Through their first 57 games, the Royals did not play the White Sox once, which rather unfortunately means that over the season's final 104 games, these two teams will battle 18 times, roughly 17% of the remaining schedule. Going a bit further, after this week's three game set, the Royals won't face the White Sox again until July 8th, meaning those final fifteen battles will give Chicago's stretch run a distinct KC tint.
Your pitching matchup is Greinke (2.88 ERA) versus Floyd (3.22 ERA). I've spent all season getting Floyd and Danks mixed up -- I know one has been pretty lucky, and one has had some no-hit bids and that these may or may not be the same person -- and I see no reason to rectify the problem now. Mainly, I'll be interested to see if Ozzie fields some bizarre, speed-tastic lineup. (FWIW, I agree with South Side Sox's The Cheat on the latest Ozzie "controversy" and happen to think Ozzero is a very good in game manager.)