Valve said in October 2021 that it was reviewing «the entire Steam catalog» to determine each game's compatibility with the upcoming Steam Deck handheld. A game's status would be indicated on the Steam storefront via a «Deck Verified» indicator showing that a game was Verified, Playable (with some limitations), Unsupported, or Unknown, meaning it hasn't been tested.
Valve's efforts are beginning to bear fruit. Members of the SteamDeck subreddit have noticed that some games have received a Deck Verified status, and while that status is not currently displayed on Steam store listings, it can be seen on SteamDB (there's also a workaround to see them on Steam—more on that below). The list is currently quite small, covering only 67 of the 60,000+ games on Steam, and further complicating the situation is that not all the games in the list are verified. The only way to check a game's status is to look at its individual listing.
Cuphead, for instance, is verified:
Subnautica, on the other hand, is only playable:
Some limitations are relatively minor: The Witcher 3, for instance, is fully functional using the default Steam Deck controller setup and «performs well» on the unit, but is only rated as «playable» because some in-game text is small and may be hard to read on the Steam Deck screen.
There are a handful of «unsupported» games in the list, but the good news for Steam Deck stans is that all but one are VR games (Steam Deck doesn't support VR). The lone standard game on the list that's unsupported is Persona 4 Golden.
As I said, there is a way to see these listings through Steam, laid out by redditor Priception_Official. It's wonky, but I tried it and it does actually work, using the Firefox browser at least—it might work
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