Another non-cited story I've heard is an A/B test, or similar, was once done where they removed the "I'm Feeling Lucky" button from the front page, and an overwhelming number of users said they did not like the solitary search button. Having both gave the users a sense of choice, even though (as the story goes), "I'm feeling lucky" is used by only a small fraction of a percent of users.
And humorously enough, the present "I'm feeling lucky" button literally cannot be pressed ... except on the initial, empty search box ... under which circumstances it leads you to ... a list old Google Doodles... Feelin' Lucky now? Guy...
this is so because we instinctively feel unbalanced when we see a single legged object rather than a two legged one. we'd feel similarly unbalanced if the two legs (the buttons) were of very different widths.