The oddest thing happened to me today. I was emptying my pockets, and a €2 coin didn't fall flat; it landed, and stayed, perfectly balanced on its edge. I’ve traveled all over the world and handled countless currencies, but I’ve never seen anything like this.

I did a little digging into the odds. According to physics models such as the reasonably famous Murray & Teare study ui.adsabs.harvard.edu/a… and en.wikipedia.org/wiki/C… , a coin landing on its edge is incredibly rare.

Murray & Teare calculated that for a US Nickel, the odds are about 1 in 6,000. Because a €2 coin is wider, the physics actually make it harder to balance. The calculated odds are roughly 1 in 7,700, a number obtained through extrapolation:

Here is the math:

1. The Aspect Ratio (η): The researchers found that the probability (P) is heavily dependent on the ratio of the coin's thickness (h) to its radius (R), so η=h/R.

2. The Formula: Their data suggest that for thin coins, the probability scales roughly with the cube of that ratio: P≈C*(h/R)^3, where C is a constant determined by the physics of the toss and the surface.

3. The Comparison: A US Nickel: h=1.95 mm, R=10.605 mm, so has a ratio of ≈0.1839, and a €2 Coin: h=2.20 mm, R=12.875 mm, so has a ratio of ≈0.1709. Those ratios represent "squatness".

4. 0.1709/0.1839 = 0.93, a number that one then has to cube. Why? Because they discovered that the probability of landing on an edge doesn't just drop linearly as a coin gets thinner … it drops non-linearly. Think of it like a sports car versus a van; even small change in height or width changes the center of gravity significantly, as famously demonstrated by Sabine Schmitz youtu.be/5KiC03_wVjc . Because the €2 coin is 7% "flatter" or less proportional for edge-standing than a nickel (from the 0.93 figure), its likelihood of staying upright is hit by that "cubed" penalty (0.93×0.93×0.93≈0.80). This means a €2 coin is statistically about 20-25% less likely to land on its edge than a nickel.

It also turns out my pleather Ikea mousepad valet tray acted as the perfect "landing strip." The weight of the €2 coin (8.5g) combined with its milled (ridged) edge allowed it to "bite" into the soft grain, creating a microscopic cradle. This is akin to what Sabine did using a Dodge Viper to create a slipstream to "bend the laws of physics" by removing some of the "bounce" variable, allowing the coin to settle where it otherwise might have failed. Whether the exact odds are 1-in-5,000 or 1-in-7,000, I was essentially witnessing a high-magnitude statistical anomaly.

Sometimes the laws of physics take a quick break just to show you something interesting.