I agree that oil is a finite resource. On the other hand, since this planet is largely covered with water, it stands to reason that much oil lies beneath the oceans. Some is too far down to extract by any technology, but probably at some time, a large amount can be extracted by technologies not yet invented or not yet cost-effective.
Many years ago, an ancestor of mine was pissed at the high price asked for the local limestone purveyor for a house he wanted to build in Gainesville, Texas. This was back in 1896. So he went to a neighboring county ad bought the mineral rights to a rather large farm, and quarried his limestone on the cheap. In the 1950's, exploration determined that there was a very high probability of oil on this property. (This is what a document my great aunt once received said). In later years, the Red River was dammed up to form Lake Texoma, and the property was submerged. My sister and I inherited the mineral rights in the 1990's, and every three years, I get a check for $35 from a fellow who peddles oil leases in this area.
I will know when oil has reached the point where it is cost-effective and I assume environmentally safe to drill under Lake Texoma, which is one of the largest recreational lakes in Texas and Oklahoma. So far, nothing has happened, so I assume that it is in some way less lucrative than drilling in ANWAR.
I suspect that tycoon status will not be reached by my generation, because oil is not so scarce or expensive to extract as the oilmen say it is.