Assuming that efficacy is randomly distributed, you're left with some very frustrating math. You'd need to try five drugs to have a better than 50/50 chance of getting a positive outcome. After seven drugs, there's still a 34% chance that none of them have worked. After fifteen drugs, there's still about a 10% chance that nothing has worked. I expect that most patients will give up on drug treatment well before that point.

I don't want to be overly negative about antidepressant drugs - they're a useful treatment for many patients - but I do feel that the popular perception of their efficacy is far greater than the reality. Many people seem to feel extremely disheartened when antidepressant drugs don't work for them, often believing that there must be something uniquely wrong with them. The language of psychiatry doesn't help, describing these people as "treatment-resistant" rather than "people we don't know how to treat".

If you try antidepressant drugs and they don't seem to do anything, don't keep taking them just because you think you're supposed to. Speak to your doctor about alternative drug and non-drug treatments. If you have access, try a range of psychotherapies. If your symptoms are relatively mild, look at lifestyle interventions. If your symptoms are particularly severe and/or chronic, give some serious thought to rTMS or ECT.