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Generate random numbers by hand?

  1. Apr 28, 2012 #1
    Hello, my calculator (sharp el-w516) can generate random fractions like 237/431. I was curious if there was a way to do this by hand.

    I would like to be able to roll any sided die by multiplying the random fraction by the side number. For example if I wanted to roll a d20 I could take the fraction and multiply by 20 and round to nearest to simulate a dice roll.

    I vaguely understand how random numbers are generated using properties of electronics so maybe its impossible to do solely by hand. I was just wondering if there was a way to do it without even tables or anything.
  2. jcsd
  3. Apr 28, 2012 #2
    If you want to generate random numbers you of course first need to think about what distribution you want.

    If for instance, which is maybe what you mean, you want to draw random numbers uniformly from an interval (a,b), then there are several algorithms that can do so. For instance linear congruential generators, which have the form:

    [itex] u_n=\frac{s_n}{M}, s_{n+1}=(As_n+C)mod M[/itex]

    The difficulty is choosing A,C, M such that the period is large, but M=2^31-1, A=7^5, C=0 is a good choice, for instance.

    On a more philosophical level, you can ask: what is randomness? Since there is a mechanism, true random cannot be achieved. You can test for uniformity properties that you would desire from random numbers.
  4. Apr 28, 2012 #3
    Hi, thanks for the quick response. I've never had a discrete math course so the formula is a bit foreign to me. Are you saying that u sub n is a coordinate pair or is that 2 separate formulas? Can you show me an example using that formula if my interval is (1, 20)? Thank you.
  5. Apr 29, 2012 #4


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    Use Icosahedron dice (20) faces number the sides 0-9 use the numbers as digits, use multiple dice or multiple throws.
  6. Apr 29, 2012 #5
    Sorry, I guess that formula was pretty trivial. I understand now, like if I chose all 7s it would be:

    s1 = (7*7+7) mod 7 = 0

    u1= 0/7 = 0

    So this would be like a 1 on a d20 roll.

    Now I would just need a way to enter the sequence (with larger multipliers, etc) at a random point, so that I'm not always going through the same numbers.
  7. Apr 29, 2012 #6
    You should realize that these are pseudo-random numbers, meaning that although they satisfy all known statistical tests for randomness, they're actually not random. They're generated by an algorithm. If you ran the algorithm a hundred times you'd get the same sequence of "random" numbers every time.

    If you want psuedo-random numbers those are easy. But generating a truly random number is very difficult. You'd have to start with some completely nondeterministic physical process, like the decay of an atomic nucleus or some such.
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