Badugi: A Discussion On Two-Card Draws

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Poker games evolve over the years and Badugi is no exception. Back when it was originally introduced, Badugi was often played in a relatively straight forward fashion. Most players contesting the pot were in there with either pat badugis or tri hands attempting to complete a badugi. Two-card draws, like A 2, were primarily only played when stealing or defending blinds.

Inexperienced players may not have realized that making a badugi was as hard as it is and may have given more respect to river bets than they should have. They would often only call the river with a badugi and sometimes even fold made, but bad badugis. It was relatively common to see the river check through even when both players held good three-card badugis!

Nowadays in an aggressive game you will hardly ever see the river check through when there are two relatively strong tris out such as A-2-4 and A-3-5. The A-2-4 will often bet for value if the A-3-5 hadn’t already done so. It is not uncommon to see call downs with A-5-6 or worse.

Many players now consider Badugi a race to the best three-card badugi and there is an increased prevalence of players entering the pot with two-card draws (D2s) such as A-2, A-3, 2-3, and A-4 from all positions. When a strong tri is obtained these players will get aggressive looking for max value and will continue searching for it on the river even without a Badugi.

Others are just addicted to the action and love the thrill of going uphill and putting some bad beats on their opponents and these players will often call multiple bets cold with their two-card draws.

Since we can often successfully value bet the river with premium tri hands the value of D2s has increased but as with any aspect of poker and life it’s best to not go too far overboard. In this issue we will analyze two-card draws, the good and the bad, and see if we can draw any conclusions.

Improvement Probabilities

When we start out with A 2 4 6 and draw two the chances of improving are as follows:

As the chart above indicates this hand has a 51 percent chance to improve to an 8 tri or better with a 10 percent chance of making a Badugi, the median badugi made being an A-2-9-10. These are decent odds to improve, however 49 percent of the time you will still have nothing and three-card sevens and eights are quite mediocre. Over the course of two draws you will have an unimproved A-2 approximately 24 percent of the time and will be hard pressed to continue on the turn.

The A 2 4 6 is one of the strongest two-card draws in that it does not block any of its own outs and also has a decent chance to block one of the low spades that our opponent may need. When our opponent requires a spade we hold significant blockers against them making a strong hand.

With a hand such as A 2 9 10 (and drawing two) we block two of our own outs to make a badugi and do not block opponents from making their strongest hands. When blocking a few of our outs we will only make a badugi around 8.6 percent of the time on the first draw; a slight reduction but still noteworthy.

Now suppose on the first draw we improve to A 2 7 and are chasing a jack Badugi. Since we discarded two of the cards we need we may now only have five outs instead of seven which is a somewhat significant 29 percent reduction. And making a tri and then drawing one is the typical route you will take when making a badugi.

The other cards in our hand are not often considered by players. However, details such as this should be factored into our decision making especially in the closer situations.

Sampling of Equities and Playability Considerations

A dealt Badugi is the two-card draw’s Achilles heel; the following are “hot/cold” equities at the beginning of the hand against various pats:

As bad as those equities are will actually fare even worse in actual game play as the two-card draws will struggle to realize their equity. While an initial dealt badugi is usually on the weaker side we still must improve early on the hand in order to remain in the pot. On the first draw when we don’t improve to at least a three-card eight or nine it is really an uphill battle with two draws to go:

A-2 is a sizeable underdog to mediocre tri hands and from a “hot/cold” perspective is also taking the worst of it against the worst three-card eight:

Once again, we also must improve in order to realize our equity and while we will often make a good three-card hand we should not overrate our implied odds. Your opponent drawing one card has around a 20 percent chance of hitting a badugi of which the median is an eight or a nine. When you hold an A-2, you have around a 10 percent chance to hit a badugi of which the median is around a 10-9. Thus, he’s twice as likely to improve to a badugi and when he does it will be stronger on average. In any form of poker, your opponent is in a commanding position when he has both the best hand and best draw.

Two card draws are also quite mediocre in multi-way pots. The value of drawing to a good three card is greatly diminished when it’s possible someone already has a badugi or when you are up against two one card draws because the odds of at least one of them making a Badugi by the end is around 75 percent.

As previously discussed, when playing D2s the two discards can have a big impact on the overall strength of your hand. For example, 2 3 4 6 is a better holding than A 2 9 10 because if your opponent requires a spade you have blockers against his hand while at the same time you are not blocking cards that you may need to win the pot. Below are a few sample equities that demonstrate the blocker effect:

When up against a three-card Badugi without a spade or a Badugi we fare much better with a hand such as 2 3 4 6. The times our opponent has a tri with a spade both hands are approximately equal, however, when holding three low spades it is more likely villain does not have one.

Concluding Thoughts

Two-card draws do not fare that well at all versus pat hands or in multi-way pots thus we should not get in the habit of playing them from early position or cold-calling a three-bet which is a huge leak. Most often these holdings should be reserved as opens from late position or when defending the big blind preferably against a single opponent.

However, given the good pot odds we are getting we can usually defend the big blind against a raise and a call especially against loose players who will often be drawing two themselves. That said one situation where we should tend to muck is when we are specifically up against an early position open followed by another call. Here we are often up against a pat and a D1 or at the very minimum two solid D1s. If the situation seems close the other two cards in your hand can act as a tiebreaker.

Since the two discards impact the value of your holding it would be a mistake to compile your opening hand standards in such a way where you may open A-2 and A-3 from a particular position but fold hands such as 2 3 4 6 that are better than your average A-2 holding. In the next installment on Badugi we will present a set of suggested openings for all hand types. ♠

Kevin Haney is a former actuary of MetLife but left the corporate job to focus on his passions for poker and fitness. He is co-owner of Elite Fitness Club in Oceanport, NJ and is a certified personal trainer. With regards to poker he got his start way back in 2003 and particularly enjoys taking new players interested in mixed games under his wing and quickly making them proficient in all variants. His new mixed-games website Counting Outs is a great starting resource for a plethora of games ranging from the traditional to the exotic. He can be reached at [email protected].