You don't understand what I'm talking about. A t test is based on the mean of your sample means, so when I said 100k times will show normalized results, I'm saying that the number of particular cards is always more likely to determine their organization than technique shuffling, baring extreme results. This is why the standard deviation is important; it let's you know how you're preforming relative to the normal distribution. Online draws may or may not be better, but until you know how it's generated, you have no idea and it's silly to assume so, and it's silly to assume it more accurately reflect distribution, because it doesn't until you demonstrate that it does by doing the math.
I think the point is, unless you're intentionally doing something stupid, both methods are completely arbitrary, and without standardization, you might as well use trial and error to figure out what works best in whatever medium you prefer.