A decoder for decoding a video from a data stream into which syntax elements are coded using binarizations of the syntax elements, comprises an entropy decoder configured to derive a number of bins of the binarizations from the data stream using binary entropy decoding by selecting a context among different contexts and updating probability states associated with the different contexts, dependent on previously decoded portions of the data stream; a desymbolizer configured to debinarize the binarizations of the syntax elements to obtain integer values of the syntax elements; a reconstructor configured to reconstruct the video based on the integer values of the syntax elements using a quantization parameter, wherein the entropy decoder is configured to distinguish between 126 probability states and to initialize the probability states associated with the different contexts according to a linear equation of the quantization parameter, wherein the entropy decoder is configured to, for each of the different contexts, derive a slope and an offset of the linear equation from first and second four bit parts of a respective 8 bit initialization value.