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The possibility engine was a cybernetic machine built by Rassilon on Gallifrey during the Last Great Time War. It could be consulted about decisions to make in the conflict, since it was able to see the past and the future in the time vortex. It needed a Time Lord whose timeline was retro-evolved. One of the effects of this was a Time Lord to be in constant flux, changing between each of their past and future incarnations.
Experiments for its construction led to the creation of the discarded race of the Interstitials. The eventual functioning specimen worked thanks to Borusa and was hidden in the Tower of Rassilon, in the Death Zone.
The War Doctor, Cinder and three Interstitials brought the possibility engine on the Doctor's TARDIS and, eventually, to the Tantalus Eye; there it was able to revert a timeline where the Daleks wiped out Gallifrey from history. (PROSE: Engines of War)