@ajfirecracker I don't think it's strange at all. You're citing to Rules in a loose way, but the actual text is not what you're suggesting.

705.3. A coin used in a flip must be a two-sided object with easily distinguished sides and equal

likelihood that either side lands face up. If the coin that’s being flipped doesn’t have an obvious

“heads” or “tails,” designate one side to be “heads,” and the other side to be “tails.” Other methods

of randomization may be substituted for flipping a coin as long as there are two possible outcomes

of equal likelihood and all players agree to the substitution. For example, the player may roll an

even-sided die and call “odds” or “evens,” or roll an even-sided die and designate that “odds”

means “heads” and “evens” means “tails.”

I bolded the relevant part. As you see, the substituted method technically must involve 1) two possible outcomes of equal likelihood AND 2) player agreement. Nothing in this Rule suggests you can simply accept one possible result, however well-justified, and then adopt it without actually resolving the random event.

You are saying that, to resolve 1,000,000 coin flips, the players simply take the standard variance and apply that in someone's favor. What is the variance, though? It's a statement about the expectation about how many more heads or tails you will usually get, on average.

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean, and it informally measures how far a set of (random) numbers are spread out from their mean. The variance has a central role in statistics.

However, the actual result of flipping the entire sequence will virtually never actually equal this exactly. Variance or not, the chance of getting precisely X heads and Y tails on a million flips is vanishingly small for any particular choice if X and Y.

Now, of course, if no one calls a judge and no judge is watching... you can do whatever you want to. But, nothing in the Rules supports the procedure you suggest.