Regular dice are made such that opposite sides of the die add to 1+the number of sides. For example, a 20-sided die has 14 and 7 opposite of each other, adding to 21.
For certain types of games, "life counter" die are used. In these, sides are numbered sequentially, so that 1 is next to 2, which is next to 3, which is next to 4, and so on. You can see a picture here: http://www.coolstuffinc.com/main_supplies.php?fpid=Acc-QWSd20SpindownLifeCounterBluewhite
Now the question: generally speaking, will these two kinds of die yield equal probabilities? (Assuming that both dice are well balanced).
- Will the probability of getting a certain number be the same?
- Will the probability of getting a number above a threshold be the same? (i.e. rolling a 10 or more)
If you want the high school answer, then no, the numbering does not matter. If all faces are equally-likely, the probability is the same regardless of how you number the die, and similarly all derived quantities (such as variance or probability to be greater than 8) are the same because the underlying distribution is the same.
If you want the real answer, it depends on the exact probability distribution of the faces of the die, which is best determined empirically (i.e. by rolling it many times).
If the die is weighted towards one face, so that face becomes more likely to be on bottom and the opposite face equally more likely to be on top, the the mean value of the normal die will not change, while the mean value of the life-counter die will change.Tweet