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

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Discussion Overview

The discussion revolves around the average value of rolls from a six-sided die, exploring the concept of fairness in dice, the implications of rolling multiple times, and the definitions of average. Participants express differing views on what constitutes the average and how it relates to the fairness of the die.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that a "fair" die means each side has an equal chance of occurring, while others question the meaning of "fair chance."
  • One participant suggests that the average can be calculated using a formula, while another argues that the average cannot simply be defined as each number having an equal chance.
  • There is a mention of the law of large numbers, with some participants indicating that more rolls lead to better results, while others challenge the notion that fewer rolls cannot be random.
  • Concerns are raised about the potential for a die to be biased or have non-standard face values, which could affect the average.
  • One participant states that the arithmetic mean of a fair die is 3.5, while another mentions a geometric average of about 3.

Areas of Agreement / Disagreement

Participants express disagreement regarding the definition of average in the context of a fair die and the implications of rolling multiple times. No consensus is reached on these points.

Contextual Notes

Participants highlight the importance of knowing whether the die is biased and the specific values on its faces, indicating that assumptions about fairness and standard values may not hold.

withoutfear
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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
 
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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"?
 
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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 ?
 
withoutfear said:
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
 
The arithmetic mean of a normal fair die is 3.5. Its geometric average is about 3.
 

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