Rolling a dice gives certainly more than 2 bits uncertainty, since 2 bits is one of 4 choices, while the dice is one in 6.
I don't follow. In 4 out of the 6 results, it gives 2 bits (00, 01, 10, 11) while in 2 out of the 6 results, it gives 1 bit (0, 1). Isn't this (4*2 + 2*1)/6 = 10/6 = 1.666 bits in each result on average?