What hints does Portia give to help Bassanio choose the lead casket in Merchant of Venice?Need more than 1 hint...
The hints Portia gives to help Bassanio choose the right casket all have to do with the same theme - the importance of looking beneath the surface to find what is important. At the beginning of Act III, Scene 2, Portia says to Bassanio,
"Beshrew your eyes, they have o'erlooked me" (lines 14-15).
The accepted meaning of these words indicate that Bassanio has bewitched Portia with his eyes, but a second meaning hints that in using his eyes to find Portia, Bassanio is missing her, the part of her that is important. A short time later, Portia, referring to the caskets, says to Bassanio,
"I am locked in one of them. If you do love me, you will find me out" (lines 40-41).
Portia here, in talking about love, is saying that if Bassanio looks at the caskets with the eyes of love, he will look beyond their surface appearances to find what is underneath, the essence of the entity, which is to what true love is drawn.
When Bassanio begins his rumination of the caskets, Portia sings softly in the background,
"Tell me where is fancy bred,
Or in the heart or in the head?...
It is engendered in the eyes
With gazing fed, and fancy dies" (lines 63-64, 67-68).
In these lines, Portia is saying that when the eyes are done gazing, fancy dies. What attracts the eyes is impermanent and, in the end, inconsequential; when Bassanio hears these words, he begins to think along the lines that Portia wants him to think, musing,
"So may the outward shows be least themselves;
The world is still deceived with ornament" (lines 73-74).
Guided by Portia's subtle hints, Bassanio eschews the showy, prettily decorated caskets and chooses the plain, lead one, which is the one that wins him Portia's hand.
Portia does indeed make some fairly subtle hints as to which is the correct casket to choose. But there are other factors to consider. For one thing, we must remember that Portia is incredibly loyal to her father, and assisting Bassanio would go against his express wishes. She would also be going back on her word, thereby destroying the integrity of her character, and if there's one thing we know about Portia it's that her integrity is impeccable.
We should also bear in mind that Bassanio enters the scene to make his choice after Arragon has already chosen the incorrect silver casket. And even then, when the messenger announces his arrival, he doesn't mention Bassanio by name. Crucially, it is Nerissa who first names him. This would appear to indicate that it is Nerissa, rather than Portia, who's been orchestrating events. After all, she's the only one who's had contact with all six suitors; and it is she who informs Portia that they are leaving. It is also instructive that Nerissa is the only one who seems to be expecting Bassanio's arrival.
Having said all that, giving someone a clue is hardly the same as outright cheating. So perhaps we should see Portia's various hints as precisely that and no more. Playing a song in which many words rhyme with "lead" is of sufficient subtlety to suggest that Portia has kept her promise, and by extension, her integrity. She also advises Bassanio to "pause a day or two before you hazard." This subtly relates to the message inscribed inside the correct casket, but it certainly wouldn't count as cheating or as rigging the lottery in any way.