That all sounds simple enough, but choosing a switch is not that straightforward. For starters, you need to be sure it handles HDCP encryption and the audio/video quality coming from your devices, particularly if they offer 4K resolution, high dynamic range and Dolby Atmos sound.
To make life more complicated you'll find both HDMI switches and HDMI splitters; they might look the same, but they do very different jobs. Basically a switch connects multiple devices to one screen — which is what most people need — whereas a splitter connects one device to multiple screens.
Chances are you don't have multiple screens in your lounge room, but there are times when this comes in handy. A few years ago I converted my coffee table into an arcade machine; cutting a hole into the top, dropping in a monitor under glass and connecting a Raspberry Pi mini-computer with arcade-style controllers.
I mostly play it like a sit-down cocktail-style arcade cabinet, like what you'd find in fish 'n' chip shops back in the 1980s running classics like Pac-Man and Galaga. But sometimes I want to plug the coffee table into my television to play Street Fighter and car racing games on the big screen.
Pulling apart the coffee table to get to the Raspberry Pi so I can unplug the monitor and plug in the television is a real hassle, so I decided to install a tiny HDMI splitter inside the coffee table. Finding the right switch for the job was harder than I expected.
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I didn't want to see the picture on the monitor and television at the same time, so instead of a splitter I actually needed a 2 x 1 "bi-directional" switch; giving me the choice of connecting two devices to one screen and choosing between devices or, like I needed, connecting one device to two screens and choosing between screens.
The next complication was that I wanted a powered switch which also plugs into a wall socket, rather than a passive switch which draws power directly from your devices — in my case the Raspberry Pi — via HDMI. Cheap passive switches can be flaky if your device doesn't supply enough juice.
In the end the powered switch I bought actually works fine only drawing power directly from the Raspberry Pi, but I didn't want to risk it. Now I can kick back on the couch, flick a switch and spend my evening batting baddies rather than battling cables.