The ancient era has a default rate of 3%. This means one story will happen sometime during every 1/0.03 = 33 turns. A story is assured of happening during that period, but the exact time within the 33-turn range is random. This rate changes depending on game speed. I think epic is 50% slower, and marathon is three times as slow.
Based on the average length of my games, with a 2% rate per era, 7 stories will occur (regardless of game speed since the rate scales).