Background Mixtures (‘cocktails’) of various analgesics are more effective in controlling post-operative pain because of potential synergetic effects. Few studies have investigated such effects in large combinations of analgesics and no studies have determined the probabilities of effectiveness. Methods We used one-hot encoding of the categorical variables reported pain levels and the administered cocktails (from a total of eight analgesics) and then applied an unsupervised neural network and then the unsupervised DBSCAN algorithm to detect clusters of cocktails. We used Bayesian statistics to classify the effectiveness of these cocktails. Results Of the 61 different cocktails administered to 750 patients, we found that four combinations of three to four analgesics were by far the most effective. All these cocktails contained Metamizole and Paracetamol; three contained Hydromorphone and two contained Diclofenac and one Diclofenac-Orphenadrine. The ML probability that these cocktails decreased pain levels ranged from 0.965 to 0.981. Choice of a most effective cocktail involves choosing the optimum in a 4-dimensional parameter space: maximum probability of efficacy, confidence interval about maximum probability, fraction of patients with increase in pain levels, relative number of patients with successful pain level decrease. Conclusions We observed that administering one analgesic or at most two is not effective. We found no statistical indicators that interactions between analgesics in the most effective cocktails decreased their effectiveness. Pairs of most effective cocktails differed by the addition of only one analgesic (Diclofenac-Orphenadrine for one pair and Hydromorphone for the other). We conclude that the listed cocktails are to be recommended.