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.

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    $\begingroup$ That would be called the "seed" of a psuedorandom number generator. There are many ways, check out that link. $\endgroup$ – Graviton Aug 2 '20 at 7:08
  • $\begingroup$ @Graviton That sounds about right, tho I added an edit to the original post now. What I seek is a way of doing this that can't be tampered, so everyone can verify the randomization through a formula, rather than one person using an online randomization tool and others trusting it. $\endgroup$ – KingOfCss Aug 2 '20 at 8:13
  • $\begingroup$ On paper it may be hard to balance "random" with "non tedious". Most random number generators use quite a few operations in order to eliminate any sort of apparent patterns. If you can use a calculator, I recommend doing something like taking the first two digits after the first two digits of $\sin(1+x)$. E.g; if $x=42$ then $\sin(1+x)\approx 0.8317$. So 17 would be the "random" number. $\endgroup$ – Graviton Aug 2 '20 at 8:20
  • $\begingroup$ Stock market data might be a good source. Not the initial digits but maybe the third digit of the Dow Jones followed by the third digit of the FTSE 100. $\endgroup$ – badjohn Aug 2 '20 at 13:29

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.

  • $\begingroup$ This really solves it. I believe 10 digit, generating a number between 0-1024 would be sufficient (ignoring the 1000-1024). This would give a percentage between 0.000% and 99.99%. Now the only trick is finding a good truly random number. Stock prices (including volumes, index prices etc.) aren't very good, because usually the first digit is fairly predictable. Basketball games are better, but still somewhat predictable. Weather temperatures too, the first digit is somewhat predictable. Preferably the number would be by a very trusted institution/market, so newspapers are out.. Hmm. $\endgroup$ – KingOfCss Aug 4 '20 at 8:39
  • $\begingroup$ @KingOfCss The best is to shrink down the source. For example, if that is the currency, do not take its full value, but the lowest calculable digits of it, only those that change even within minutes. That could be random, but does not have to be. In any case modulo/remainder is your best friend here. Why not using these kind of generators in reality? It turned out that all such sources even though apparently random, have some rules like Benford's law. So do not count on digits, rather some remainder of them. $\endgroup$ – Alex Peter Aug 4 '20 at 17:52
  • $\begingroup$ Thank you Alex! The system looks good now, but I wonder if it's unnecessarily complicated. What's the difference between: 1. Grabbing the last 2 digits of the day before's closing price of top 1 nasdaq stock 2. Grabbing the last 2 digits of the day before's closing price of top 7 nasdaq stocks, dividing it by 3 using modulo/remainder, converting if remainder is odd/even to binary number, convert the 7-digit binary number to decimal, divide the decimal by 127 to get a percentage. Is it overcoming Benford's law? Why is Benford's law in last 2 digits of Nasdaq of the top Nasdaq stock? $\endgroup$ – KingOfCss Aug 6 '20 at 9:14
  • $\begingroup$ @KingOfCss A big difference. Modulo, especially by a prime number, we can even talk about which prime number is best for each particular case is preventing hitting the inner invisible dynamics. Taking last 2 digits is modulo itself, by 100. And that is not a good choice at all. 100=2*5*2*5 and that is a lot of inner structure and a lot of possibilities to hit something that lurks in those numbers. I would go maybe for 7 or 19, but definitely not 100. $\endgroup$ – Alex Peter Aug 10 '20 at 19:49

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