How can a random number 0-100 be generated from an initial number? A group of people want to do a random drawing with no person involved, just grabbing an initial number from public events (ex. score of a team in a NBA game) and then make it as equally likely that it become any number between 0-100. How can this be achieved?
Edit: each person should be able to verify the formula, so it wouldn't require one person drawing ex. a randomization tool, which can be tampered. Ex. if a team in NBA score 86 and it was sequence 23 (the 23th time the randomization is done), the randomization formula generate 45%. The formula can be verified via an online tool and each time it's done it will get the same result.
 A: Any such formula would depend on the distribution of the data from the event source you want to use. There is no formula that gives random number from another potentially random number. What we do have is a formula that gives a series of random numbers starting from one fixed or potentially random number. Then each next is calculated based on the previously encountered values, one or more. The randomness is hidden in hiding the seed and somewhat in the formula you use.
What you can do, however, is take some public data and take a small portion of it. Instead of looking at the final score of the game you take its parity, or remainder when divided by 3 or 4 or 5, some small number anyway. However, depending on the sport game this might not be, statistically speaking, random or nicely distributed. Suppose you take chess, white or black winning - no. Tennis, number of sets or games - no. Basket, final score - it would have to carefully analyzed. A letter from a word, like third letter - no, the number of babies born in a specific year, in a specific country, taken at random - possibly if you take its parity. Temperature in a particular city on a particular date - it would need to be analyzed which part of it is random.
Ah, you are asking now, but wait if I have a random source where my formula fits in. Well, if you have a relatively good random source, say it is a series of 0's and 1's (odd and even, as we mentioned above, that is parity) then there are methods that can combine them without losing the average best randomness that your sources have.
So in order to have a number from 0 to 100 you would need at least 7 parity sources. You do pick whatever your choice is at random, like city and date, 7 times, calculate if it is odd or even 7 times and concatenate the result, say you have got 0110101. You interpret this as a binary number $0110101_2=53$. If you want the best precision, you discard all those greater than $100$, an treat the rest as your random source of information.
Notice that the only purpose of the formula is to combine a random source of information that has a greater quality but a lower range.
A general problem here is skew, no matter what public source of information you have, it is not reliable source of random information even if you have analyzed it thoroughly. Either computer or human can err or maybe reduce the values to something that is different from real values for whatever reason.
For example, even if you have, and we have it, a perfect quantum randomness, you have Web sites with these, nobody can prevent this perfect random source becoming useless suddenly, because statistically it can start spewing billion years of 0's, and still to be perfectly random.
For daily usage just take a couple of dices, and use your desired method of extracting randomness from it, start repeating it, analyze if there is any bias, and when you are happy use it as a sufficiently good source of randomness.
