I googled does the flu shot work. This is the first thing that popped up.
https://www.focusforhealth.org/may-n...SAAEgJjEvD_BwE
Seems like not much has changed in a decade.
The CDC site says "recent studies show that flu vaccination reduces the risk of flu illness by between 40% and 60% among the overall population during seasons when most circulating flu viruses are well-matched to the flu vaccine."
Which means if their guess as to which 3 strains of flu will be present is correct, the best you can hope for is 60%. Even at that, the measure is that you didn't get sick enough to go to a hospital, if I read it correctly. I couldn't find anything on the CDC site that states how often the guess at which 3 stains to vaccinate against is the correct guess, but I'm certain they do not bat at 1000 and once in a while they may strike out.