You need one "fantasy deck" and 2 players. The rules can be expanded to more players, but you need to reduce the number of cards dealt, which may also require tweaking the scores.
They can also probably be tweaked to use a real-life card deck.
The goal is to tactically aquire cards in order to make combinations and score the most points.
The top card of the deck is set aside, then each player is dealt a hand of 10 cards. Then 10 cards are dealt face up to the table, creating the river. The deck is then placed face down next to it.
And finally, the card set aside is revealed and placed next to the deck, distinct from the river. The suit of this card becomes the prized suit for the round.
Players alternate taking turn. During a player's turn, they start by turning the top card of the deck face up and adding it to the river. Then they take one of two actions:
A card may be fished by any card with either the same rank or the same suit. Additionally, Blanks may fish or be fished with any card, regardless of suit.
A player is forced to take exactly one of those actions, and may choose to discard a card even if that card could have fished another card in the river.
When both players no longer have cards in their hand, the game ends. Players then count their points from the cards on their side.
Either whoever has the most points wins, or players accumulate score until someone reaches a given value (like 500 for example).
This is the section that I think needs the most refining. I am not happy with the scoring from my notes, but I'm sharing it as that's what I have.
The points of certain combination depends on the "value" of the cards. Number cards are worth their face value. Flowers and Dragons are worth 12.
Blanks are worth nothing and are set aside. They do not contribute to the final score or any combination.
The highest possible score I could figure out is 180. It requires getting all 12 number cards of the prized suit, the other three 12s and 11s, and two other 10s.
This gives 24 from the prized suit, 60 from the straight, 40 for having 8 cards of the same suit, 24 from the four 12s, 22 from the four 11s, and 10 from the three 10s.