Okay, Tolkien's kind of eucatastrophe was not what got the characters out of trouble in the first place. What got them out was some normally set up and more or less expected thing (or possibly some surprise, like an eagle helping). But that's not what he meant by eucatastrophe.

What he meant was, following the actual problem-solving event, some bonus good thing, some unexpected icing on the cake. It kind of depended on wording, and I don't have Tolkien's examples to hand, so here's a modern example:


Tie a yellow ribbon 'round the old oak tree
It's been three long years
Do you still want me?
If I don't see a ribbon round the old oak tree
I'll stay on the bus
Forget about us
Put the blame on me
If I don't see a yellow ribbon round the old oak tree

Now the whole damn bus is cheering
And I can't believe I see
A hundred yellow ribbons 'round the old, the old oak tree

One yellow ribbon was the expected, logical, problem-solving end. Then we get a double eucatastrope: 99 more yellow ribbons, AND the whole damn bus cheering.

In the Black Bull example, imo the surprise/bonus is in the wording: the last line almost repeats the next to last.