Generate random numbers with fix probability

问题:

I red a lot in the forum about this, but all answers were so specific to the the asked question. The nearest one I found to my need was:Probability Random Number Generator by Alon Gubkin.

The difference is that, Alon ask to give a one face (which is six) extra chance. In my case, I want to divide the chance for the six faces so that they add up to 100%. For example, face 1 has chance of 40%, face 2 has only 10%, face 3 has 25%, ... etc.

How can I do that?

回答1:

The single probability check with linear probability can be easily done with:

function checkWithProbability($probability=0.1, $length=10000)
{
   $test = mt_rand(1, $length);
   return $test<=$probability*$length;
}

For example, this will produce:

for($i=0; $i<10; $i++)
{
   var_dump(checkWithProbability(1/3));
}

Something like:

bool(false)
bool(true)
bool(false)
bool(false)
bool(false)
bool(false)
bool(false)
bool(false)
bool(true)
bool(false)

And you can use that principle to get your edges check with desired probability:

function checkWithSet(array $set, $length=10000)
{
   $left = 0;
   foreach($set as $num=>$right)
   {
      $set[$num] = $left + $right*$length;
      $left = $set[$num];
   }
   $test = mt_rand(1, $length);
   $left = 1;
   foreach($set as $num=>$right)
   {
      if($test>=$left && $test<=$right)
      {
         return $num;
      }
      $left = $right;
   }
   return null;//debug, no event realized
}

The idea is to use geometry probability - i.e. split some line part into pieces with corresponding length and then check to which part our random number belongs.

                 0.75  0.9
                  |    |
                  V    V
*--------*--*-----*-*--*--* <-- (length)
^        ^  ^       ^     ^
|        |  |       |     |
0      0.4 0.5     0.8    1

Sample will be:

$set = [
  1 => 0.4,
  2 => 0.1,
  3 => 0.25,
  4 => 0.05,
  5 => 0.1,
  6 => 0.1
];
for($i=0; $i<10; $i++)
{
   var_dump(checkWithSet($set));
}

With result like:

int(1)
int(2)
int(2)
int(6)
int(3)
int(1)
int(1)
int(6)
int(1)
int(1)

You can increase $length - in theory, this will increase "quality" of randomize check, but that's not too easy thing - because mt_rand() uses pseudo-random generator, Mersenne Twister (and in ideal case that's not true linear probability)

回答2:

A quite simple approach would be to have an array with the length 100, writing your "faces" numbers in it, shuffle it and get the first element.

So for your example in that array are 40x 1, 10x 2, 25x 3.

Little code example (not tested):

$probabilities = array(
    1 => 40,
    2 => 10,
    3 => 25,
    4 => 5,
    5 => 10,
    6 => 10
);

$random = array();
foreach($probabilities as $key => $value) {
    for($i = 0; $i < $value; $i++) {
        $random[] = $key;
    }
}

shuffle($random);
echo $random[0];

回答3:

In your case you might generate random from 1 to 100 and then:

if random in 1:40 -> face 1
elseif random in 41:50 -> face 2
and so on. 

Of course, real code would be a little more complex to get real ranges and not hardcoded ifs

回答4:

I can think of a very simple solution. This one does not alter the random number generator's generation pattern but interprets the outcomes so as to suit your problem above. I'd ask the random number generator to generate numbers between 0 and 9. And then do the following mapping where I assign ranges of the generated number to values of my intrest based on the probability I am intered in assigning to that value:

If result <= 3, face=1
else if result <=5, face =2
else is result <=25 face =3
//and so on