By Any Chance research: A literary angle

chance 

n.

1.

a. The unknown and unpredictable element in happenings that seems to have no assignable cause.

b. A force assumed to cause events that cannot be foreseen or controlled; luck: Chance will determine the outcome.

2. The likelihood of something happening; possibility or probability. Often used in the plural: Chances are good that you will win. Is there any chance of rain?

3. An accidental or unpredictable event.

4. A favorable set of circumstances; an opportunity: a chance to escape.

5. A risk or hazard; a gamble: took a chance that the ice would hold me.

6. Games A raffle or lottery ticket.

7. Baseball An opportunity to make a putout or an assist that counts as an error if unsuccessful.

adj.

Caused by or ascribable to chance; unexpected, random, or casual: a chance encounter; a chance result.

v. chanced, chanc·ing, chanc·es

To come about by chance; occur: It chanced that the train was late that day.

To take the risk or hazard of: not willing to chance it.

Phrasal Verb:

chance on/upon

To find or meet accidentally; happen upon: While in Paris we chanced on two old friends.

Idioms:

by chance

1. Without plan; accidentally: They met by chance on a plane.

2. Possibly; perchance: Is he, by chance, her brother?

on the off chance

In the slight hope or possibility.

Luck /–noun 

1. the force that seems to operate for good or ill in a person's life, as in shaping circumstances, events, or opportunities: With my luck I'll probably get pneumonia. 

2. good fortune; advantage or success, considered as the result of chance: He had no luck finding work. 

3. a combination of circumstances, events, etc., operating by chance to bring good or ill to a person: She's had nothing but bad luck all year. 

4. some object on which good fortune is supposed to depend: This rabbit's foot is my luck. 

—Verb phrases Informal . 

5. luck into / onto, to meet, acquire, become, etc., by good luck: She lucked into a great job. 

6. luck out, to have an instance or run of exceptionally good luck: He lucked out when he made a hole in one during the tournament. 

7. luck upon, to come across by chance: to luck upon a profitable investment. 

—Idioms 

8. down on one's luck, in unfortunate circumstances; unlucky: She hated to see her old friend so down on her luck. 

9. in luck, lucky; fortunate: We were in luck, for the bakery was still open. 

10. luck of the draw, the luck one has in or as if in drawing cards. 

11. out of luck, unlucky; unfortunate: When it comes to getting world Series tickets, we're usually out of luck. 

12. push one's luck, Informal . to try to make too much of an opportunity; go too far. Also, crowd one's luck.

“Luck is what happens when preparation meets opportunity.”

“We all dream a lot - some are lucky, some are not. But if you think it, want it, dream it, then it's real. You are what you feel.”

“Nothing happens by chance, my friend... No such thing as luck. A meaning behind every little thing, and such a meaning behind this. Part for you, part for me, may not see it all real clear right now, but we will, before long.”

“I'm a great believer in luck, and I find the harder I work, the more I have of it.”

“If one is lucky, a solitary fantasy can totally transform one million realities.”

“Your luck is how you treat people”

“Luck never gives; it only lends”

“It is by chance that we met, by choice that we became friends.”

“I will study and get ready, and perhaps my chance will come.”

“All human actions have one or more of these seven causes: chance, nature, compulsions, habit, reason, passion and desire.”

“If you are never scared, embarrassed or hurt, it means you never take chances”