Simple question : what is the average of a six sided dice rolls ?

[withoutfear]

The dice is 'fair' - does that mean it is a fair chance to roll any number ?

I say the answer is just the average forumula.

My friend says the answer is 'each has a fair chance of occurring' or something like that < ---
but that's not the average roll

I also know that the more times you roll the dice the better the results become

So without knowing how many times we're rolling the dice how can we say the chances are equal b.c it won't be perfectly random if we only roll the dice twice

 

[HallsofIvy]

A die is "fair" means that each side has an equal chance of occurring. I don't know what a "fair chance" means.

I also know that the more times you roll the dice the better the results become.

Tnen you know something that is not true. I suspect you are remembering a garbled version of the "law of large numbers".

Why would it not "be perfectly random if we only roll the dice twice"?

 

[withoutfear]

I remember making a program once that made a random number generator (1-10). You had to do many iterations before the random number generator was truly random. ( I can't remember the specifics of the program).

so i guess I am trying to say a shorter time means there is more variability in the results

but how can the average be : 'they all have the same chance' the average would have to be a formula ?

 

[Elucidus]

The dice is 'fair' - does that mean it is a fair chance to roll any number ?

I say the answer is just the average forumula.

My friend says the answer is 'each has a fair chance of occurring' or something like that < ---
but that's not the average roll

I also know that the more times you roll the dice the better the results become

So without knowing how many times we're rolling the dice how can we say the chances are equal b.c it won't be perfectly random if we only roll the dice twice

Minor point: One needs to know if the die is biased and also what the values are on its faces (just because a die has six faces does not mean they are marked 1, 2, 3, 4, 5, 6 - in fact I have one that's marked 0, 2, 3, -4, 5, -6.)

If the die is unbiased (aka "fair") then you are correct that the expected value is the arithmetic average of the die face values.

--Elucidus

 

[CRGreathouse]

The arithmetic mean of a normal fair die is 3.5. Its geometric average is about 3.