There are two halves because you told half the victims one prediction and the other half the opposite prediction. It does not come from the probability of the outcomes. The probability of the two outcomes doesn't matter at all for this thought experiment's goal: that you can appear to correctly make N yes-or-no predictions in a row to one victim if you have 2^N-1 other victims that you can tell incorrect predictions to. This process guarantees that one of the victims in the pool ends up getting the correct series of predictions.

I'm not sure how else to explain this but please ask again if you feel like this isn't making sense; any failure here is mine, not the thought experiment's. This is an extremely well-known thought experiment. This wasn't thought up by anyone here.