Stocky projected the ship and crew of the Enlightenment from it's very vast memory banks. Stocky can maintain full ship functions whilst also projecting 2,000 hologramatic crewmembers, although any more would be too much of a drain on it's systems.
It is unknown what form the computer took (since the ship is composed entirely of light) but Stocky is said to have stochastic capabilities, from which the computer took it's name.
Stocky's ability to ascertain all known variables and outcomes meant that it had an almost precognition with the future, much like other apparently future-telling computers such as Cassandra and Pree.
Stocky decided that Nirvanah Crane was Rimmer's best chance at beating and so matched the two up for the test, perhaps deliberately knowing the outcome (that Rimmer would cheat and win, but eventually give up his commission voluntarily since he'd fallen in love with Nirvanah who he'd replaced. Therefore, Stocky didn't lose any of it's brilliant crewmembers).