The ultimate oil and gas resources of the Niagaran pinnacle-reef belt of northern Michigan, and the likely outcome of future exploration drilling in this play, were estimated using the Arps-Roberts discovery process model. For each of ten field-size classes, the parameters of the model are the ultimate number of fields, and a discovery efficiency coefficient (DEC). The parameters are derived from the actual historic exploration record, consisting of a time-ordered list of exploration drilling and the sizes of the field discoveries. The data-base consisted of 539 fields that were discovered during 1968-1982 by the drilling of 1,965 new-field wildcats. The parameters were estimated both by non-linear least-squares curve fitting, and by a heuristic ＇＇back-forecasting＇＇ calibration procedure. The DECs were found to increase with field size. Within the historic data, the model＇s emulation was shown to be excellent. The ultimate recoverable oil and gas reserves of the belt are estimated at about 1,200 million brls oil-equivalent (MM brls o.e.), predicted to be distributed in some 920 fields. Of this amount, 1,030 MM brls, reservoired in 539 fields, had already been discovered by the end of 1982. All the fields in the three largest size-classes were duly discovered by end-1986. The approximately 200 MM brls undiscovered by that date were believed to reside in about 380 small fields, more than half of which are smaller than 0.25 MM brls. The play is clearly in a very mature state, and the cost per barrel of finding new reserves will constantly increase.