Rogue ocean waves and the St. Petersburg paradox

Powerful rogue ocean waves have been objects of fascination for centuries. Elusive and awe-inspiring, with the potential to inflict catastrophic damage, rogue waves remain unpredictable and imperfectly understood. To gain further insight into their behavior, we analyzed 3 441 188 683 ocean surface waves to determine the statistical height distribution of the largest waves. We found that the distribution of rare events which resolves the St. Petersburg paradox also describes the relative height distribution of the largest waves. This result is expected to contribute to the modeling of ocean surface dynamics and improve the accuracy of marine weather forecasts.