Randomize MySQL results the right way?

I wanted to get some randomized results but read many warnings about the dangerous inefficiency of using MySQL’s “ORDER BY RAND()” functionality. After searching around, I came across this solution which seems very good! Copied without permission for posterity.

Often around the internet I find people asking how to get random rows out of MySQL. Typically I see helpful people giving this:
SELECT * FROM table ORDER BY RAND();

However what a lot of people don’t realise, while ok for systems will small tables and limited accessed, this as a huge performance hit when used like this.
The correct way to order your results by a random number is:
SELECT *, RAND() as rand FROM table ORDER BY rand;

Why? Well the answer is actually very simple, ORDER BY RAND() causes the order to be recalculated every time MySQL fetches a new row as for each row RAND() returns a different value. When used in the select the value is only calculated once per row and the results are only ordered once.