For the record:
Darth Sidious did lose the lightsaber duel against Mace. It was a legitimate duel, and one that he simply did not win. Other than Yoda, Windu is perhaps the greatest Jedi duelist in the movies, and he is leagues above the vast majority of the Jedi. Whereas Windu had 13+ years of actively training with a lightsaber, Sidious was a politician who did not so much as touch his saber for the better part of those 13 years. Thus it is highly obvious Windu had the advantage; but the very fact that Sidious was able to put Windu to the test counts for something. I would have hated to see what the Dark Lord could have done had he trained with his saber as long as Yoda and Mace did.
Sidious faked being weak and helpless. Mace had him at his mercy, and if not for the intervention of Anakin, Windu would have most likely killed the Dark Lord. But, I will say that Sidious took advantage of the scenario when Anakin walked in. In that moment, he then decided to have Anakin kill Mace, and thereby push Anakin to the brink of the Dark Side. At that moment, he manipulated the outcome of the duel.
As for Yoda v. Sidious . . . Most people assume Yoda would've flat out owned Sidious, and I disagree. In my opinion, the Dark Lord and the Grandmaster of the Jedi are both counterpoised and very nearly evenly matched, with Yoda having the only noticeable advantage due to his overwhelming experience as a practitioner of the Force, where Sidious only has a fraction of that time under his own belt. Yes. Sidious did fight against Yoda far more viciously than he did against Mace. But I think that he was not as overconfident as he was with Mace either. All of the Jedi are in awe of Yoda, so it would seem that Palpatine understood that Yoda presented an immense threat to the Empire. Thus, he was not as arrogant as he was with Mace.
This is my own opinion, though.