[Aetae]

Длинноник, не вижу рандома вообще.

function RandomSplit( A, parts, min ) {
    var numbers = [];
 
    for ( var i = 0; i < parts; i++ ) {
        var part = ( A / (parts - i) - min) * Math.random() + min;
        part = Math.round( part );
        numbers[i] = part;
        A = A - part;
    }
 
    for ( var i = 0; i < numbers.length; i++ )
        numbers[i] += A / parts;
 
    return numbers;
}
      
var counter = [0, 0, 0];

for (var i=0; i<10000; i++) {
  counter[RandomSplit(1, 3, 0).indexOf(1)]++;
}
 
alert(counter);