player := &game.Player{
+					ID:       playerID,
+					Nickname: name,
+				}
+				gi.Join(&game.PlayerSession{
+					Player: player,
+					Sync:   c,
+				})
+			} else if sessionNickname != "" {
+				// Reconnecting player with existing nickname
+				player := &game.Player{
+					ID:       playerID,
+					Nickname: sessionNickname,
+				}
+				gi.Join(&game.PlayerSession{
+					Player: player,
+					Sync:   c,
+				})
 			}
-			gi.Join(&game.PlayerSession{
-				Player: player,
-				Sync:   c,
-			})
 		}
 
 		c.View(func() h.H {