Android - New phone: How to transfer game progress?

If you are on Android 4.0 or up, you can use the adb backup resp. adb restore command even without rooting your device. The syntax is:

adb backup [-f <file>] [-apk|-noapk] [-shared|-noshared] [-all] [-system|nosystem] [<packages...>]

To do a full backup, this would e.g. mean adb backup –apk –shared –all –f /backup/mybackup.ab (resp. adb restore /backup/mybackup.ab to restore the backup on the new device). But keep in mind this would mean "all-or-nothing" -- you cannot restore single apps this way. So you rather might want to include the package names of the apps to transfer. To find those, e.g. look up the apps on Google Play -- you'll find the package names in the URL (id=<package_name>). Your backup command then would look like:

adb backup –apk –shared –f /backup/mybackup.ab com.foobar.app1 org.foobar.app2 net.foobar.app3

Restore stays the same, as adb restore always restores everything from the backup file (no selection of parts available here).

For a list of available ADB commands, see e.g. here.

There are two places you should look for, the external memory (SD card or a directory that is used for similar purpose) and the internal memory (the /data/data directory). You may need to be rooted to access the latter.

In the best case scenario, the game saves all your progresses in the cloud, then you just need to reenter your login and it's all restored. This is typically only the case for online games.

Some games may provide a menu to export the save data or an external app to do so, if they exist then you should preferably use them.

You might also look into an app like Titanium Backup or MyBackup Pro and choose to save user apps + data and then restore to your new phone.