Generate random player strengths in a pyramid structure (PHP)

Question

For an online game (MMORPG) I want to create characters (players) with random strength values. The stronger the characters are, the less should exist of this sort.

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Answer 1

You can simulate a distribution such as the one you described using a logarithmic function. The following will return a random strength value between 1.1 and 9.9:

function getRandomStrength() 
{
    $rand = mt_rand() / mt_getrandmax();
    return round(pow(M_E, ($rand - 1.033) / -0.45), 1);
}

Distribution over 1000 runs (where S is the strength value floored):

S | Count
--+------
1 -  290
2 -  174
3 -  141
4 -  101
5 -  84
6 -  67
7 -  55
8 -  50
9 -  38

Note:

This answer was updated to include a strength value of 1.1 (which wasn't included before because of the rounding) and to fix the name of the mt_getrandmax() function