This should be so easy, local and optional internet saves for single player, account based internet saves for online multiplayer, PC has offered easily transferable local saves for decades, Android offers seamless and easily transferable Google Play account saves, I can even play the same game with the same account on many devices, one at a time, but choosing the most suitable each time, smartphone on the go, tablet at home, and if I want I can use a PC Android environment too. Yep, some games don't use it, I stopped playing Goddess: Primal Chaos because last time I played it, it used different and not coordinated servers, I ignored the potential problem and I didn't take note of which server my saves were on, so after for some reasons it didn't load my save automatically, I wasn't able to recover it and my game account and character, losing every game progress. Not a big loss, it's a game that ends up becoming boring, as it tries to hide a dull combat system under a bloated stats, magic, items, mount, familiar and countless other stuff system. But the system is there, and most multiplayer Android games use it almost without any problem (you only need to check you are connected to your Google account to avoid losing game progresses, sometimes you must connect manually, and after having connected a device to one or more accounts the first time, the following times just one or two clicks and it's done).
Stwike him, Centuwion. Stwike him vewy wuffly! (Pontius Pilate, "Life of Brian")
A fart without stink is like a sky without stars.
TGS, Third Grade Shooter: brand new genre invented by Kevin Butler exclusively for Natal WiiToo Kinect. PEW! PEW-PEW-PEW!