hanged, our case is miserable.

Gonzalo then says the Boatswain looks like a man born to be hanged (i.e. hanged for committing some sort of crime!). His complexion (appearance) is "perfect..." for the "gallows". Therefore, Gonzalo hopes, Fate will not let him be "drowned", but save the ship in order that the Boatswain can fulfil his destiny - and be hanged.

It's the ugliness of the Boatswain that Gonzalo hopes will save the ship. Even if the ship was really weak, and leaking like a woman on her period (an "unstanched" - freely flowing - "wench"), then Gonzalo would warrant (bet against) the man drowning:

GONZ:
I'll warrant him for drowning, though the ship
were no stronger than a nutshell and as leaky as an unstanched wench.

Hope it helps!

Gonzalo shows he is a shrewd judge of character, as he more than once expresses confidence the boatswain won't let them all drown during the violent storm that opens The Tempest. He perceives that the boatswain is a tough, defiant person who will do whatever it takes to survive. He is competent and not a person who will give into fear.

While the passengers are panicking, Gonzalo tries to point out the toughness of the sailor they are depending on, saying he is more likely the type to be hanged than to give into a storm. He also says is sure that this boatswain wouldn't let them drown even it the "ship were no stronger than a nutshell."

Gonzalo is right. The boatswain does what it takes, which includes not being afraid to rudely tell the high-ranking guests to be quiet and stay out of the way. Of course, he can't overcome Ariel's magical powers, but he fights the good fight. The scene also helps characterize Gonzalo as having more sense that his royal patrons.

In the opening scene of the play, the royal court is aboard a ship that is being viciously tossed by powerful waves in the middle of an intense tempest. As the Boatswain shouts orders to the sailors, Alonso and Gonzalo attempt to give him directives and he replies in an insolent manner. The Boatswain directs the royal court to get below deck and mentions that their titles mean nothing to the storm. Gonzalo is offended at the Boatswain's lack of respect and proceeds to say,

"Methinks he hath no drowning mark upon him. His complexion is perfect gallows. Stand fast, good Fate, to his hanging. Make the rope of his destiny our cable, for our own doth little advantage" (Shakespeare, 1.1.23-27).

Essentially, Gonzalo believes that the Boatswain is such a despicable person that he is destined to be hanged instead of drowning at sea. In Gonzalo's opinion, the Boatswain acts more like a criminal than an integral member of the ship's crew. The Boatswain continues to curse the royal court and speaks disrespectfully towards Sebastian and Antonio, which prompts Gonzalo to reiterate his prophecy that the Boatswain is destined to be hanged rather than drown at sea.

The Tempest opens aboard a ship in the midst of a terrible storm. Shakespeare must have enjoyed simulating a storm at sea on his stage. It makes a great attention-grabber. The stage directions read:

On a ship at sea. A tempestuous noise of thunder and lightning heard.

The characters would all be shouting at each other as if to make themselves heard above the thunder, wind, and crashing waves, some of which would be provided by sound effects offstage. We later learn that the storm was aroused by Prospero, who has powers of sorcery.

Gonzalo is an elderly counselor to the King of Naples, who is also aboard the ship. Gonzalo persists in annoying the Boatswain, who is trying desperately to save the ship by issuing orders to the sailors. The Boatswain has a natural contempt for landsmen, or landlubbers, anyway; but he is particularly annoyed at having to cope with them at this critical time. Gonzalo, for his part, feels free to ask anything he likes because he is of a far higher social status and actually represents Alonso, the King of Naples. It is a funny situation because the storm changes the relations between the working men and the noblemen aboard. The Boatswain and his men fear for their lives, and this puts them temporarily on an equal footing with the noblemen whose lives are in equal danger. The equality of the risk of losing their lives makes all men equal while the storm lasts. When Gonzalo tells the Boatswain to remember whom he has aboard, the Boatswain replies with the great line:

None that I more love than myself.

When Alonso, Sebastian, Antonio, Ferdinand, Gonzalo, and other passengers appear, they have evidently been cowering below decks and have all come up together to see what is happening. They may be very important men on land, but the Boatswain feels contempt and annoyance. The Boatswain speaks very rudely to all these gentlemen. He and Gonzalo take an immediate dislike to each other because Gonzalo insists that the Boatswain should treat his superiors with proper deference even in these perilous conditions.

There is a strong contrast between these two characters. The rough, plainspoken Boatswain makes Gonzalo seem more of a genteel aristocrat, while Gonzalo makes the Boatswain seem more like an uneducated workman who knows his occupation thoroughly and despises men who can do nothing but talk and display their fine clothes and fine manners. The audience will sympathize with the Boatswain and enjoy hearing him insult the passengers, and especially Gonzalo, who is the biggest nuisance of the bunch. The Boatswain exits to tend to serious matters after telling Gonzalo:

Out of our way, I say!

This is where Gonzalo declares he is sure that the ship will not sink. He says to himself:

I have great comfort from this fellow. Methinks he hathno drowning mark upon him; his complexion is perfectgallows. Stand fast, good Fate, to his hanging. Makethe rope of his destiny our cable, for our own doth littleadvantage. If he be not born to be hanged, our case ismiserable.

In other words, if the Boatswain is born to be hanged, as Gonzalo prognosticates, then the Boatswain cannot be drowned in this storm. And if the Boatswain survives in order to be hanged later on, that means that everybody else will survive with him. Later Gonzalo repeats his presentiment:

I'll warrant him for drowning, though the ship
were no stronger than a nutshell and as leaky as an
unstanched wench.

By "warrant him for drowning," Gonzalo means he will guarantee that he will not drown because he has the hanging look in his features. Some people used to believe that men could have a hanged-man's look about them while they were still alive. The French use the word pendard, which originally meant a man who had been hanged. They may call a living man a pendard because he looks as if he is bound to be hanged sooner or later. There may be no validity to this bit of physiognomy, but there certainly are more than a few men who look as if they are destined to do something that will result in their being hanged.