What is the ruling on health insurance for doctors' errors, whereby an amount is paid equally by the doctor and the hospital to compensate the injured patient?

This type of insurance is unlawful (haram (definition)) because it involves harm and uncertainty. The insured person may pay a large sum of money and commit no error, in which case what they paid is lost without a return. Alternatively, they may pay a small amount and commit errors that necessitate many times what they paid. This constitutes forbidden gambling (maysir (definition)). It is not permissible to engage in it except in cases of necessity, and it is disliked to engage in it. If one is given something, they should not take more than what they paid.