1. A playback device for playing back a subtitle stream in synchronization with a video stream, the playback device comprising: a video decoder operable to decode the video stream; a subtitle decoder operable to decode the subtitle stream to obtain a bitmap of a subtitle; and a color conversion unit operable to convert bit values of the bitmap into display colors based on a color lookup table, the display colors including a character color, a background color, and one or more gradation colors for gradation between the character color and the background color, and the color lookup table including pieces of color information corresponding one-to-one to indexes of the bit values of the bitmap, wherein, prior to the conversion of the bit values of the bitmap into the display colors, the subtitle decoder: detects a period on a time axis of the video stream, in which a pair of (i) an index corresponding to a piece of color information of the character color and (ii) an index corresponding to a piece of color information of the background color is continuously used; and updates the color lookup table by assigning a piece of color information of each of the one or more gradation colors to one of the indexes other than the indexes used in the period, and wherein a number N of gradation colors used for the gradation in the period is calculated according to the following formula: the number N of gradation colors=(2 n −M)/a number of pairs of character colors and background colors, where M represents a number of used indexes in the period and n represents a bit width of each index.