To show a muted YouTube movie with looping and autoplay, use an url like https://www.youtube.com/embed/pvTCuenxTsc?autoplay=1&loop=1&playlist=pvTCuenxTsc&mute=1. Note the use of
playlist, set to the id of the video.
If you don’t mute the video, autoplay will not work, so if you want to annoy your visitors you have to think of something else.
More info on YouTube parameters.
I decided to use HTML5 <video> though, which loops fluently.