Aside from the idea of luck and coincidences not existing (Which is a debate all in itself), you are presuming one thing though: that Sidious couldn't have killed Mace Windu and still played the scenario out.
He could have said "I had to kill the jedi; they were trying to usurp power." Anakin doesn't know any better, he's still wrapped around Sidious' finger, and in any case, Anakin has already shown that he'd choose Sidious over the jedi any ways.
The main assumption for "He faked it" supporters is that Sidious needed to have everything go just like that. I disagree. From his actions against Mace Windu and his mistrust of the jedi, we already know that Anakin wouldn't have turned on Sidious if there were four dead jedi in the room. While it's very likely the case that Sidious was playing Anakin like a drum the moment he barged in, I disagree that he was able to overcome Mace Windu and save himself.
That would be possible, but it'd still leave some things unassured: This way, Sidious knew without a doubt he had Anakin who couldn't go back. If he obliterated Mace on the window, there would be lingering doubts...he had to make Anakin realize what losing him really meant. Anakin took a step you couldn't go back from, killing Mace broke him, moreso than if Palpatine just showed him the corpses. Anakin's trust in Palpatine was already very badly shaken with the whole Sith Lord thing.
What better way to break Anakin, than to have him turn on the Jedi personally right there when he realized they were about to murder a prisoner, when Anakin tells Mace 'I need him'...Palp knows how much Padme means to Anakin and what Anakin's done in anger and desperation before, unlike Mace...and it just seems too, too perfect