I don't care what the theory is. I may not understand it, in which case my changes to the code are non-sensical, but they basically boil down to this:

$num1  = rand(1000);
$num2  = rand(1000);  # pretend $num2 != $num1

$guess = rand($num1 * 2);
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Are we asserting that $num2 > $guess more than 50% of the time?