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I know that the there are equal chances( i.e $\frac{1}{6}$ ) for a regular cubic dice! But one interesting puzzle raised a question/misunderstanding.Here is what happened.

I wanted a possibility between 1 and 40(using the regular dices). What I did was taking 8 of these cubic dices, and roll them, then adding what`ever the possibility was, and finally subtracting 8. But one of the users of stack exchange commented me not to do that because the distribution will skew to the center(middle numbers). Is that right ? If it is, can anyone explain ?

Amanuel Getachew
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  • $1+1+1+1+1+1+1+1-8=0$ and yes, the data will skew to the centre. Might elaborate when I have the time. – For the love of maths May 01 '19 at 16:48
  • See what your method would do if you wanted to get a number between $1$ and $10$ using two dice: roll, add, subtract $2$. Write down all $36$ cases and tabulate frequencies. You'll see the unfairness. – Ethan Bolker May 01 '19 at 16:51
  • If you want equal probability for all numbers from 1 to 40, just rolling dice will not help. For example, if you have two dice, the probability to get $2$ is $1/36$ while the probability to get $3$ is $1/18$ – Vasili May 01 '19 at 16:56
  • take a look at the related question that generated a number of excellent responses: https://math.stackexchange.com/questions/1314460/how-to-generate-a-random-number-between-1-and-10-with-a-six-sided-die – Vasili May 01 '19 at 17:12

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The problem here is that there are more ways to roll certain numbers than others, so you don't have equal chances of rolling each number between 1 and 40 in this way. For example, if you roll a dice 8 times then subtract 7, how can you get 1? There is only one way to do this: you have to roll 1 every time.

Now let's see how you would get 2: You would have to roll all 1's except for one time, when you would have to roll a 2. So, there are 8 ways to do this (get a 2 on the first roll, OR get a 2 on the second roll, etc...). That means a final value of 2 would be 8 times more likely than a final value of 1. That means this isn't a good way to "roll" a 40-sided dice because the possible values from 1-40 don't occur with equal probability.

ChocolateAndCheese
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