written by Matt Flynn DeucesCracked Contributor
published over 2 years ago

A call came in a few months ago on a Wednesday. “Hey, Doc, we got a badugi game Friday. Come play. Blinds start at $200-$400. Should be a full table.”

The game had been going for a couple of weeks. Several of the regulars were familiar to me. They were players, guys who had paper bags of money and no fear. It sounded great. There was just one problem: I’d never played badugi.

“Sure, see you Friday.”

After work and family, there were only a few hours left to analyze the game. What would you do if you’d never played badugi before and were heading into a $200-$400 game?

I tapped 2+2 and called TT. He generously gave me a bunch of pointers. That helped get me thinking.

General Concepts

Limit badugi is simple as poker games go. In many ways it plays like Omaha. Usually when you get it you should bet it, so there’s not much checkraising. Position counts, especially in shorthanded pots. In loose games, you’ll get enormous pots and typically need to make the best hand to win. And, once the pots get big, drawing cannot be a serious error provided no one is likely to have a low badugi.

Badugi plays straightforwardly before the first draw. Other than blind stealing from late position, in general in 8-handed games you play your hand.

After the first draw, bluffing plays a major role. The classic bluff is raising or reraising after the second draw to encourage an opponent to fold a badugi. For example, your opponent bets after the second draw, and you raise. Suppose he caught a queen badugi. You either have him crushed or you’re bluffing. If he started with A45, he might call and pitch the queen, hoping to catch a better badugi. Alternatively, suppose he has A45-blank. If the odds are sufficient, he will call. When he pitches one, you can stand pat, representing a badugi. Your opponent may then check-fold the river if he fails to improve. Your bluff only has to succeed a modest fraction of the time in large pots to make it worthwhile. Reversing that shows why you should sometimes keep any badugi when raised after the second draw. You should also call down with good tri hands against opponents who snow. Don’t let them bluff you into the poorhouse.

Position helps tremendously when bluffing in badugi. With position, you learn how many cards your opponents draw before you act. If instead you are out of position and facing a potential bluff raise, you must decide whether to break weak badugis or fold modest tri hands before you see what your opponent does.

Starting Hand Probabilities

There are (52 choose 4) = 270,725 possible starting hands in badugi. There are 17,160 badugis. Overall, dealt badugis are uncommon, so you must play and raise with tri hands.

Here’s how they break down:

Badugi Rank Ways % of Deals Odds Against
Any 4 24 0.0089 11279-to-1
Any 5 96 0.035 2819-to-1
Any 6 240 0.089 1127-to-1
Any 7 480 0.177 563-to-1
Any 8 840 0.31 321-to-1
Any 9 1344 0.496 200-to-1
Any 10 2016 0.745 133-to-1
Any J 2880 1.064 93-to-1
Any Q 3960 1.463 67-to-1
Any K 5280 1.95 50-to-1
Any badugi 17160 6.339% 14.8-to-1

Here it is in cumulative form:

Badugi Rank Ways % of Deals Odds Against
4 24 0.0089 11,279-to-1
5 or better 120 0.044 2,255-to-1
6 or better 360 0.133 751-to-1
7 or better 840 0.31 321-to-1
8 or better 1680 0.621 160-to-1
9 or better 3024 1.117 88.5-to-1
10 or better 5040 1.862 52.7-to-1
J or better 7920 2.925 33.2-to-1
Q or better 11880 4.388 21.8-to-1
K or better 17160 6.339 14.8-to-1

For comparison, in hold ‘em you’ll be dealt aces 0.45% of the time. Any badugi 7-high or better is about as rare as aces in hold ‘em. 8-high badugis or better are about as rare as aces or kings. If you wait around for a pat 8 or better on the deal, you cannot win.

A dealt 7-high or better badugi is a monster. When you get one, you should normally cap the betting. A dealt 8- or 9-badugi is still strong. Once you get to 10-badugis and higher, you are much more vulnerable to being outdrawn.

Over half the dealt badugis are queen-high or king-high. Watch carefully to learn when your opponent will keep a dealt queen or king badugi. Together these hands form 3.4% of an opponent’s starting hands and a far higher percentage of his potential raising hands. If you can accurately eliminate them from his range, you gain a huge advantage.

If no one makes a badugi, the best three-card hand (“tri hand”) wins the pot. This is a critical difference from other triple-draw games like deuce-to-seven lowball. By definition, if you have a tri hand, you cannot have a badugi. Here are the probabilities of being dealt tri hands, courtesy of Mark Roh:

Tri Rank % of Deals Odds Against
A23 0.332 300-to-1
Any 3 to a 4 0.944 105-to-1
Any 3 to a 5 1.78 55.1-to-1
Any 3 to a 6 2.79 34.8-to-1
Any 3 to a 7 3.92 24.5-to-1
Any 3 to an 8 5.12 18.5-to-1
Any 3 to a 9 6.33 14.8-to-1
Any 3 to a 10 7.5 12.3-to-1
Any 3 to a J 8.58 10.7-to-1
Any 3 to a Q 9.51 9.52-to-1
Any 3 to a K 10.24 8.77-to-1
Any tri hand 57.05 0.753-to-1

Here are the tri hands in cumulative form:

Tri Rank % of Deals Odds Against
A23 0.332 300-to-1
3 to a 4 or better 1.28 77.3-to-1
3 to a 5 or better 3.06 31.7-to-1
3 to a 6 or better 5.85 16.1-to-1
3 to a 7 or better 9.77 9.23-to-1
3 to an 8 or better 14.9 5.71-to-1
3 to a 9 or better 21.2 3.71-to-1
3 to a 10 or better 28.7 2.48-to-1
3 to a J or better 37.3 1.68-to-1
3 to a Q or better 46.8 1.14-to-1
3 to a K or better 57.05 0.753-to-1

Any tri hand is a dog to any queen badugi or better. Technically a tri hand can be a slight favorite over a king badugi. In practice that’s not too relevant, because the player with the tri hand must know to hold if he makes a king badugi on any street. For example, imagine a straightforward opponent with position has reraised on the deal and discarded none. It’s extremely likely he has a badugi. Now you make an A23K badugi on the first draw. Should you hold? Often not, because your opponent will have a weaker king badugi less than a third of the time even if he always plays his king badugis.

In an 8-handed game, 3 to a 5 is a strong starting hand. Your default is to raise, especially from middle and late position and if your opponents will discard dealt king and queen badugis. You can also call raises with 3 to a 5. However, you should often not reraise 8-handed unless you likely have the best hand or can sometimes force opponents to break weak badugis to tri-hands weaker than yours, either immediately or later in the hand. You are a dog to a better tri or any queen badugi.

An average 3 to a 6 will be the best starting hand around half the time in an 8-handed game. It will be the best non-badugi over two-thirds of the time. Under the gun you might well fold all but A26 (and even that under some game conditions), but after a couple players fold, you can raise profitably with A36 and 236, especially if you have a chance of taking the blinds.

Three to a 7 is only playable if you are raising in part to steal the blinds or your 7-tri has two of A23. You would for sure raise a strong seven-tri first in from the cutoff, and weak sevens first in from the button and small blind. Unless you have a good reason to do otherwise, fold three to a seven in early or mid position. If the button or small blind reraises first in, you would call or reraise with it, assuming the raiser opens with a wide range of hands from those positions.

Three to an 8 does not play well in 8-handed games. It suffers from negative implied odds against made badugis and better tri hands. Each remaining opponent will have roughly a 1 in 6 chance of having A28 beat, either with a badugi or a better tri hand. Further, they can easily hit a better tri. Your default is to fold in early and middle position. If you are first in, raise a strong eight from the button and any eight from the small blind. If the blinds are tight, you might move those positions back one. In general, taking down the blinds is what makes the button raise profitable.

Blind stealing can play a major role in badugi. If your three remaining opponents will fold unless they have a badugi or 3 to a 7 or better, you nearly break even from the CUTOFF on stealing the blinds alone. So you should raise with a huge range of hands until they wise up. This is one reason you should play many two-card hands out of the blinds against a solitary late-position raiser.

If two players enter a raised pot, you should normally fold 3 to an 8, even for one bet in the big blind. If the preflop raiser is tight with raises, you might fold 3 to a 7 and 3 to a 6 too, particularly if you did not think worse hands would come in behind you. In a single-raised multiway pot, if dealt A28 or A38, you would still play the big blind and sometimes from the small blind or button.

As in hold ‘em, preflop play depends heavily on the action. Many hands that should fold to early position raises and reraises should raise when first-in from the cutoff, button, and small blind. Some should also reraise a late position opening raise.

The blinds play differently depending on where the initial raise was made and how many players are in the pot. Against a late position single raise from a loose opener, you should at least call with the best two-card hands A2, A3, 23 and sometimes much weaker, any three to a 7 unless the raiser is tight, and three to an eight against a loose raiser, and any badugi. Generally you should reraise with a badugi and any tri hand with 3 to a 5 or better. Against a loose raiser you might reraise with a strong 3 to a 6. Also, against a single preflop raiser, you can consider reraising on a stone bluff, draw no cards, and fire all the way down, strongly representing a badugi.

Here are the overall starting hand frequencies:

Starting Hand % of Deals Odds Against
Any badugi 6.34 14.77-to-1
Any tri 57.05 0.753-to-1
Two card hands 35.55 1.81-to-1
One card hands 1.06 93.23-to-1

My First Game

Friday night after work I headed on to the game after confirming it was $200-$400. I had calculated a few draw probabilities to go with the above charts and took a printout with me.

When I got there an hour later, the game had already been going a few hours. They pulled the old bait-and-switch: “Sorry Doc, it’s 5-handed $500-$500 with a $1,000 straddle.”

It took an orbit to learn I was a favorite and another to realize it didn’t matter much. Variance runs high in this game. They ended up getting me for 15 dimes, but at least the hot dogs were free.

I love badugi.