Running it twice new variation: Twice Mean

Everyone is familiar with the idea of running it twice by this point. In fact most local poker rooms like Borgata allow for running it twice with no additional rake in the poker room games I play.

However in one of the social clubs I play, one of the regulars came up with a new variation called Twice Mean (he claims he saw it on a stream somewhere, but I am not sure if it might be his own invention) and the opposite version Twice Nice. The idea is that if you choose Twice Nice, it is just a traditional Run it Twice, while if its Twice Mean, the dealer runs two boards, and if someone scoops they take the pot, while if it is 1-1, a 3rd board is dealt and whoever wins 2 boards out of 3 takes 2/3 of the pot. It is my gut feeling that unlike traditional Run it Twice or Run it Three Times, where the equity always stays the same mathematically, Twice Mean actually shifts some of the equity from the player who is behind (i.e. has less than 50% equity in the pot) to the player who is ahead (the player who has more than 50% equity in the pot). The logic for that would be that if the player who is behind fails to hit her outs on the first two boards, she does not get a chance at a 3rd board. While if she does hit one or both of the first two boards, she now has less outs for the 3rd board, creating an additional mathematical advantage for the player who was already ahead. Note, that the regular who came up with this is a winning player on a tighter side who is in fact more often than not ahead when all the money goes in.

I had no problem shutting down this nonsense in pots involving myself. I just tell that player 'once or twice' and if any nonsense or extended discussion starts just tell the dealer to go ahead and run it once. However, if this does in fact steal equity from rec players (in addition to slowing the game down tremendously which is my objection as well), it would be nice to shut this down once and for all (but of course would require some concrete justification about why this is in fact unfair beyond my hunch above).

With that in mind I have a couple of questions that someone on this forum could hopefully answer:
1) Have you heard of this Twice Mean concept under this or another name before or seen it in any games?
2) Is there a way to mathematically show if Twice Mean does in fact shift equity from a player who is behind to a player who is ahead?