Actually, your code does cause $count to be incremented.
The main problem would be that you want:
1. Increment $count
2. Assign $count to $incremented_count
but your code is doing:
1. Assign $count to $incremented_count
2. Increment $count
A solution would be to use ++$count instead of $count++
or, use $count++, then $incremented_count = $count
if you dont even plan to use $count later, then best is $incremented_count = $count + 1;