Scratch Random Number Generator Formula

Mr-Games

Hello!

Recently I was curious on what formula Scratch uses for generating random numbers, so I asked @Za-Chary*, and he said to check the forums. After some unsuccessful searching I couldn't find any answers. If you know, or have suggestions on who might know, or where I could look that would be awesome.

Happy Scratching!
@Mr-Games

Last edited by Mr-Games (July 9, 2020 00:02:37)

Basic88

I'm sure the computer just thinks “Random Number between (foo) and (foo)? I'll just pick the first apparent number that comes to mind”. It's just the way the Computer works.

Mr-Games

Basic88 wrote:
I'm sure the computer just thinks “Random Number between (foo) and (foo)? I'll just pick the first apparent number that comes to mind”. It's just the way the Computer works.

Yeah, but isn't there a formula for how it generates the number?

Basic88

Mr-Games wrote:
Yeah, but isn't there a formula for how it generates the number?

Yes, but that's a lot of complicated math.
Fun Fact:

The Scratch Wiki wrote:
The numbers given with this block are not truly random — they are merely unpredictable. It is nearly impossible to generate truly random numbers using a computer.

Abigblueworld

Mr-Games wrote:
Hello!

Recently I was curious on what formula Scratch uses for generating random numbers, so I asked @Za-Chary*, and he said to check the forums. After some unsuccessful searching I couldn't find any answers. If you know, or have suggestions on who might know, or where I could look that would be awesome.

Happy Scratching!
@Mr-Games

Number layout:
1-2-3-4-5-6-7-8-9-10,
Side number layout
11-12-13-14-15-16-17-18-19-20
For the random number to happen, the computer has to do short math, the numbers here 10, 20 are not seen
For 20 in random, 11 + 9.
This won’t do it.
4+17=uh oh, it’s 21.
So the math here will use 1-28 because, 9 + 19 = 28
So that’s 1-28, the computer has to do the math…
For 1-3
1 2
1 2
It has to do 1-2 or 1+2. Or 3-2.
Sorry if this ain’t true.

Mr-Games

Basic88 wrote:
Mr-Games wrote:
Yeah, but isn't there a formula for how it generates the number?
Yes, but that's a lot of complicated math.
Fun Fact:
The Scratch Wiki wrote:
The numbers given with this block are not truly random — they are merely unpredictable. It is nearly impossible to generate truly random numbers using a computer.

Thanks!

ioton

Math.round(Math.random() * (max - min) + min)

Also, as a function:

function randomNum(min = 0, max = 0) {
    return Math.round(Math.random() * (max - min) + min)
}
// the line of code below will result in a random number between 2 and 4 being generated and logged to the console if the function is defined.
console.log(randomNum(2, 4))

hedgehog_blue

The math to actually get the random part is complex, but the main details you need to know is that the probability of each output is equal (although when using decimal values the probability of each result is 0, so in that case it would be better described as the probability of any 2 ranges of equal size within the random range having equal probabilities).

If the inputs are both integers, it returns an integer between or equal to the inputs. If any of them are decimal, it returns a random decimal amount between the inputs or equal to the lower bound of the range (the upper bound will never be the result, although that doesn't matter too much because the decimal amounts are theoretically infinitely precise, meaning the result can be infinitesimally close to the upper bound).

ioton wrote:

Math.round(Math.random() * (max - min) + min)

Also, as a function:

function randomNum(min = 0, max = 0) {
    return Math.round(Math.random() * (max - min) + min)
}
// the line of code below will result in a random number between 2 and 4 being generated and logged to the console if the function is defined.
console.log(randomNum(2, 4))

The general concept is correct, but the details don't quite match up with the way scratch chooses random numbers. Because you are rounding the result to the nearest integer, you end up with a 25% chance of 2, a 50% chance of 3, and a 25% chance of 4. However, scratch has an equal probability of each result, so it would be good to round down, and to add 1 to the max because the range is inclusive of the maximum.
This is how it would look:

function randomNum(min, max) {
    return Math.floor(Math.random() * (max - min + 1) + min);
}

Here's some other details that aren't really necessary to include but it is more accurate to how scratch works.
Scratch also does not round if any of the inputs are not integers, so you would want to add this case:

function randomNum(min, max) {
    if(Math.round(min) === min && Math.round(max) === max) {
        return Math.floor(Math.random() * (max - min + 1) + min);
    } else {
        return Math.random() * (max - min) + min;
    }
}

It also has support for putting the range in descending order like this:

(pick random (10) to (1))

So add that in as well:

function randomNum(min, max) {
    let realMin = Math.min(min, max);
    let realMax = Math.max(min, max);
    if(Math.round(min) === min && Math.round(max) === max) {
        return Math.floor(Math.random() * (realMax - realMin + 1) + realMin);
    } else {
        return Math.random() * (realMax - realMin) + realMin;
    }
}

Of course, your version still works to get random numbers, this just gets all of the details of exactly how scratch gets the value.

Edit: This basically matches up with the official code for the pick random block

Last edited by hedgehog_blue (July 9, 2020 18:51:04)

Mr-Games

I have my own forum!

SlenTheOoof

Mr-Games wrote:
Hello!

Recently I was curious on what formula Scratch uses for generating random numbers, so I asked @Za-Chary*, and he said to check the forums. After some unsuccessful searching I couldn't find any answers. If you know, or have suggestions on who might know, or where I could look that would be awesome.

Happy Scratching!
@Mr-Games

The way it works is it makes ‘psuedorandom’ numbers that are generated using large numbers, and you can find projects on scratch that make use of them

Mr-Games

SlenTheOoof wrote:
Mr-Games wrote:
Hello!

Recently I was curious on what formula Scratch uses for generating random numbers, so I asked @Za-Chary*, and he said to check the forums. After some unsuccessful searching I couldn't find any answers. If you know, or have suggestions on who might know, or where I could look that would be awesome.

Happy Scratching!
@Mr-Games

The way it works is it makes ‘psuedorandom’ numbers that are generated using large numbers, and you can find projects on scratch that make use of them

Thanks!

ScratchCatHELLO

This looks like it belongs in advanced topics, but it's resolved, so I won't move it.

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