According to the US EIA, the consumed about 7.5 billion barrels in 2018.
https://www.eia.gov/tools/faqs/faq.php?id=33&t=6
Proved reserves are about 39 billion barrels as of the end of 2017.
https://www.eia.gov/dnav/pet/pet_crd_pres_dcu_NUS_a.htm
So a lot less than 200 years worth if you are using proved reserves, defined as “the estimated quantities of all liquids defined as crude oil, which geological and engineering data demonstrate with reasonable certainty to be recoverable in future years from known reservoirs under existing economic and operating conditions.”
Note that “Estimates of proved crude oil reserves do not include the following: (1) oil that may become available from known reservoirs but is reported separately as “indicated additional reserves”; (2) natural gas liquids (including lease condensate); (3) oil, the recovery of which is subject to reasonable doubt because of uncertainty as to geology, reservoir characteristics, or economic factors; (4) oil that may occur in undrilled prospects; and (5) oil that may be recovered from oil shales, coal, gilsonite, and other such sources. It is necessary that production, gathering or transportation facilities be installed or operative for a reservoir to be considered proved.”
Estimates that include more speculative oil reserves could bring the number up to about 20 times current yearly consumption, not 200 times current yearly consumption. However, an estimated 1-3 trillion barrels seem to be locked up in kerogen (“oil shale” that is different from “shale oil” that frackers are pumping oil from) that is currently uneconomical to extract oil from; including those would bring reserves to where the 200 times current production is in the ballpark.