# Largest cumulative equity swing

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 poker player might answer the question best.

Assume we have two players, P1 and P2 holding some hole cards. 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.

After the flop comes, there is some new equity for P1. Similarly after the turn, and after the river. Every combination of cards and runouts has a "total equity swing" which I'll define as

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).

Flop 8h 9h 9c (4.34%)
Turn Ac (97.73%)
River 9s (0%).

Total equity swing is approximately 280.86%. You're absolutely correct; postflop equities can be calculated by determining the number of outs available. In the above scenario, the turn is a one-outer for P1, and the river is also a one-outer but for P2. The only piece of the puzzle you were missing was the pair of two hands that had the greatest equity difference.