There was an app (Carrot Fantasy, already removed) that I can't install directly from the Play Store on Android tablets. It does run on a Samsung Galaxy Note 3 smartphone, but I have not yet had any luck with any tablet I have tried.
I managed to have the Play Store on a Google Nexus 7 shown the app, but it would not offer an Install option and just said This app is not compatible with your device. without any further information.
On other devices such as Samsung Galaxy Note 10.1 2014, the app does not even show up in Play Store.
I have searched for other similar questions, but they usually seem to be asked from the developer point of view, i.e. how to modify the app manifest or how to check one's settings in Play Store. They did not provide any insights into what to do on the user side.
Certainly, there must be a way for me as a user to diagnose why the app is deemed incompatible, what specific requirements it has, and then pick an Android device that fulfills those requirements - how?