How is the lottery of caskets in The Merchant of Venice a test for the suitors who have come to woo Portia?
Portia's father has, in his will, set the requirements for the suitors who wish to marry her: they must choose between three caskets of lead, silver, and gold. Whoever chooses correctly will win the right to marry Portia. The whole exercise is, in simple terms, a lottery, as Nerissa states in Act 1, scene 2:
...therefore the lottery,
that he hath devised in these three chests of gold,
silver and lead, whereof who chooses his meaning
chooses you, will, no doubt, never be chosen by any
rightly but one who shall rightly love.
Nerissa here also states the belief that destiny is to determine that the person who chooses correctly will not only have made the right decision but will also be the one who truly loves Portia.
Added to this, the will requires that suitors undertake a solemn vow that, if they fail to choose the correct casket, they will never approach another woman for marriage and, therefore, spend the rest of their days as bachelors. Before they are given the opportunity to choose, the suitors have to visit the chapel and undertake the vow in the presence of Portia and other witnesses, as Portia informs the Moroccan prince in Act 2, scene 1:
You must take your chance,
And either not attempt to choose at all
Or swear before you choose, if you choose wrong
Never to speak to lady afterward
In way of marriage: therefore be advised.
Breaking the vow will, of course, mean eternal damnation for the transgressor. If one takes into regard the deep religious convictions held by the general populace at the time, uttering the pledge is a critical step and not one to be easily dismissed.
This, in itself, is probably the greatest test for all the suitors. If they are successful, they will benefit grandly, for not only will they win the hand of a beautiful and intelligent woman, but they will also own half of the enormous wealth her father has left her. If they fail, though, they are bound to the vow. There is thus an enormous risk involved in the decision to choose.
To complicate matters even further, the will forbids Portia to provide any form of assistance to the suitors. She undertook a vow to this effect and should she transgress, she will be disowned. She has no choice in the matter and will have to accept the outcome, whether she likes it or not, as she states in Act 1, scene 2:
...O me, the word 'choose!' I may
neither choose whom I would nor refuse whom I
dislike; so is the will of a living daughter curbed
by the will of a dead father...
Portia is obviously enormously relieved when Bassanio, the one she loves, eventually makes the right choice, for she had no desire to marry any of the other suitors.