93,000 Coldcard-Generated Seeds Is All It Takes for a 50% Chance Two People End Up With the Same Wallet

You probably heard the birthday paradox, having 23 people in a room creates a 50% chance that at least two of them share the same birthday.

Applying it to the vulnerable search space in the ColdCard bug (Following reports that search space was reduced to 2^32, approx 4 billion)

50% collision odds ≈ √(2 × 4.3 billion) ≈ 93,000 ColdCard Wallet Generated Seeds.

If this bug was somehow never discovered and Coldcard sold around 93k units that generated a seed on the vulnerable firmware, there would be a 50% chance that two innocent, unaware people would end up with the exact same seed phrase, and by extension every bitcoin address derived from it, giving each other access to the others funds.

Just a fun thought experiment in these dark times.