Bias of flipped coins

Hmmm.  The claim from Nate Silver is that flipping a coin is not truly random and that a flipped coin will land heads up 50.5% of the time.  Specifically, from A random number generator determined the “favorite" in our forecast by Nate Silver.  

From the model’s standpoint, though, the race is literally closer than a coin flip: empirically, heads wins 50.5 percent of the time, more than Harris’s 50.015 percent.

The fundamental claim seems quite plausible.  Are all coins equally weighted along the front to back axis?  Is there a bias in terms of whether people initiate the flip with heads or tails up?  Does the technique of flipping affect the outcome?  All plausible questions.

If it were true that a coin favors Heads by 50.5% of the time, I would have thought that to be common knowledge.  Since I have never seen that claim before, it makes me curious.  What is the empirical reality?  

Nate Silver is a pretty careful writer, so I am surprised at what I find.  It seems he is accidentally mischaracterizing the research.  

As far as I can tell, the research is answering a slightly different question than that which Silver asks.

Silver is asking something along the lines of:

Given a real coin, what percentage of the time will it land Heads?  And the answer according to him is 50.5%

The research seems to be:

For any coin that is tossed vigorously and high, and caught in midair (rather than bouncing on the ground), what is the probability that it will land with the same face as it was launched?  The answer is that there is a 50.8% chance that such a coin will be caught with the same face showing as launched.  

That is a reasonably distinct difference.  Maybe Silver has better sources that answer his question but his links go to research that is answering the second question.  

The original research back in 2007 was Dynamical Bias in the Coin Toss done by Persi Diaconis, Susan Holmes and Richard Montgomery and then further reported in The Fifty-One Percent Solution.   Further research, Flipped coins found not to be as fair as thought by Bob Yirka, backed the original Diaconis findings.  Further reporting in Scientists Destroy Illusion That Coin Toss Flips Are 50–50 by Shi En Kim.  

The original research used a mechanical flipping device while the 2023 research used humans.  Different methodologies, similar results.

Whatever the currency, if you can see the face and call that before it being flipped, you will be correct 51 percent of the time.  

Which is interesting knowledge but with limited utility.  

For day-to-day decisions, coin tosses are as good as random because a 1 percent bias isn't perceptible with just a few coin flips, says statistician Amelia McNamara of the University of St. Thomas in Minnesota, who wasn't involved in the new research. Still, the study's conclusions should dispel any lingering doubt regarding the coin flip's slender bias. “This is great empirical evidence backing that up,” she says.

There is a bias with flipped coins and it is 51% towards the top surface when flipped.  However, given that the face is often not visible, that the coin is not always caught in the air, and other minor factors, the actual bias will fluctuate unpredictably and therefore the flipped coin is functionally random.  The bias is less than the operational noise in the process.