Create 3 random int params with sum of 100 - php

Question

I need to create a player with 3 properties:
Life (must be a random integer from 1 to 100);
Attack (must be a random integer from 1 to 100);
Defense (must be a random integer from 1 to 100);
But the total sum of all properties must be 200 (Life + Attack + Defense = 200). No more or less.
I’ve tried to make something like this:
public function initPlayer(){
$life = random_int(1, 100);
$attack = random_int(1, 100);
$lifeAttack = $life + $attack;
if($lifeAttack >= 100) {
$defense = 200 - $lifeAttack;
} else {
$defense = random_int(1, 100);
}
echo $life . '-' . $attack . '-' . $defense;
}
But it works correctly only if the sum of two params is equal or more than 100.

Answer 1

If the three values of life + attack + defense are to be real random numbers in the range 1..100, then the total is only 200 with a very low probability.
When the third value is calculated, it is no longer random.
The correct solution is: The 3 values have to be determined again and again until the total is equal 200.
for($sum = 0;$sum !== 200;){
$life = random_int(1, 100);
$attack = random_int(1, 100);
$defense = random_int(1, 100);
$sum = $life + $attack + $defense;
}
var_dump($life,$attack,$defense,$life + $attack + $defense);
Output example:
int(65) int(77) int(58) int(200)

Answer 2

That's basically because $lifeAttack must be greater than 100 to meet all your conditions. You could recurse when it isn't, like this:
public function initPlayer()
{
$life = random_int(1, 100);
$attack = random_int(1, 100);
$lifeAttack = $life + $attack;
if($lifeAttack >= 100) {
$defense = 200 - $lifeAttack;
} else {
$this->initPlayer();
return;
}
echo $life . '-' . $attack . '-' . $defense;
}
Of course you can do the same without recursion. Perhaps it would be nice to return these values from the function?

Answer 3

check this algorithm, that produce an array of values in a defined range with a defined sum :
function generate_values($total, $range_min, $range_max, $nb_values) {
// impossible conditions
if($total < $range_min*$nb_values || $total > $range_max*$nb_values) {
return null;
}
$values = [];
for($i=0; $i<$nb_values; $i++) {
$current_total = $total - array_sum($values);
// the last value is the remaining total
$value = $current_total;
if( $i < ($nb_values-1) ) {
$current_range_min = max($range_min, $current_total - ($nb_values-$i-1)*$range_max);
$current_range_max = min($range_max, $current_total - ($nb_values-$i-1)*$range_min);
$value = rand($current_range_min, $current_range_max);
}
array_push($values, $value);
}
shuffle($values);
return $values;
}
// test with your needs
for($i=0; $i<10; $i++) {
$values = generate_values(200, 1, 100, 3);
var_dump($values, array_sum($values));
}

Answer 4

This would be a case where only 2 numbers would be I inherently random. I would recommend first randomizing life from 1 to 100, and set the upper bound for attack as 100 -$life (I.e. 1 to 100 - $life) . Finally, defense would be pre-determined as 100 - lifeAttack.