How can I display TOP players in my game without using my server? Are there any third-party services?
Application, for example, the number of taps per button. Whoever tapped more – he is in the TOP in the first place.
Apple has such a thing as Game Center and with it you can, as far as I know, you can display the top players in this application in the application, without using your own server.
Everything has already been invented and prepared for use – https://developers.google.com/games/services/android/leaderboards
That is, Android Play provides everything you need, your application will only need to send statistics and achievements.