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How do I pick a random number within a range, but weighted relative to one part of that range? (in Java)

I want to select random numbers in a range of numbers, but heavier than a portion of that range. For example:

  • Pick a random number between 1-10
  • Weight so that 1-5 can be 20% more than 6-10

Is it possible? How should I do it?

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4 answers


It depends on how you want your probability distribution to look.

For example:



Pick a random number between 1-10
If it is <= 6
    Return a random number between 1-5
Else
    Return a random number between 6-10
EndIf

Picks a number at 1-5 60% of the time and a number at 6-10 40% of the time.

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Roll and add multiple cubes to form a bell-shaped probability curve. Then subtract the average. Repeat roll if negative. The more cubes roll, the more it weighs.

Here's one path, completely untested.



float sum;
do {
   sum = rollThreeDice(); // returns 3 to 18, with an average is 10.5
   sum -= 10.5;           // Now the range is 0 to 7.5, with the lower end being more likely.
   } while(sum < 0);
return sum;

Of course, you can roll the dice on any number of sides to get the range you want. You control the frequency curve by choosing the number of bones.

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Two solutions come to mind. First, do an arbitrary case twice:

java.utils.Random randomGenerator = new java.utils.Random();
int random = randomGenerator.nextInt(11);
if(random <= 6) { //This is 20% more
    random = randomGenerator.nextInt(5) + 1;
} else {
    random = randomGenerator.nextInt(5) + 6;
}

Or, if you always have a static range, you can fill the array with digits by adding more numbers you want more and pick a random value along the length of the array.

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Try the following:

public int weightedRandom() {
  int rand = Math.floor(Math.random() * 5 + 1) // From 1 to 5
  if (Math.random() >= 0.6) {
    ++rand;
  }
  return rand;
}
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