Fats tells Jesse that because he is legendary, in a sense he lives forever.
Fats goads him into a match in which if Jesse loses, he will die, but if he wins, he lives - seemingly gaining nothing from victory.
With Jesse needing to sink only one more ball to win, Fats distracts him by scuffing his pool chalk, making him miss.
This episode was written by George Clayton Johnson for the original Twilight Zone series.
In that 1961 version, starring Jack Klugman and Jonathan Winters, Jesse wins and is bound to take up Fats's mantle as the greatest pool player in history.