The d4 can be used to generate 25% incremental probabilities, random numbers from 1 to 4, with + 1 it generates a linear 2-5, etc. It can be used to get 1 or 2 (1 or 2 = 1,3 or 4 = 2) or in conjunction with any other dice to get linear or bell-shaped probability curves. For example, 2d4 = 2-8, 3d4 = 3-12, d4 + d6 = 2-10, d4 + d20 (as d10) = 2-14. When rolled in conjunction with another die, the d4 can be used to determine linear number ranges twice that shown on the other die, thus: d4 reading 1 or 2 means that whatever is read on the other die is the number shown; but if the d4 reads 3 or 4, add the highest number on the second die to the number shown - so if d8 is the second die 1 to 16 can be generated, if a d12 is used 1 to 24 can be generated. If a d20 is used either 1-20 (assuming the use of a standard d20 which is numbered 0-9 twice without coloring one set of faces to indicate that those faces have 10 added to the number appearing) or 1-40 (assuming that one set of faces is colored) can be gotten by adding 0 if 1 or 2 is rolled on the d4 and 10 or 20 (depending on die type) if a 3 or 4 is rolled.