Badugi Odds: Probabilities Every Player Should Know

You are dealt a complete four-card badugi only about 6.3% of the time, or roughly 1 in 16 hands. Far more often you start with a three-card badugi and spend three draws trying to swap one card into a fourth clean rank and suit. Those two frequencies — how rarely you start made, and how a draw fills — drive nearly every decision in the game.

This page assumes you already know that a badugi is four cards of four different ranks and four different suits. If not, start with the badugi rules and strategy guide.

What the deal hands you

Every card in a four-card badugi has to be a unique rank and a unique suit. Of the 270,725 possible four-card starting hands, exactly 17,160 qualify.

Best badugi on the deal	Combinations	Chance
Complete 4-card badugi	17,160	6.34% (1 in 16)
3-card badugi	154,440	57.05%
2-card badugi	96,252	35.55%
1-card only	2,873	1.06%

The three-card badugi is your default reality: one of your four cards is dead weight — it pairs a rank or repeats a suit — and you draw to replace it. But a three-card badugi’s quality swings wildly. A-2-3 drawing to a fourth low card is a monster; 9-J-Q drawing is nearly worthless, because even a completed jack-badugi loses to almost any smooth four-card hand. Judge the three cards you keep, not the count.

Counting outs on a one-card draw

Holding a three-card badugi and drawing one, an “out” is any card of a different rank and different suit from all three kept cards. About 47 cards are unseen after the deal, and outs shrink as ranks and suits get blocked.

Keep A♠ 4♥ 7♦ and draw one. A completing card can’t be a spade, heart, or diamond — so it must be a club — and it can’t be an ace, four, or seven. Thirteen clubs, minus the club ace, four, and seven, leaves 10 clubs that complete a badugi (a low one makes a better badugi, but any of them works).

That’s a strong draw. Keep three cards that already burn three suits with high ranks and the completing suit is fixed while many of its low cards are gone — fewer outs. Fewer suits used and lower ranks kept both widen the draw.

Filling across three draws

One draw is only part of the picture, because badugi gives you three. A single one-card draw with 10 outs hits about 21% of the time (10 of 47), but chained across three attempts the chance of hitting at least once climbs into the neighborhood of half for a clean draw. A smooth three-card badugi is therefore a genuine favorite to complete some four-card badugi by showdown.

The catch is quality. Making a badugi is common; making one that beats your opponents is not. A king-high badugi beats no badugi worth calling with, and that is exactly where the game punishes chasers — they draw, they “make their hand,” and they still lose. Which completed hands actually win is covered in the best badugi hand guide.

Estimating at the table

No calculator required:

1. Identify the suit you still need — the one your three kept cards haven’t used.
2. Count how many cards of that suit are low enough to help and not already dead.
3. Divide by the unseen cards (about 47 after the deal, fewer later) for your one-draw chance.
4. Remember you get up to three attempts, so a live draw is worth much more than one shot suggests.

Two forces decide whether a draw is playable: how many outs you have and how low they are. A draw to A-2-3 beats a draw to 8-9-10 with the same out count, because it targets winning badugis rather than losers.

One last number to internalize: since a complete badugi arrives only 6.3% of the time, an opponent who stands pat on the first draw is representing something genuinely rare and strong. Weigh your draw against the real chance you are already behind a made hand — not just chasing an empty pot. And remember the standard poker hand rankings don’t apply here: pairs and flushes hurt you, and all of this math is about assembling four unique ranks and suits as low as possible.