There has been much debate surrounding the fight between Mace Windu and Palpatine/Sidious in Revenge of The Sith. Many, who like to think that Palpidious is all powerful and all knowing, can not accept that he could be beaten by anyone. They feel that the fight went exactly as he wanted it. Others believe that Mace clearly beats him and that he never had a chance against Mace.

I tend to think both are right. Here is my take.

"You have lost" - Mace
In terms of a straight lightsaber fight, it is clear to me after viewing the scene a couple of times that Mace beats Palpidious. The dropkick to the chest disarms Palpy and leaves him with no saber.

However, once Anakin comes into the room, Palpidous sees an opportunity to kill 2 birds with one stone. This is Palpy's best weapon, his ability to manipulate others, and he uses it well. Once Mace makes it clear that the Sith have lost, Palpidious realizes this is something he can not accept and fires lightening off at Mace. Now make no mistake, he wants to kill Mace, but he also wants to turn Anakin. Once he sees that Mace is able to hold and deflect his lightening, its time to go to plan b....Anakin.

So Palpidious begins to play the "oh, I'm so old and weak...I can't hold on..." role to tug at Anakin's emotional strings. He also makes sure that Anakin knows what is at stake. "I have the power to save the one you love ...you must choose". He knows that Anakin will not let him die because he has already associated his death with Padme's death. All he has to do is to continue to play the weak and dying old man.. and wait. Anakin will save him, and in doing so will start on his path to the dark side. Evil Genius.

Now, I don't know for sure if Palpidious' face is revealed for simply warped during this exchange, but it doesn't matter. Anakin does the only thing he can, and forcably stops Mace from killing Sidious.

"POWER, UNLIMITED POWER!
Once Mace is disarmed and in shock and pain..he is dead meat. Sidious lights him up like a Christmas tree immediatly. Kill the threat quickly. This movie showed me one thing about Sidious. He is a coward, a punk. He is only brave when he has the advantage, othewise he is a cowardly snake. This is also revealed when he tries to run from his confrontation with Yoda after Yoda knocks him across the room.

"If so powerful you are...why leave?"
So there you have it. Not all powerful, but a master manipulator. He survives the Mace duel and prevails against Yoda not because he is all powerful, but because he knows how to take advantage of situations for his benefit. That is his greatest power.