chinese emporer2 aha!!

Same as chinese emporer 1:

A chinese emperor had to choose a new adviser amongst 3 sages, all of them equally wise. He placed a problem to them: "To choose one of you, you'll play a simple and fair game: In this sack there are 3 white balls and 2 black balls. Each of you will be blindfolded and will pick one ball and place it on your head. After that, the blindfolds will be removed and each one in turn will try to guess the colour of the ball upon his head, by observation of the other picked balls. However, beware. You may pass your turn in guessing, but if you state a colour and fail, you're disqualified. This way I'll learn which one is the most intelligent amongst you" The sages talked briefly to each other and promptly refused: "Dear lord, it's of no use, since the game is not fair. The last one of us to guess in the first round will know the answer." and the sages promptly demonstrated this to the emperor, who was so amazed by their wits that he appointed all 3 has his advisers. Could you demonstrated it ?

Now chinese emporer 2:

But then...another sage came forward and proved to the king that if the sages really are as smart as they seem, sage 3 would never even get a guess because sage 1 or sage 2 would always be able to guess the correct answer. He explains the logic to the king. The king fires the other three sages and hires the smarter sage with three times the pay. How did he explain this?