Download the x64 setup from ftp://ftp.opera.com/pub/opera/desktop/51.0.2830.40/win/, launch it, click "options", set "install path" to "C:\Program Files\Opera" (not "C:\Program Files (x86)\Opera"), set "install for" to "all users", check "Make Opera default browser", set the bookmarks import option to what you want and install. You can then delete "C:\Program Files (x86)\Opera".
If you don't need to save anything in your OPera profile, before you install, you can delete "C:\Users\yourusername\AppData\Roaming\Opera Software\Opera Stable" and "C:\Users\yourusername\appData\Local\Opera Software\Opera Stable".
That should fix the registry settings for Opera so that it shows up in Default Programs. If it doesn't, you might have to wait till Opera 52 comes out or go through the registry yourself and see what's wrong.
When Opera starts up, you can go to opera://components in the address field and click "update" for Widevine if you want to makre sure you have the newest so Amazon Prime works right.
@haleba said in Unable to set Opera 50 as the Default Browser (Win8.1):
Profile Guided Optimization
This is a compiler option to run and test a built Opera and then recompile it to be faster in certain areas. It is unlikely that those optimizations introduced a bug in Opera reading and writing of its (and or the installer's) registry settings. So, I wouldn't worry about that.