From the article:

> Diaconis himself has trained his thumb to flip a coin and make it come up heads 10 out of 10 times

10 out of 10 isn't really that impressive.

If his actual success rate is, say, 70 out 100 10/10 is easy enough to get by chance.

990 out of 1000 would be much more pressive.

It's a popular piece. ‘10 out of 10’ probably just means ‘reliably’.

I calculate that 70/100 gives you a 6 in a million chance of getting 10 in a row.

6 in a million is the chance to fail 10 times in a row with 70% odds. 10 successes is 3%.

Aw dang it, got it backwards!

Flip the coin the same number of times, catch consistently and get good at adjusting the catch. Use a large and heavy coin like a silver dollar. - former magic enthusiast.

Former Pokémon TCG enthusiast (circa 1999) here! Kids back then had the same approach, large and heavy coin, flip from a consistent height, consistent strength. Heads every time.

There were popular coins made specifically for Pokémon TCG then, and they happened to be large and thick and plastic and heavy, so the cheating was widespread.

I was one of the many kids who did this routinely. But there was one kid who took first place nearly every week, out of a field of 50+ entrants. “He must cheat the coin, AND be an amazing deck builder and card player on top of that”, I thought.

Then one week I was matched against him, winner goes to top 8.

Our decks were nearly identical, I could flip heads every time, I was a strong player. “50-50” I thought.

Turn one. Retreat Scyther, in Electabuzz, Thundershock. I flip my giant coin, and before it flattens, he picks it up and hands it back to me. “Flip it higher please.”

He must know I’m cheating. I assumed he must be cheating too though, every other kid is, and he wins this tournament every week!

Guilty, I flipped the coin fair this time, higher. Before it flattens he picks it up again, hands it back to me. “Higher please.”

I lost every coin flip that match. He won, went to the top 8, later won the tournament for the nth week in a row.

It wasn’t until adulthood that I realized how he was winning every tournament. In a field full of cheaters trying to flip heads every time, all he had to do was wait for the coin to enter that terminal spinning motion every coin does right before it flattens. Well practiced at this, if he sees that it’s about to flatten heads, he quickly grabs it and hands it back to you. “Higher please.” Repeat until the coin flattens tails.

His tactic was a silver bullet in a field full of flip cheaters. Nobody ever questioned his intentions when he grabbed the coin and asked for a higher flip.

I can imagine that on a slow, lazy flip with a big coin, but is this realistic with what I think of as a "normal" flip, i.e. a US quarter, flipped rapidly end-over-end with the thumbnail, 2+ feet in the air? It's hard to believe that even decades of practice would get this reliable, and I don't think I've ever seen a stage magician rely on it in a routine.

For comparison, the other method (where the coin rotates about its vertical axis) is something you can learn to do tolerably well in a few minutes, and to do very well after a month or two at most. The motion of the coin will look perfect, and you can even get the "ding!" noise of a real flip. The only giveaway is the hand position; a real flip is done with the thumb under the coin, and this trick (for me, anyway) requires the thumb to be on top.

Source: taught myself to do this many years ago. I'm not a magician and have never used it to win money, I just use this to settle arguments between my kids.

In this sense, I found the 51% surprising (surprisingly close to 50%).

If you have a very practiced, consistent flip, you can always get the same result.

The article notes that he got to 100% when intentionally biasing the flip, the 51% was for ordinary people doing ordinary coin flips (no attempt to bias).

To clarify, this is exactly what I found surprising: that any unintentional bias that exists, in those ordinary cases, cancels out almost (but not quite?) perfectly.

Appreciate the much-needed TLDR on this.

What do you do to bias the outcome?

Flip it with the right amount of force, like a juggler with bowling pins.

No. You need to put a lot of horizontal torque on it so it never flips over at all.

That’s not a coin flip! I agree that’s a method to achieve the outcome though. If you get the wobble right it’s almost imperceptible.

no audience is going to fall for that...

They do, occasionally it doesn’t wobble enough and looks obvious but done right it’s not perceptible. As a tip do it physically close to someone and catch it high so they have a worse angle to see the lack of flipping. For a real “performance” there is significantly better methods though.

You catch it at the right moment. You learn to feel the right timing by practice.