To properly decide I need to know if I am Jones or Leftie.

EDIT: Given that the Ultimate Trolley only directly kills Jones or Lefty, any agent that tries factoring either Omega's or the lottery's number must be Jones or Leftie. To decide whether it's better to factor the number and die by trolley it's necessary to know the answer to the Ultimate Trolley Problem and whether it's better for Jones or Leftie to die. The expected utility of the final outcome of the Ultimate Trolley Problem certainly dwarfs the expected utility of either the lottery or Omega's bank.