@udongle @ceo_of_monoeye_dating @roboneko @hidden @Inginsub @tiskaan @scenesbycolleen @MercurialBlack @jeffcliff
Let me respond to this and @PoalackJokes88 's posts together:

If Jeff didn't have the Delta bomb, then CMD could guarantee a survival rate of 2/3 by just camping on one of the inner rooms. When Jeff hits CMD with an Omicron bomb, CMD knows that he'll get to choose one of 3 rooms randomly, so he survives at a rate of 2/3 > 1/2.

But if Jeff has the Delta bomb, then CMD can't use this camping strategy, because Jeff will just Delta bomb and win with probability 1. Or, if CMD switches randomly between the two inner rooms, then Jeff can Delta bomb and win with probability 1/2.

For the 'extra credit,' if Jeff had no Delta bomb, then CMD could achieve a 4/5 survival rate by camping in the central room, as Poalack pointed out. But using the threat of the Delta bomb, Jeff can prevent CMD from camping in one room. (I don't know the numerical answer for the extra credit.)