New game invented while dreaming

It's rare for me to come up with new ideas while dreaming. Apparently some people do so all the time. Nevertheless, I invented a new, simplified poker variant while dreaming, and I think I'll try solving it.

The betting structure is identical to that of 2/4 Limit Hold'em, but there are no community cards and each player only receives one card. There are two rounds of betting, with the betting capped at three, and a small and a big blind the first round. Similar to Crazy Pineapple, each player may choose, between the two betting rounds, to randomly exchange his or her dealt card for a new one. Discards and folds go into the muck and may not be drawn by subsequent players. Whether or not each player chooses to exchange is hidden information (not to themselves, of course, but I could change that or other things to explore imperfect recall and absentmindedness).

The payoff is determined by summing two contributions. First, the pot is split among all the winners, where the comparison for winning is the rank of the card. In the case of a tie, the pot is split evenly among all the tying players (yes, allowing for non-integer, rational payoffs). Second, a unique super-winner is declared, based first on rank and then on suit, with a suit ordering from best to worst of diamonds, hearts, clubs, then spades. All the non-folded players must pay the super-winner an amount determined by the suit and rank of the super-winner's card. If the super-winner's card is red, the amount is simply the rank of the card (0 for deuce up to 12 for ace). If the super-winner's card is black the amount is 13 plus the rank of the card.

That is all.