That used to be the method or an equivalent, "random" pairings.Geoff Chandler wrote: In such cases where both
players were due a white would it not suffice to do the pawns behind the back routine.
"Random" pairings are now unpopular, because of the fear that it enables arbiters to be partial towards some players more than others. So pairing systems are supposed to be deterministic. Given the same sets of data and the same set of rules, all arbiters or their programs would be expected to come up with the same set of pairings.
As regards the Board 1 colour in the first round, tournaments have different rules. The British Championship has the rule that the top seed is White in odd numbered years. That's a tournament where in the past and present, the top seed was likely to be the same player for several years running. e2e4 link it to the result of a recent sporting event. Others don't disclose.