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Badugi

Badugi is a draw game for the lowest hand, with a twist: your four cards only all count if they are four different suits and four different ranks. Here are the rules, how hands are compared, and how often each kind of badugi is dealt, counted over all 270,725 four-card hands.

Lesson: Seven cards, best five (needs an invite). In the glossary: Hand rankings, Draw, Showdown. How the numbers are made.

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Badugi rules

  1. The game uses blinds like Hold'em. Everyone gets four cards face down.
  2. After a round of betting, each player may throw away any number of cards and draw new ones.
  3. There are three draws, each followed by a round of betting, so four rounds in all.
  4. At the showdown the best badugi wins. Aces are low, and straights do not count.

Which hand wins

A hand counts only its cards with no two of a suit and no two of a rank. More cards beats fewer: any four-card badugi beats any three-card hand. Between hands with the same number of cards, compare the highest card first, then the next, and the lower one wins.

How often each badugi is dealt

Counting every four-card hand you can be dealt, before any draw:

All 270,725 four-card hands by the size of their best badugi
Cards that countHandsChance
Four: a badugi17,1606.34%
Three154,44057.05%
Two96,25235.55%
One2,8731.06%

Only 6.3% of deals are a four-card badugi from the start, about 1 in 16. Most hands, 57.0%, start with three cards that count, and the game is about turning those into four.

Drawing to a badugi

With three good cards you draw one. Say you hold A♠ 2♥ 3♦ and throw a fourth card away. Any club from 4 to king completes the badugi: ten cards among the 48 you have not seen. Ignoring the cards other players hold or threw away:

  • With 1 draw left: 20.8% to make it.
  • With 2 draws left: 37.7% to make it.
  • With 3 draws left: 51.2% to make it.

Every other game is compared on the types of poker games page.