How did Nucky rise to power?

According to the Boardwalk Empire wiki:

Nucky was the Atlantic County Sheriff from 1908 to 1912. During this period he married Mabel Thompson. In 1912, the Atlantic City organization was the target of a campaign of depuration led by the then Democratic Governor of New Jersey Woodrow Wilson; Nucky and The Commodore made a deal under which The Commodore would take the fall and go to jail for a number of years, while Nucky would succeed him as County Treasurer and take control of the organization, ensuring that things continued the same and The Commodore still received a share of the profits.

This information seems to originate from the episode Belle Femme (season one, episode nine):

The Commodore reminds Nucky that he spent five years in prison following his time in the throne. Nucky counters that he knew that one of them had to go. The Commodore shakes his head and says that he had no choice. Nucky asserts that he also had none and that was the reason they made their deal, he asks if they can drop the subject.

Which is explained in depth in the episode A Return to Normalcy (season one, episode twelve):

The Commodore says that Jimmy should not talk to him about justice. He recalls his own prosecution at the hands of Woodrow Wilson, then an ambitious State Governor looking to run for President. Jimmy asserts that Wilson is the reason The Commodore went to jail. The Commodore counters that Nucky was responsible, explaining that they made a deal with the prosecutor that one of them would go to prison on the election rigging charges so that Wilson would get his headlines and the other could keep running things. Jimmy wonders why it was The Commodore and not Nucky who took the fall. The Commodore explains that Nucky was an untarnished "golden boy" figure in local politics at the time so it made sense. The Commodore confides his resentment for what he perceives as Nucky for forgetting about him during the five years he was in prison.