Abstract: Ammunition cartridges for hunting big game with an AR15 rifle are provided while maintaining a size of the ammunition cartridge that permits multiple ammunition cartridges to be inserted into an AR15 rifle magazine in alternating side by side relation. Each cartridge has a rim diameter of 0.422 inches, extractor groove and a slight tapered main body base of 0.36°. In one embodiment, the main base body extends to form a cartridge with total length of 1.8 inches and nominal body taper of 0.020 inches to accept a bullet with a diameter of 0.400 inches. In other embodiments, the main body base extends to a shoulder and a neck to form a cartridge with a total length of 1.66 inches. The shoulder tapers to the neck at a 35° angle with a nominal body taper of 0.014 inches. These embodiments accept bullets with diameters of 0.277, 0.284 and 0.308 inches.