It does have an effect. If it didn't, then no one would bother with double blind trials.
Whether consciously or not, simply knowing who is getting the real treatment or the placebo can affect how medical staff treat patients and how patients behave as well. This all has a bearing on the outcome.
You should read about placebo trials - trials testing the effect of placebos. It may seem crazy but the placebo effect can be pretty amazing... which unfortunately is a likely outcome here.
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