What this badugi odds calculator does
Badugi is the four-card draw game where suits matter as much as ranks: the best hand is four cards of four different suits and four different ranks, lowest wins, and a hand that cannot manage four different suits is a three-card hand, which loses to any badugi. That makes the drawing arithmetic unlike any other game, because a card can be a perfect rank and still be useless if it matches a suit you hold. This calculator evaluates every possible result under the real rules, picks the best badugi, three-card or two-card hand from what each player ends up with, and plays out the draw exactly.
A one-card draw is 45 outcomes; two players each drawing one is 45 times 44; a three-card draw against a two-card draw is a few thousand. Everything you would meet at the table is enumerated in full.
Entering hands
Type what each player keeps, spaces between players, up to four cards each: Kc2d3h4s Ac2h3d is a pat king badugi against a three-card A-2-3 drawing one. Three cards draw one, two cards draw two. Up to eight players. Known discards go in Dead cards.
Worked examples, computed by this engine
| Match-up | Equity | Method | |
|---|---|---|---|
| Pat king badugi vs A23 three-card drawKc2d3h4s vs Ac2h3d | 80.00% / 20.00% | Exact · 45 deals | Load → |
| Pat 8-badugi vs pat 5-badugi8c4d3h2s vs 5c4h3d2s | 0.00% / 100.00% | Exact · 1 deal | Load → |
| A24 three-card vs 356 three-card, one drawAc2d4h vs 3c5d6h | 80.72% / 19.28% | Exact · 2,070 deals | Load → |
| Pat 9-badugi vs two-card draw to A29c6d4h2s vs Ac2d | 96.91% / 3.09% | Exact · 1,035 deals | Load → |
The king badugi against A-2-3 is the lesson everyone learns once. The three-card hand needs a spade, and not an ace, deuce or three; the king hand holds the four of spades; so nine of the 45 unseen cards make a badugi, and the other 36 leave the three-card hand exactly where it was, losing to a badugi it would be embarrassed to show. Pat ugly beats drawing pretty 80% of the time. The second row is a reminder that among badugis rank is everything: 8-4-3-2 loses to 5-4-3-2 every time. Two three-card hands drawing one, A-2-4 against 3-5-6, is 81-19, because the low three-card hand wins the showdown whenever both miss and usually has the better badugi when both hit. A pat nine badugi against a two-card draw to A-2 is 97% safe with one draw left, the two-card draw needing both cards to be the right suits and the right ranks at once.
The ranking
Four-card badugis beat all three-card hands, which beat all two-card hands, which beat one-card hands. Within the same size, compare the highest card first and lower wins, then the next card. Aces are low. A card that pairs a rank or repeats a suit is simply not counted, so Ac-2d-3h-3s is a three-card A-2-3 and Ac-2c-3c-4c is a one-card ace. The calculator checks every subset of each player's cards to find the best one, which is the only correct way to score a badugi hand and the thing most quick tools skip.
One draw, exact
Badugi is a triple-draw game, and this calculator gives the exact equity with one draw to come. Earlier draws depend on what each player keeps after each draw, which depends on what they catch and on strategy, and no calculator can give a single honest number for that. The one-draw figure is exact for the last draw, where the big bet goes in, and is the floor for any drawing hand before it. The other draw games on the site have their own calculators with their own rankings: 2-7 Lowball, A-5 Lowball and 5-Card Draw.
Frequently asked questions
Four cards of four different suits and four different ranks. Aces are low, so A-2-3-4 with one of each suit is the best possible hand. Any badugi beats any three-card hand, any three-card hand beats any two-card hand, and within the same size the hand with the lowest highest card wins, then the next card down.
Type the three cards the player keeps, such as Ac2h3d. The calculator deals one card; if it is a spade that is not an ace, deuce or three, the hand becomes a badugi. If it pairs or matches a suit, the player is still three-card.
Because K-4-3-2 rainbow is still a badugi and A-2-3 is not. The draw needs one of the nine spades from 4 to K (the 4s is held by the king hand) out of 45 unseen cards, which is 20%. The rest of the time the pat king wins, however ugly it is.
It covers the final draw exactly. With two or three draws to come, the equity depends on each player's discard decisions after each draw, which needs a strategy model. The one-draw number is the right starting point, and in practice the last draw is where most big badugi decisions are made.
