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Badugi is a game of triple draw. IE you draw 3 times.
1. Each player is dealt 4 cards.
2. There is then a round of betting
3. Then you make your first Draw (ie hand the cards you dont want, face down, back to dealer and receive different cards)
4. Betting round 2, then draw again
5. Betting round 3, then draw again
6. Betting round 4.
Who wins?
In Badugi the lowest hand wins but variation in the suits of the cards is crucial
If you have a hand with 4 different suits and 4 different cards eg As Jc 7h 4d, then you have a BADUGI.
The best hand in Badugi (ie the best "Badugi") is A234 (all different suits). This is different from a lot of lowball style poker variants, because suits really matter. You are searching for 4 different suits
It is simply a case of the best BADUGI wins. If no player has a Badugi, then you look at 3-card hands. The thing to remember is that the only way a hand is valid is if there are different suits, so if you have say 2 spade cards at the end, you can effectively disregard one of those cards, and just look at your 3 card hand.
The worst Badugi is Ks Kd Kh Kc, but this is still better than a 3-card hand. The best possible 3-card hand is A23 with all different suits. You get the picture.