A method of drilling a well while distinguishing circulated gas or air from pumps-off gas in a drilling fluid at downhole pressure and temperature, the method comprising: a) drilling a well with a drilling fluid, a drill string, and a drill bit from an earth surface through a high pressure, low permeability formation encapsulating a high pressure, high permeability formation (16, 18, 20, 22, 24, 26), the drilling fluid being pumped through the drill string, drill bit, and into an annulus between the drill string and a wellbore, the drill string comprising one or more sensors (54, 55) sensing a parameter indicative of circulated gas or air in the drilling fluid flowing through the drill string, at least one of the sensors located in the drill string behind and near the drill bit; b) measuring, while drilling, a parameter of the drilling fluid indicative of circulated gas or air inside the drill string behind and near the drill bit using the sensors; c) supporting at least one annulus gas sensor by the drill pipe behind and near the drill bit to sense an amount of gas in the drilling fluid in the annulus behind and near the drill bit during pumping at a depth of the at least one annulus gas sensor; d) detecting an amount of gas in the drilling fluid in the annulus behind and near the drill bit using the at least one annulus gas sensor and tracking detected gas levels volumetrically as a function of drilling fluid volumes during drilling periods before and after a period when pumping has stopped and correcting the annulus gas volumes to remove the effects of circulated gas or air; e) communicating the result of steps (b)-(d) to a human-readable interface at the surface while drilling to allow an operator to compare the amount of gas in the drilling fluid in the annulus at the depth of the at least one sensor during the periods before and after the period when pumping has been stopped, and thus determine if pressure of the wellbore fluid is greater than formation fluid pressure behind and near the drill bit; and f) assessing formation pressure relative to wellbore pressure and adjusting a parameter of the drilling fluid. a) drilling a well with a drilling fluid, a drill string, and a drill bit from an earth surface through a high pressure, low permeability formation encapsulating a high pressure, high permeability formation (16, 18, 20, 22, 24, 26), the drilling fluid being pumped through the drill string, drill bit, and into an annulus between the drill string and a wellbore, the drill string comprising one or more sensors (54, 55) sensing a parameter indicative of circulated gas or air in the drilling fluid flowing through the drill string, at least one of the sensors located in the drill string behind and near the drill bit; b) measuring, while drilling, a parameter of the drilling fluid indicative of circulated gas or air inside the drill string behind and near the drill bit using the sensors; c) supporting at least one annulus gas sensor by the drill pipe behind and near the drill bit to sense an amount of gas in the drilling fluid in the annulus behind and near the drill bit during pumping at a depth of the at least one annulus gas sensor; d) detecting an amount of gas in the drilling fluid in the annulus behind and near the drill bit using the at least one annulus gas sensor and tracking detected gas levels volumetrically as a function of drilling fluid volumes during drilling periods before and after a period when pumping has stopped and correcting the annulus gas volumes to remove the effects of circulated gas or air; e) communicating the result of steps (b)-(d) to a human-readable interface at the surface while drilling to allow an operator to compare the amount of gas in the drilling fluid in the annulus at the depth of the at least one sensor during the periods before and after the period when pumping has been stopped, and thus determine if pressure of the wellbore fluid is greater than formation fluid pressure behind and near the drill bit; and f) assessing formation pressure relative to wellbore pressure and adjusting a parameter of the drilling fluid.