An ounce of cure is equivalent to two glasses of liquor. Or at least, this is what the author, Alice Munro, is trying to tell us. She drops many hints during the course of the story that suggest that alcohol solves all your problems.
Liquor is tempting when one needs to forget about his or her "humiliatingly personal thoughts". The narrator "gave up [her] soul for dead and walked into the kitchen and decided to get drunk", in hopes of filtering out the embarrassing thoughts that her music had conjured. The "three tall beautiful bottles, all about half full of gold" on the counter were just too tempting. But it worked. She could not think properly after drinking two full glasses, and therefore could not have had those thoughts anymore. This is one of the more common problems in life, which can apparently be solved by drinking.
Another hint was left when the narrator called her friend, Joyce. Joyce was busy, and was "going to play cards"; she refused to come for a friendly visit, but soon changed her mind when she had heard that Alice was drunk. She brought over her new friend, Kay Stringer, who the narrator did not know very well. They became better acquainted after this incident, and Kay found joy in helping Alice with her problem. The author is obviously attempting to point out the fact that becoming drunk will gain you friends. .
Drinking also summons a sort of unwanted "courage". The narrator spoke uncontrollably to her mother about everything that had happened, including the incident involving the aspirin and about Martin Collingwood. If she were not drunk, she may have wanted to talk about these things, but was too afraid of her mother's reaction to such a situation. She was then disallowed to go out with another boy until after her sixteenth birthday, which was not a "concrete hardship at all." The whole town soon knew about her suicide attempt over Martin. But since she was grounded, her love for Martin slowly faded; it was "a positive, a splendidly unexpected, result" of drinking that night.