Mastering Badugi Part 2 – Badugi Essentials

Last month we received an introduction to the exciting game of Badugi and walked through some sample hands.  Building your poker game is very similar to constructing a house. A solid foundation of fundamentals is crucial so this month’s article works from the ground up and examines the key fundamentals of Badugi.  The first essential is a thorough knowledge of the hands that you are dealt.  Before the first draw, the probability of being dealt certain type of hands is as follows:

Badugi 6.3%
Tri 57.0%
2 Card 35.6%
1 Card 1.1%


Distribution of Badugis

You are dealt a badugi around 6.3% of the time which is about as often as getting a pocket pair in hold’em.  There are 715 different badugis where the frequency of getting dealt specific badugis is as follows:

Cumulative Cumulative
# Hands % of Badugis % of Badugis % of Overall Hands Dealt % of Overall Hands Dealt
4 High 1 0% 0% 0.0% 0.01%
5 High 4 1% 1% 0.0% 0.04%
6 High 10 1% 2% 0.1% 0.13%
7 High 20 3% 5% 0.2% 0.31%
8 High 35 5% 10% 0.3% 0.62%
9 High 56 8% 18% 0.5% 1.11%
10 High 84 12% 29% 0.7% 1.85%
J High 120 17% 46% 1.1% 2.91%
Q High 165 23% 69% 1.5% 4.36%
K High 220 31% 100% 1.9% 6.30%
              715 100% 6.3%

As the chart indicates, more than half of the initial badugis are either Queen or King high.  The median dealt badugi is around a Q7.  You get dealt a 7 high or better badugi less than you would pocket aces in hold’em.

Badugi is somewhat of a paradoxical game in that the object of the game is to obtain a badugi but you typically don’t want to be dealt one right away. That’s because initially dealt badugis are usually not very strong and weaker badugis are only slight favorites over tri hands and are big money losers in a multi-way field.  Strong players correctly fold queen or king badugis in early position so it is useful to examine a badugi distribution when we exclude queens and kings:

% of Jack or Cumulative
# Hands Better Badugis Cumulative % % of Overall Hands Dealt % of Overall Hands Dealt
4 High 1 0% 0% 0.01% 0.01%
5 High 4 1% 2% 0.04% 0.04%
6 High 10 3% 5% 0.09% 0.13%
7 High 20 6% 11% 0.18% 0.31%
8 High 35 11% 21% 0.31% 0.62%
9 High 56 17% 38% 0.49% 1.11%
10 High 84 25% 64% 0.74% 1.85%
J High 120 36% 100% 1.06% 2.91%
              330 100% 2.91%

When you exclude king and queen badugis, more than half of the badugis will now be jacks or tens with a median of around a T7.  So if you know a tighter player would be folding queens or kings in a particular situation you should put him on a ten badugi until further evidence comes to light that would cause you to reevaluate.

Distribution of Three Card Badugis (Tri Hands)

You are dealt a three card badugi or tri hand around 57% of the time but the vast majority will be unplayable. You should probably never enter the pot with a ten high tri or higher trying to make a badugi.

However, the good three card starts are the bread and butter hands in Badugi.  If you have the best tri hand you can confidently bet your hand for both value and protection and almost always realize your equity.  The following chart summarizes the frequency of dealt three card badugis:

Cumulative Cumulative
# Hands % of Tris % of Tris % of Overall Hands Dealt % of Overall Hands Dealt
3 High 39 1% 1% 0.5% 0.5%
4 High 108 2% 3% 1.3% 1.8%
5 High 198 4% 7% 2.4% 4.2%
6 High 300 6% 14% 3.6% 7.8%
7 High 405 9% 22% 4.9% 12.7%
8 High 504 11% 33% 6.1% 18.8%
9 High 588 12% 45% 7.1% 25.9%
10 High 648 14% 59% 7.8% 33.7%
J High 675 14% 73% 8.2% 41.9%
Q High 660 14% 87% 8.0% 49.8%
K High 594 13% 100% 7.2% 57.0%
                 4,719 100% 57.0%


Two Card Hands

You are dealt a two card hand around 35.6% of the time, the strongest of which are useful for stealing blinds and defending them.  However many players will religiously play ‘A2’ in any situation.  This appears to be a substantial leak as there can be difficulty in realizing equity and one can make the case that you will probably experience reverse implied odds. Next article will take a closer look at playing ‘A2’.

The distribution of the two card hands is shown below.  It only extends down to ‘56’ as you would hardly ever consider playing anything worse.

% of Overall Hands Dealt % of Overall Hands Dealt
A2 1.7% 1.7%
A3 1.5% 3.2%
23 1.5% 4.7%
A4 1.3% 6.0%
24 1.3% 7.3%
34 1.3% 8.5%
A5 1.1% 9.6%
25 1.1% 10.7%
35 1.1% 11.7%
45 1.1% 12.8%
A6 0.9% 13.6%
26 0.9% 14.5%
36 0.9% 15.4%
46 0.9% 16.3%
56 0.9% 17.1%


Key Badugi Facts

Now that we know how often we are dealt certain type of hands, let’s move on to some important Badugi facts and concepts that impact the overall strategic view of the game and guide your play within a hand:

  1. Odds of Drawing a Badugi

On the first draw, if you have a three card badugi there are ten cards that will make you a badugi among forty-eight unseen cards.  Thus the odds are (10/48) or approximately 21% chance that you will make a badugi on the first draw.  If you do not acquire a badugi on the first draw the odds are then (10/47) on the second draw and (10/46) on the third.

The odds that you will not acquire a badugi over three draws is (38/48)*(37/47)*(36/46) = 49% so over the course of three draws you have around a 51% chance to obtain a badugi.

Hold’em has lots of pre-flop all ins that are called coin flips but the pocket pair is actually a solid favorite (around 55%) over an unpaired hand.  A23 vs KQJT is the real coinflip as it is almost exactly 50/50.

  1. Average Dealt Pat Badugi is a Queen

This is an important concept that we learned earlier but its importance bears repeating.  More than half of dealt pat badugis are kings or queens and the median is a good queen.  If a player has a tighter badugi range of jacks or better, more than half are jacks and tens and the median is around a T7.

  1. Average Drawn Badugi is Usually a Strong Hand

Ten different cards will give an A23 a badugi.  50% of them will make an 8 badugi or better.  Thus if someone pats after drawing a card you must take into consideration that mathematically they have (or are at least trying to represent that they do) a stronger range than a dealt pat badugi.  So you must evaluate your situation and pot odds assuming they have around an eight or nine badugi.  Of course you must also consider the chances they are snowing.

  1. Improvement is Possible Without Making a Badugi

It is possible to improve your hand without making a badugi.  For example if you are holding A♠ 2 6, in addition to your ten badugi outs you could also draw the 3, 4, or 5 which would give you a stronger tri hand.  This is called reducing your incomplete.

Thus in this case you have a (13/48) or 27% chance of improving your hand.  So it is important to note that your lowest two cards have some significance.  In some situations after the 2nd draw it can mean the difference between a fold and a call if you believe there is a chance you could possibly win by reducing your incomplete.

  1. A Weak Badugi is a Big Underdog in a Multiway Pot

When two players holding tri hands take three draws at least one of them will make a badugi around 75% of the time.  With three players the odds are around 88%.  The odds are stacked against weak badugis so extreme caution should be taken to avoid playing them in multiway pots.

  1. Odds of Improving A2 (and Other Two Card Draws)

If you have A♠ 2♣, you have six cards (3, 3, 4, 4, 5, 5) that will give you a five high tri hand or better.  With two discards the odds are around 20% that you will get one of these cards.  Six other cards will give you a six through eight three card badugi.  Thus around 40% of the time you will improve to an eight or better tri hand.

10% of the time you will obtain a badugi, however, the mean badugi obtained when drawing two is only a T9.  The relevance of this fact is that A2 (and other two card draws) hands may have less implied odds than many players think.  They may think they hit gin but if an opponent holding a tri hand improved as well chances are better than average that it would be of the bathtub variety.

  1. With One Draw Left, the Better Hand is a Huge Favorite

A tri hand that is chasing a badugi has at most ten outs or a 22% chance of making the best hand.

In a battle of tri versus tri, the better hand is also a huge favorite with one draw to go.  An A23 is around an 81% favorite over both an A24 and 678 thus having the second best tri is a bad place to be with only one draw to go.  This means that the A23 has a clear bet on the turn even with an incomplete hand.

In 2-7 Triple Draw Lowball, equities between two drawing hands with one draw left is a lot closer.  For example, a 2347 is only a 55% favorite over 8653 with one draw left.  Therefore playing after the 2nd draw will be dramatically different between the games.

Admittedly this month’s article may not have been the most exciting piece of work but we laid the necessary groundwork required to begin a discussion on more advanced strategies.  Next month we will begin to formulate our strategy before the first draw.