That's the sort of paradox that makes my brain tick, but the math says the probability of a coherent wave packet surviving a macroscopic barrier is essentially zero. Unless you throw in some exotic tunneling medium or a perfectly engineered superposition, it’s a one‑in‑a‑billion chance, so I'd say the trick stays on the chalkboard rather than the ice. But hey, if you ever want to calculate the exact amplitude, I’m happy to crunch the numbers.