数学和JavaScript | 随机机会

Question

I'm trying to figure the math behind a pretty known site called bustabit .

I can't seem to find the right math behind it since whenever I'm trying the things I come up with the odds seem to always be way different. According to the site you can find the odds here, calc .

Okay, so basically I'm trying to generate a random number that can go up to unlimited with chances attached to them, if we remove all edged the chance of the number being 200 should be about fifty percent, 300 thirtythree, and 500 about twenty percent.

What I figured out to replicate the system, which in my opinion doesn't really fit the odds.

var mainMultiplier = 99;

var numerator = 100;
var denominator = 101;      

var chance = 1;

for(;;){
    var randomInt = random.real(0, 1.0); 

  if(numerator/denominator > randomInt){
    numerator = numerator+1;
    denominator = denominator+1;
    mainMultiplier = mainMultiplier+1;
    chance = chance*(numerator/denominator);
  }else{
    break;
  }
}

Is there a way of doing this in a better way?

You can figure out the odds in the calculator that I'm trying to replicate.

Answer 1

It sounds like you just want:

var number = 100.0 / (1 - Math.random());

Generating a million samples like this just now, the relative distribution went like this:

100 - 199 : 499817
200 - 299 : 166405
300 - 399 :  83643
400 - 499 :  50002
500 - 599 :  33155
600 - 699 :  23717
700 - 799 :  18030
800 - 899 :  13811
900 - 999 :  11140

generated thus:

// make array
var a = [];
for (i = 0; i < 1e6; ++i) {
    a.push(100.0 / (1 - Math.random()));
}

// count the distribution
var dist = a.reduce((p, n) => {
    n = 100 * Math.floor(n / 100);
    p[n] = ++p[n] || 1;
    return p;
}, {});

Note that numbers below 100 are not generated - deducting 100 from the value (and perhaps adjusting the 100 in the initial dividend) would resolve that.