money. 

Paul's mother was attractive, married for love, and had beautiful children, but something was missing from her life. She always felt "the centre of her heart go hard" when her children were present. This is because she wanted more money. She associated her potential happiness with money. Therefore, she describes luck (to Paul) as that which causes one to have money, that which causes one to become happier. 

Paul, going strictly by this definition, determines that luck is some mysterious psychological force that is only associated with acquiring money. From his discussions with Bassett, he determines that it would make the most sense to use luck to gamble and thereby acquire more money. The acquisition of money becomes all-encompassing. Paul just wants to quiet the whisper of the house, "There must be more money!" It is this constant emphasis on money, from his mother (but partially enabled by Uncle Oscar and Bassett) that conditions Paul to equate using luck to find money as the family's greatest necessity. It is a lost cause because Paul's mother (Hester), obsessed with money, is also irresponsible with it. She is wearing an expensive white fur coat (after receiving the money from Paul's winnings) when she goes to check on Paul near the end of the story. This is money she should have used to pay debts or for the children's schooling. 

Paul's mother says she is "very unlucky" because she "married an unlucky husband".  This indicates that she does not take responsiblity upon herself, but instead blames others for her lack of happiness.  When Paul asks her if she was lucky "by herself", she responds that she "used to think (she) was, before (she) married", but when Paul looks at her closely he perceives that "she (is) only trying to hide something from him".  Paul's mother is unlucky because her values are skewed.  She is so consumed by desire for material things that she is unable to see what is really important in life.  She has a son, at least, who loves her beyond measure, but she herself can "not feel love, no, not for anybody".

Paul's mother thinks that luck is "what causes you to have money".  She says that it is "better to be born lucky than rich", because "if you're rich, you may lose your money...but if you're lucky, you will always get more money".  It is ironic when Paul is confused about the term "filthy lucker".  He has heard his Uncle use the term "filthy lucre", and since "lucker" and "lucre" are pronounced similarly, and his mother associates "luck" so closely with money, he thinks the two terms are the same.  Although his mother points out that they are not, in reality they kind of are.  Using his mother's interpretation, both refer to money and its power to corrupt and destroy.

At the beginning of the story the narrator tells the reader, “There was a woman who was beautiful, who started with all the advantages, yet she had no luck. She married for love, and the love turned to dust. She had bonny children, yet she felt they had been thrust upon her, and she could not love.”  This woman and her husband live above their means.  There is never enough money to meet the cost of the appearances they try to portray.  Because she never has enough money she feels unlucky.  She says she is unlucky because she married a man who was unlucky.  She appears to be a selfish, arrogant woman who thinks she is “superior” to others.  She comes across as someone who does not accept responsibility for any of the failures the family suffers.  She blames everything on being unlucky.

The section where Paul talks about filthy lucre is ironic because that is exactly what ends up killing Paul.  The struggle to earn money by gambling is a risky business. Many people today still feel that money gained through endeavors such as gambling is “filthy lucre.”  Paul’s mother says,  “Filthy lucre does mean money," said the mother. "But it's lucre, not luck."  It is very ironic that this is exactly the type of money Paul is earning for his mom.

Luck is good fortune and lucre is money. As Paul explains to his mother, he had believed lucre and luck were the same: "I thought when Uncle Oscar said filthy lucker, it meant money," he says. His mother states that lucre does mean money. When Paul asks her what luck is then, she says it is what enables a person to have money. She tells him that it is better to have luck than money, because a lucky person will "always get more money."

It's not surprising that Paul conflates luck with lucre, since to his mother, the two are closely joined. Money is everything to the mother, and to her, the definition of luck is nothing more the ability to get more money. She doesn't perceive that one might be lucky in other ways. Paul internalizes her definition of luck and believes he is lucky when he can ride his rocking-horse furiously enough to discern the winner of the next race. He does not realize that the relentless pursuit of money he engages in might, in fact, be unlucky enough to kill him.

In a phrase, Paul defines "luck" as money for those he loves. Look at what drives him to seek his "luck"—it is a combination of forces. Some of it is his mother's failure to love her family freely and fully. Some of it is her need for more money. Those two forces get fused in Paul's world. It isn't his fault, though. This comes pretty directly from his mother, who says the following about luck: "It's what causes you to have money. If you're lucky you have money. That's why it's better to be born lucky than rich. If you're rich, you may lose your money. But if you're lucky, you will always get more money."