We have an Xbox one, and my father-in-law, who lost a hand years ago, is unable to play games using a controller. We're a gaming family, and we're constantly looking into games he can play, and the only ones on the Xbox are some of the kinect games. I say some, because the kinect now reads finger movements on games such as rock climbing in kinect sports rivals. The kinect can't read the grasping motion his prosthetic limb makes.
I agree with Elmo about the Wii, but I more strongly recommend looking into the new Apple TV. Out of the games I own, Bruce Lee, Crossy Road, Alto's Adventure, Edge EX, Mr. Jump, Rayman Adventures, Mr. Crab, Jetpack Joyride, Albert, Doodle Jump, Badlands, and Peg Ballet only require one hand, with more games surely out there.
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I just did some digging around the internet, and found this option for a modded, one-handed Xbox one controller from
Ben Heck.
If you've never heard of him, he's a legendary console modder (his mods have been featured in Popular Science, Wired, and Engadget), and the host of a popular internet show. It's pricey... twice as much as an Apple TV... but Christmas is coming...
Another website to check out is
The Controller Project, run by an editor for Make Magazine, and featured on BBC news and various other news outlets. It appears you order the parts you need and mod the controller yourself.
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Good luck to your friend. My father-in-law was an avid guitarist before the loss of his hand, and he continued to be after. He had a special prosthetic created that is able to hold a guitar pick, and he sounds just as good as any of the guys he plays with. In everything else in life, the guy's unstoppable; he splits his own wood, re-roofed his house not to long ago, and goes camping alone quite often. There's nothing your friend can't do as well as, and often times better, than someone with all their limbs.