Interesting to see that ... it takes a few dozen iterations to actually reach middle ground:

That is the nature of randomness. If it was exactly 50:50, it wouldn't be random.

But the more trials you run, the closer it will tend. This is more evident if you run this version with various different resets:

C:\test>perl 
-E"{++$t;$r=`perl -E\"say rand()\"`;$r<.5?++$a:++$b; printf qq[\r%.3f 
+: %.3f], $a*100/$t, $b*100/$t; $t>$ARGV[0] and say and $t=$a=$b=0; re
+do}" 10
45.455 : 54.545
27.273 : 72.727
36.364 : 63.636
54.545 : 45.455
72.727 : 27.273
63.636 : 36.364
36.364 : 63.636
45.455 : 54.545
27.273 : 72.727
36.364 : 63.636
72.727 : 27.273
45.455 : 54.545
54.545 : 45.455
63.636 : 36.364

C:\test>perl 
-E"{++$t;$r=`perl -E\"say rand()\"`;$r<.5?++$a:++$b; printf qq[\r%.3f 
+: %.3f], $a*100/$t, $b*100/$t; $t>$ARGV[0] and say and $t=$a=$b=0; re
+do}" 100
52.475 : 47.525
52.475 : 47.525
52.475 : 47.525
46.535 : 53.465
45.545 : 54.455
51.485 : 48.515
41.584 : 58.416
46.535 : 53.465
42.574 : 57.426
40.594 : 59.406

C:\test>perl 
-E"{++$t;$r=`perl -E\"say rand()\"`;$r<.5?++$a:++$b; printf qq[\r%.3f 
+: %.3f], $a*100/$t, $b*100/$t; $t>$ARGV[0] and say and $t=$a=$b=0; re
+do}" 1000
49.750 : 50.250
51.349 : 48.651
48.651 : 51.349
53.047 : 46.953
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