For one you can't establish a standard deviation in one set of 30 coin flips.
Sure you can.
Strong Law of Large Numbers
Two, it's been mathematically proven that even though there are only two sides to a coin, the odds aren't close to within 1-2% of 50, no matter how many samples you take.
says f*ck your theory. Now, I'll agree that 30 samples isn't enough to get a ~3% margin of error, but with enough coin flips you will.
Case in point, I just generated 1000 random integers from random.org. The results were either a 1 or a 0. Assuming a completely random distribution, it should be 50% 0s and 50% 1s, so 500 1s and 500 0s. Copied the list into excel and ran a SUM of the numbers. 498. Within a .5% margin of error.