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Polish health care system, my experience. [32]
no, there are 3 separate contribution to ZUS, one covers old pension, the other health, and the third one I forget. Ask your accountant if you can contribute to the "health" one, so this way you will have a coverage to free health. He/she should know if you do and if there is a minimum numbers of months one has to pay for in order to qualify. If you have a registered "dzialalnosc gospodarcza" I think you actually obliged to pay the minimum ZUS, but I am not sure how this work if one is a foreigner.
I just checked the minimum health contribution to ZUS and it is 224.24 PLN per month.
Compare it to private/UK health insurance and see what the coverage is and how much you would have to pay for those two against ZUS monthly contribution. Voila!!!!!!!
As for you being responsible, well, maybe you were provoking them, but they could have broken your bones, so even if you are from Glasgow, there is no excuse to accept violence for refusing to give away a fag;)