Increase random number probability swift - swift

Question

I'm trying to make a game where the hero damage is generated randomly within a range but the more luck the hero has, the higher probability the hero will have to hit with the max damage number within that range.
I'm using a Double extension to make it easier on myself.
public extension Double {
public static func random(lower: Double = 0, _ upper: Double = 100) -> Double {
return (Double(arc4random()) / 0xFFFFFFFF) * (upper - lower) + lower
}
//Assigning the random number to a constant
let heroDamage = Double.random(5, 15)
Let's say the hero has now an 80% of probability on getting the max damage(in this case 15), how would I approach this?, Thanks in advance.

Answer 1

For a given max damage probability of pMaxDamage (say, pMaxDamage = 0.80), one simple solution is to generate a random number, say r, in [0,1] and output:
maxDamage if r <= pMaxDamage,
a random damage in range [minDamage, maxDamage], otherwise.
E.g.:
class Hero {
let heroName: String
let pMaxDamage: Double // probability to generate max damage
init(heroName: String, pMaxDamage: Double) {
self.heroName = heroName
self.pMaxDamage = pMaxDamage
}
func generateDamage(minDamage minDamage: Double, maxDamage: Double) -> Double {
let r = (Double(arc4random()) / 0xFFFFFFFF)
return r <= pMaxDamage ? maxDamage
: round(100*((r-pMaxDamage)/(1-pMaxDamage)*(minDamage-maxDamage)+maxDamage))/100
}
}
For the above implementation the r-damage (r uniform random number in [0, 1]) response curve looks as follows:
Example usage:
let myHero = Hero(heroName: "Foo", pMaxDamage: 0.80)
for _ in (1...10) {
print("Slash! <\(myHero.generateDamage(minDamage: 5, maxDamage: 15)) damage>")
}
Example output:
Slash! <15.0 damage>
Slash! <12.68 damage>
Slash! <15.0 damage>
Slash! <15.0 damage>
Slash! <5.72 damage>
Slash! <15.0 damage>
Slash! <15.0 damage>
Slash! <15.0 damage>
Slash! <15.0 damage>
Slash! <15.0 damage>
If you want your damage values to only take integer values, an alternative solution would be roulette wheel selection with
pMaxDamage probability of picking maxDamage,
uniform (1-pMaxDamage)/(numDamagePoints-1) probability of picking any of the remaining {minDamage, minDamage+1, ..., maxDamage-1} damage values.

Answer 2

Maybe add a luck to the random function? Pure linear implementation here. You could use some advanced curves though.
private let MaxLuck = 1000.0
public extension Double {
public static func random(lower: Double = 0, _ upper: Double = 100, luck: Double) -> Double {
let weight = min(luck / MaxLuck, 1)
return (Double(arc4random()) / 0xFFFFFFFF) * weight * (upper - lower) + lower
}
}