Ra is a Knizia auction game, which means simple, elegant, and practically theme-less.
Ra'a components are tiles and a bag from which to draw them. This makes it an easy and obvious candidate for replicating with cards. It's actually rather easy to build an auction game with new rules, because auction games lend themselves automatically to a certain amount of balance. You only have to avoid a situation where a single event will grant automatic victory for someone who can guarantee winning the auction.
Ra's auction works as follows: on your turn draw a tile. You can opt to start a once around auction on all open tiles, or pass. If you start an auction, you have to bid if no one else does. Then it's the next player's turn. Continue until everyone has used up their bidding cards, or the last "Ra" tile is drawn. Whenever there are 8 open tiles, an auction is forced. No one has to bid, and if no one does, the tiles are discarded. Due this three times (three rounds).
Player's bid with bidding tiles, each of which is a unique value. You have three or four with which to bid each round, and when you win a bid with one, it goes to the center and you take the one already in the center for use on the next round.
Every tile you own at the end of a round, or end of the game, is worth some combination of points, including your final bidding tiles.
Use one suit from one of the decks as the bidding cards, e.g. the clubs. Place the ace of clubs face up to prime the bidding card exchange, and distribute the remaining twelve cards in a fair fashion to the 2-4 players (see the Ra rules sheet for example).
We'll use all the other cards to form the draw deck. Aces count only for marking the ends of rounds: the first round ends after the third ace. Mix one of the aces back into the deck, and then the second round ends after the third ace again. Repeat for the third round.
Face cards are hazards. Whenever you take a face card, you have to toss out two cards of that suit and keep the hazard (unless it is the only card in the suit you have left to toss).
When it's your turn, you can skip your turn by tossing a 6 and taking any one face up card in the pool or face down from the drawn deck (if it's an ace, you lose out and scoring is triggered if it's the third one).
Now we just need to create a scoring system. Every card is worth it's face value (2-10). In addition:
- Kinds: 2-4 cards: +5/card, 5-7 cards: +10/card, 8 cards: +100
- Flush: 3-6 cards: +5/card, 7+ cards: +10/card. Flushes only score if you have at least one of the 2, 3, or 4 of the suit within the flush.
- Straight: 3-5 cards: +5/card, 6-8 cards: +10/card, 9 cards (2-10): +100
- Straight flush: 3-5 cards: +10/card, 6+ cards: +15/card
Cards can be kept single, or assigned to one of the above types; once assigned, they cannot be moved. Additional scoring:
- No 7's: -5 points; most 7's: +20 points
- Hearts: +5/heart, 0: -2 points
After every round, you keep cards in your flushes - except 2s, 3s, and 4s - up to three single tiles, and all hazards. At the end of the game:
- every JQK in one suit is worth 50 points, and every 4 hazards of the same rank and different suits are 100 points (hazard cards may count for both scoring types).
- Player with the highest set of bidding cards +20, lowest -20.
OK, I just made these up while I was typing, but they'll probably work pretty well as is. If they don't, it will be obvious that one strategy seems useless or dominant. In which case, adjust the scoring as needed to bring the problem into line.