Four cards · rainbow suits · three draws

Badugi Cheat Sheet

The four-card game where suits matter: exact dealing odds over all 270,725 starts, what the table holds, and all 167 starting shapes — pat badugis down to one-card salvage — ranked by showdown win rate.

4-card hands, aces lowcards pair by rank or suitthe nuts is A-2-3-4 rainbow4 > 3 > 2 > 1-card handsX = a dead card (paired or suited)

What you’ll be dealt

Exact odds — every possible starting hand enumerated.

6.34%

dealt a pat badugi — about 1 hand in 16

57.0%

dealt a 3-card hand — the standard start

35.6%

dealt only a 2-card hand

0.009%

the dealt nuts A-2-3-4 — once per ~11,200 hands

Holding off the deal	Odds	Holding off the deal	Odds
pat badugi, any	6.34%	3-card hand	57.05%
pat T-badugi or better	1.86%	3-card hand with an ace	16.09%
pat 8-badugi or better	0.62%	2-card hand	35.55%
pat 6-badugi or better	0.13%	1-card hand	1.06%
the nut badugi A-2-3-4	0.009%	at least one ace	28.13%
premium: 5-high tri or any badugi	9.40%

What the table holds against you

200,000 simulated deals per table size, card removal honored. “Premium” is a 5-high three-card hand or any pat badugi.

Opponents	≥1 pat badugi	≥1 pat 8-badugi	≥1 premium	Pat badugis out there
1	6.4%	0.6%	9.5%	none 94% · one 6.4%
2	12.2%	1.2%	17.8%	none 88% · one 12% · both 0.4%
3	17.8%	1.8%	25.7%	none 82% · one 17% · two 1.1%
4	22.9%	2.5%	32.6%	none 77% · one 21% · two 2.2%
5	27.9%	3.1%	39.1%	none 72% · one 24% · two 3.4%

At 6-max, 28% of deals put a pat badugi behind you — but only 3% put a pat 8 or better out there. Most pats you run into are rough Q-J-T material: respect the pat, not the hand.

Draw counts telegraph everything in this game — the sheet pairs with the trainer’s draw-history displays.

Should you stand pat?

Second draw is done: you’re in position with a pat badugi and everyone drawing missed. If you stand pat, these are the exact odds a tri completes into a badugi that beats yours on the final draw. Heads Up: one opponent, outs over 45 unseen cards. Vs. 2 Opponents: both opponents hold the listed tri type and each catches one card — the odds at least one gets there.

You stand pat with	vs 7-6-2 tri	vs 6-3-2 tri	vs 5-3-2 tri
8-4-2-A	8.9%4 outs: A·3·4·5	8.9%4 outs: A·4·5·7	8.9%4 outs: A·4·6·7
7-6-2-A	0 outschop only	6.7%3 outs: A·4·5	8.9%4 outs: A·4·6·7
6-4-2-A	drawing dead	2.2%1 outs: A	4.4%2 outs: A·4
5-4-2-A	drawing dead	drawing dead	2.2%1 outs: A

You stand pat with	vs 7-6-2 tri	vs 6-3-2 tri	vs 5-3-2 tri
8-4-2-A	16.0%both get there: 0.7%	16.0%both get there: 0.7%	16.0%both get there: 0.7%
7-6-2-A	0 outschop only	11.6%both get there: 0.3%	16.0%both get there: 0.7%
6-4-2-A	drawing dead	2.4%both get there: 0.0%	7.0%both get there: 0.1%
5-4-2-A	drawing dead	drawing dead	2.4%both get there: 0.0%

This table is why pat badugis print money: the drawing hand needs one specific suit and a non-pairing rank that also beats you, so even the roughest pat here — 8-4-2-A — never faces worse than 8.9% heads-up or 16.0% against two live tris. A pat 7-6-2-A is literally unbeatable by the same-rank 7-6-2 draw (best case: chop), and a pat 5-4-2-A concedes exactly one out in the whole deck.

Outs are cards of the tri’s one missing suit whose rank neither pairs the tri nor loses to your pat. Chops are not counted as outdraws. Exact enumeration — no simulation noise.

Every starting shape, ranked

All 167 classes — every pat badugi over A-8 (plus A-2-3 with each broadway top), and every 3-, 2-, and 1-card keep — 10,000 showdowns each, heads-up versus a random hand.

The pat line is sharper than it looks: every pat 9-badugi or better (A239, 90.9%) beats every drawing hand, and even pat A23J wins 78.1%. But a king-top pat is barely a hand — A23K (58.0%) ranks below more than forty three-card draws, with A23X (68.5%) well ahead of it. And the floor is high: the worst one-card salvage still wins ~43%, because in Badugi everyone is usually drawing. Add opponents and the king-top pat finishes the collapse: 6-handed, A23K is the single worst holding on the sheet at 6.5% — below every bare one-card hand — while the nut A234 barely notices five opponents (99.7%).

Method: hero’s first draw discards exactly the dead cards; later draws follow the frozen rollout heuristic on both sides, no betting, ties split. ±0.5pt noise per figure. Generated by the engine that trained the app’s blueprints.