A screenshot from Mystery Case Files, one of the games available through Big Fish Games' new cloud-gaming service.

Seattle game publisher Big Fish Games has rolled out a game subscription service for mobile devices -- a kind of Netflix for games, and a first for the Apple App Store.

Called Play Instantly, the cloud gaming service lets iPad users with a WiFi connection stream 20 games, including a number of hidden object adventures titles, from the Big Fish catalog. The service is free for a limited time every day, or users can pay $4.99 per month for an unlimited subscription.

As gamers play, their progress is stored in the cloud, so they can pick up from wherever they left off. Play Instantly is initially only available on the iPad, but will be adapted for other mobile devices and platforms in 2012, allowing gamers to pick up a game from where they left off on any device.

“Our cloud gaming service will transform the marketplace for premium casual games by bringing our millions of mainstream customers that much closer to the thousands of wonderful games created by our in-house Studios and game development partners,” said Big Fish CEO Jeremy Lewis in a press release.

Big Fish was the first game company to win approval from Apple to offer games through a subscription service, rather than sell them one at a time, reports Bloomberg.

It looks like the service isn't available right now, but I've reached out to Big Fish for more information. Here's what it says at the App Store:

"The exclusive first look of Play Instantly! is available to a limited number of customers. Due to a high level of interest we are currently full, but sign-up within the app and we will notify you via email as soon as we have room."

Update: A Big Fish spokesperson said the service launched last Friday for internal testing and opened yesterday to a "select group of external customers." The app will be available more widely -- though still on an invitation-only basis -- for the remainder of of 2011, then opened to all consumers in 2012.

"We worked collaboratively with Apple over several weeks to ensure the service met all their guidelines, but it was handled via their standard submission and review process," said the company via email. "Apple wanted to verify that the service we were offering was a good customer experience and that the value proposition warranted a recurring monthly charge."

The service launched with 20 games (the company originally said it had 30 games but later clarified), but Big Fish said it plans to add nearly 80 more games before the end of 2011, and several hundred more in 2012.

Big Fish said Play Instantly is an extension of its popular subscription service available on PC and Mac. The 4-year-old more service offers more than 2,500 games, which are being virtualized for Play Instantly.

Here are a few of the titles available to white-listed users: "Wild West Story: The Beginning", "Hidden Wonders of the Depth 2", "Mystery Age: The Imperial Staff", and "Hidden Mysteries: Vampire Secrets".