Which casket did the Prince of Morocco choose and why?

Prince Morocco chooses the gold casket, and Act II, Scene VII is dedicated mostly to walking us through his reasons behind the choice.

The prince is trying to win Portia's hand in marriage. In order to do so, he must pass the test Portia's father has created for any of her potential suitors. As a suitor, he must choose from three caskets (decorative boxes) to try to find the one that holds a picture of Portia, which will be an indication that he has permission to marry her. Each box is made of different material; gold, silver, and lead. Each box also has an incription on it. For gold, the inscription reads, "Who chooseth me, shall gain what many men desire." On the silver casket, it says, "Who chooseth me, shall get as much as he deserves." The message on the final casket says, "Who chooseth me, must give and hazard all he hath."

Prince Morocco first decides to examine the lead casket closely. Upon reading the incription, he decides that the message is a warning to men who will risk a lot for worthless things, and he believes "A golden mind stoops not to shows of dross (line 20)." In other words, he doesn't choose the lead box because a man of worth won't bother gambling for something of such little value as lead.

Moving on to silver, he interprets the inscription to be a question of his own opinion of himself. He says he doesn't want to assume that everything he deserves includes Portia, However, he eventually concludes that if he says he doesn't deserve her he is only professing a low opinion of himself. He almost seems like he is going to choose the silver casket based on his feelings that he does, in fact, deserve Portia. "What if I strayed no further, but chose here (line 35)?" However, he decides to look over the gold casket before he makes his final decision.

It is here that Prince Morocco is most convinced by what he reads on the box. "Who chooseth me, shall gain what many men desire." This immediately makes up his mind about which casket to choose, because in his mind every man in the world desires Portia.

All the world desires her;/ From the four corners of the earth they come/ To kiss this shrine, this mortal breathing saint/...Is't like that lead contains her?/'Twere damnation/ To think so base a thought.../ Or shall I think in silver she's immur'd,/ Being ten times undervalued to tried gold?/ O sinful thought!Never so rich a gem/ Was set in worse than gold.

In the end, he chooses the gold casket because Portia is a highly desirable woman, so surely her picture would only ever be contained in a casket made of the most expensive, valuable material.