You will need to install a user script manager extension to install this script.
This script adds a "Feelin' Lucky" button to Youtube. This button functions the same way as the "I'm Feeling Lucky" button found on Google.
Navigate to Youtube and enter some search criteria in the search bar. You can click the "Feelin' Lucky" button to open the first result in the current window, or middle click the button to open it in a new tab.