

The dissociation constant of pure water at RT is 1x10^-14. This is many magnitudes more than just one per avogadros number. The “trick” is that any given molecule of water basically has that 1x10^-14 chance of being split or otherwise whole at any given time.
Based on it just sitting on a stream bed for thousands of years after isildur was killed gotta at least have more intelligence than a fish.