We present a new Monte-Carlo methodology to forecast the crude oil production of Norway and the U.K. based on a two-step process, (i) the nonlinear extrapolation of the current/past performances of individual oil fields and (ii) a stochastic model of the frequency of future oil field discoveries. Compared with the standard methodology that tends to underestimate remaining oil reserves, our method gives a better description of future oil production, as validated by our back-tests starting in 2008. Specifically, we predict remaining reserves extractable until 2030 to be 5.7 +/- 0.3 billion barrels for Norway and 3.0 +/- 0.3 billion barrels for the UK, which are respectively 45% and 66% above the predictions using an extrapolation of aggregate production. (C) 2014 Elsevier Ltd. All rights reserved.