New answers tagged distribution
One thing you didn't specify clearly: What is the measure of success? Number of Pieces? Total importance? Something else? For so few pieces, an exhaustive search ("testing all combinations") is perfectly reasonable. Out of those 10 pieces, there's only a few hundred unique combinations to try. I'll assume "Total importance" for now... But more ...
I dislike Google's stuff on Android due to their apk Google Services which eats battery and RAM, updates itself and who knows what else... so that ticks off Google Play from my list of apk sources. I'm using Amazon App store, SlideME store, Aptoide and such, and there is actually a lot of users doing the same, so uploading on one of those could be an option ...
Yes there are other platform where you can publish your game and they have huge market there. Amazon App Store Samsung Galaxy Apps
Apart from the usual communication methods (such as email, and just downloading it from a website) there are places you can upload an APK (like an alternate store. For example, Aptoide). Naturally, these are (most likely) less well known than the Google Play Store, and probably get less traffic.
Android is an open platform, so you are free to exchange APKs by other means—for instance by email. The Android Development Center discusses this. The caveat: App installation from non-marketplace sources is disabled by default in the security settings of most Android distributions. Users must manually enable the option first.
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