Generate random numbers by hand?

In summary, the conversation discusses the possibility of generating random numbers by hand using a formula and various algorithms. The concept of randomness is also explored, and it is noted that truly random numbers are difficult to achieve without a completely nondeterministic physical process. The formula mentioned is used to explain how to generate random numbers, but it is noted that they are actually pseudo-random numbers.
  • #1
mishima
556
34
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.
 
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  • #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.
 
  • #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.
 
  • #4
Use Icosahedron dice (20) faces number the sides 0-9 use the numbers as digits, use multiple dice or multiple throws.
 
  • #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.
 
  • #6
mishima said:
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.

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.
 

1. How do I generate random numbers by hand?

To generate random numbers by hand, you can use a variety of methods such as coin tossing, dice rolling, or shuffling a deck of cards. These methods rely on physical actions to produce random outcomes.

2. Why would I need to generate random numbers by hand?

Generating random numbers by hand can be useful in situations where a computer or other electronic device is not available. It can also be used as a teaching tool to demonstrate the concept of randomness and probability.

3. What is the difference between truly random and pseudo-random numbers?

Truly random numbers are generated using a physical process that is unpredictable, such as radioactive decay. Pseudo-random numbers are generated using algorithms that simulate randomness, but they are not truly random as they follow a predictable pattern.

4. Can I generate large sets of random numbers by hand?

Yes, you can generate large sets of random numbers by hand, but it can be time-consuming and prone to human error. It is more efficient to use a computer or other electronic device for generating large amounts of random numbers.

5. How can I ensure that the random numbers I generate by hand are truly random?

To ensure that the random numbers you generate by hand are truly random, you can use standardized methods such as shuffling a deck of cards multiple times or using a random number table. It is also important to follow strict guidelines and avoid any patterns or biases in your method of generation.

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