Handout 04 · Limit
Badugi
Four cards, three draws, and a ranking found nowhere else: you want four low cards of four different suits. Most hands never get there, so the game is largely about who has the best three.
- Cards
- Four, all face down
- Draws
- Three
- Betting
- Fixed limit, four rounds
- Players
- Up to eight W
- Best hand
- A-2-3-4, one of each suit
- Ace
- Low (but see Badeucey)
1How it is dealt and bet
Button and blinds. Each player gets four cards face down and there is a round at the small bet. Then a draw, in which each player may replace from none to four cards, and another round at the small bet. A second draw and a round at the big bet. A third draw and a last round at the big bet. Showdown. B W N6
The WSOP's rules add the usual draw-game procedure: an exposed card is replaced; until someone acts after a draw, you and the dealer must say how many you drew if asked; check-raising is allowed on every round. W
2Hand ranking
A badugi is four cards with four different suits and four different ranks. Aces are low, and straights mean nothing. W B Reading a hand takes two steps.
- Count how many cards play. Find the largest set of your cards in which no suit and no rank repeats. Four is a badugi. If two of your cards share a suit or a rank, only one of them can play and you have a three-card hand (a "tri"); it can fall to two cards, or one. More cards always beats fewer: the worst badugi, K-Q-J-10, beats the best three-card hand. B N6
- Among hands with the same number of cards, the lowest wins, read from the highest card down, as in lowball. B If two sets of the same size are possible, you play the lower one.
- A♠2♥3♦4♣ beats 2♠3♥4♦5♣Both are badugis. A-2-3-4 is four-high, the best possible hand.
- K♠Q♥J♦10♣ beats A♠2♥3♦3♣A badugi beats any three-card hand. The second hand has two threes, so only A-2-3 plays.
- A♦2♣3♥6♥ beats A♣3♦4♥5♥The WSOP rulebook's own example. Each hand has two hearts, so each plays three cards: A-2-3 against A-3-4. W
- 6♠5♥4♦3♣ beats 7♠3♥2♦A♣Read from the top: a six-high badugi beats a seven-high one, whatever is underneath.
- A♠2♠3♠4♠Four of one suit: only one card plays. This is a one-card ace. One-card hands are the lowest class of hand in the game.
- A♠5♠2♥3♦Two spades. Keep the lower one: the hand plays as a three-card 3-2-A, not 5-3-2.
Suits decide whether a card plays, but they never break a tie: two hands with the same ranks split the pot.
All the sources we read agree on this ranking. The one thing that changes from game to game is the ace: it is low here and in Badacey, and high in Badeucey, where 2-3-4-5 is the best badugi. W B A1 The WSOP's rules also mention a high version of badugi in which four aces is the best hand. W
| Your best hand is | Share of deals |
|---|---|
| A badugi | 6.34% |
| of which queen- or king-high | 53.8% of badugis |
| eight-high or better | 0.62% |
| Three cards | 57.0% |
| Two cards | 35.6% |
| One card | 1.06% |
This confirms a figure given in the published strategy literature: about 6% of dealt hands are badugis, and about half of those are weak ones headed by a queen or a king. N6
3The draws, step by step
You are dealt A♠2♥3♦K♠. The king is a second spade, so it cannot play. You hold the best three-card hand there is, and you draw one card hoping for a club.
Thirteen clubs, less the ace, two and three of clubs that would pair you: 10 cards make a badugi. With your discard counted as gone, 48 cards are unseen.
| Three-card A-2-3, draw one | Cards that hit | 1 draw left | 2 left | 3 left |
|---|---|---|---|---|
| Any badugi | 10 of 48 | 20.8% | 37.7% | 51.2% |
| Eight-high badugi or better | 5 of 48 | 10.4% | 19.9% | 28.6% |
| Seven-high badugi or better | 4 of 48 | 8.3% | 16.1% | 23.4% |
Every three-card hand normally has the same 10 cards to complete a badugi (9 if the card you threw away was one of them). What a low three-card hand buys is a better badugi when it gets there, and a better hand when it does not. Even with all three draws to come, the best three-card hand makes a badugi only about half the time.
4Starting hands
- Badugis of seven-high or better are strong. Eight-high to jack-high is the middle. Queen- and king-high badugis are easily overtaken when several players are drawing. N6
- Strong three-card hands are valuable starting hands. Prefer the one that makes the better badugi: 8-3-A over 8-7-6, though both are one card away. N6
Share of hands raised when everyone before you has folded, six-handed, from heads-up proxy solves of a simplified game (hand classes, no card removal). How to read these numbers.
| Seat | UTG | HJ | CO | BTN | SB |
|---|---|---|---|---|---|
| Raises first in | 18% | 21% | 23% | 38% | 50% |
These are tighter than the same solver's shares for either five-card triple-draw game in every seat. We have no heads-up detail for badugi beyond these shares.
5The key decision on each draw
- While everyone is drawing: if you probably hold the best three-card hand and nobody has shown a badugi, bet, so that the others pay to draw. The best three-card hand becomes a bigger favourite as the draws run out. N6
- When someone stands pat: with one draw left and an unfinished hand against a likely badugi, calling is often wrong unless the pot is large or your draw is excellent. N6
- At the end: against experienced players, be willing to call a last bet with a three-card hand that might be best, because a pat hand can be a bluff. Standing pat on three cards and betting (a snow) works best against players who fold when they miss, and when your hand could not win a showdown anyway. N6
The arithmetic behind the first point: a player drawing one to a badugi misses 79.2% of the time on the last draw (38 of 48).
6Common mistakes
- Counting a suited card. A-2-3 of three suits plus the 4 of a suit you already hold is not a badugi. It is A-2-3.
- Keeping the wrong duplicate. When two cards share a suit, the lower one plays.
- Falling in love with a king-high badugi. Published It beats every three-card hand today and loses to every other badugi. N6
- Expecting to get there. Computed One draw: 20.8%. Three draws: 51.2%.
- Carrying the ace into Badeucey. There it is the highest card. See Badeucey.
Badugi: cheat sheet
Seminar 27 · Handout 04 · limit, four cards, three draws
The order of play
Deal 4 → bet (small) → draw → bet (small) → draw → bet (big) → draw → bet (big) → showdown.
Ranking in one breath
- Badugi = four cards, four suits, four ranks. Ace is low. Best: A-2-3-4.
- Same suit or same rank twice? Only one of the two plays.
- More cards beat fewer: any badugi beats any three-card hand.
- Same count: lowest wins, read from the top card. Suits never break ties.
Odds to carry
| Dealt | Share |
|---|---|
| A badugi (half are Q- or K-high) | 6.3% |
| A three-card hand | 57.0% |
| Two cards or fewer | 36.6% |
| Three-card hand, draw one | Hits/48 | 1 left | 2 left | 3 left |
|---|---|---|---|---|
| Any badugi | 10 | 20.8% | 37.7% | 51.2% |
| A-2-3 to a 7-high or better | 4 | 8.3% | 16.1% | 23.4% |
Published rules of thumb
- Seven-high badugis or better are strong; queen- and king-high are fragile.
- Best three-card hand and nobody pat: bet. Facing a pat hand with one draw left: usually not worth a call.
Solver baseline (simplified heads-up game, not a full solution)
First-in raise share six-handed: UTG 18 · HJ 21 · CO 23 · BTN 38 · SB 50 (%).
seminar27.com · Odds computed by the site's own script. Rules: WSOP live-action rules and the BARGE rulebook. For education.