Our main objective, after stealing all the oil we could, was to make sure there would not be another ARab Oil Embargo. So we sowed division and confusion and made sure everyone was armed and afraid of the other. Keeping Iran and Saudi Arabia at each other's throats was done by aggravating the Sunn-Shia civil war.
It must have been a shock to see the Saudis and the Iranians try to make up.