I don't know the best way to phrase this question, so I'll apologize in advance if it seems a little confusing. I also don't know if it's more appropriate for poker.se or stats.se (or some other forum- please point me in the right direction if anyone knows a better place). I'm posing it here because the problem doesn't seem computationally viable and the intuition of a board/card gamer might be appropriate.
Assume we have two players, P1 and P2 holding some hole cards and playing Texas Hold-Em. These two pairs have some certain pre-flop equity against each other (representing the probability that each hand will win come showdown.) Without loss of generality, assume we will keep track of P1's equity in our experiment.
I'm wondering what the largest possible equity swing is across all pairs of hole cards and runouts is.
It's most likely that some one-outer will have to be hit on the river, and something close to a one-outer on the turn (if that even makes sense).