[PetChemMan]

If the 303 is mated to a Hydramatic as the drivetrain came from the factory, it is a 4 speed automatic transmission. The later 3 speed " Slim Jim" automatic transmisssion , used on Oldsmobiles in the early 60s, was never mated to the 303 , 324, or 371 engines, but only to the 394 CID engine. Your 303 Olds is a 1953 or earlier engine. The old 4 speed Hydramatics were great transmissions. They were strong, had "stump puller" first and second gears that made the cars super fast ( up to about 42 miles per hour , when the relatively tall third gear kicked in) , and were beefed up and used in drag racing Gasser class cars in the early to mid 1960s. Until the Chrysler TorqueFlite was introduced, the Hydramatics were the only successful racing automatics. Your early 4 speed Hydramatic is the preferred unit, and was considered better for high performance than the 4 speed Hydramatic used in 1957 through 1959 ( 1960? ) cars.
Note that first gear does not appear on the shift quadrant as a gear you can select manually, which may be why you didn't realize your transmission is a 4 speed. " Low" is actually second gear, with "Super" and "Drive" being third and fourth gear respectively. ( I'm not certain if the shift quadrant on the 1953 and earlier Hydramatics used the Drive, Super, and Low terminology, but they did as of 1954. ) A nice thing about the 4 speed Hydramatic is that you could use a 3.23 or 3.42 rear axle, but get "off the line" acceleration like you had a 3.90 rear gear.