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Badugi: An Introduction

by Kevin Haney |  Published: Mar 11, 2020

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Badugi is a very unique poker variant with a slick name to boot. As in Deuce-to-Seven Triple Draw Lowball (27TD) the game is played with blinds and there are three draws, however, each player is only dealt four cards instead of five. The object of the game is to obtain the lowest hand possible with cards of all different suits and ranks. If you hold four different ranks with all different suits you have made a badugi. For example, 8Diamond Suit 6Club Suit 5Heart Suit 2Spade Suit is an eight badugi. Aces are considered low so the best possible holding is A-2-3-4 of all different suits.

When you do not hold four different ranks of different suits your hand is considered “incomplete.” At showdown if your hand is 8♥ 6♣ 5♥ 2♠ you do not have an eight badugi, you have what is identified as either a “six high tri” or a “three-card six.”

Sometimes you may only be able to showdown two cards; 8♥ 6♥ 5♥ 2♠ is simply a two-card hand. To my knowledge, a two-card hand has no special term associated with it. I tend to simply refer to this holding as nothing; for example, “Nice call, I have nothing.”

Any badugi beats any tri hand, for example K♥ Q♣ J♦ 10♠ will take the money if your opponent rolls over A♦ 2♠ 3♣ 4♣ at showdown. It happens very rarely, but A♦ 2♠ 3♣ 4♣ would chop the pot with A♥ 2♣ 3♦ 10♥. In this case both players are playing the best possible three-card hand A-2-3; the fourth card has no relevance if it does not make a badugi.

Some Basic Math And Intricacies Of Badugi

Consider a hand where one player starts out with the worst possible badugi K♦ Q♣ J♥ 10♠ while the other holds the best possible draw of A♦ 2♠ 3♣ 4♣. The A♦ 2♠ 3♣ 4♣ will discard the 4♣ and attempt to draw a heart that is not an ace, deuce, or three and any of these remaining nine hearts will make the best hand. On any particular draw there is around a 20 percent chance of this occurring and over the course of all three draws the “hot/cold” equities are almost exactly 50/50.

However, at some point in the hand the A♦ 2♠ 3♣ may elect to raise and put the weak badugi to the test sometimes succeeding in getting it to fold. And sometimes the player drawing will make a reasonable decision to discard the K♥ or Q♥ along the way and in the process break a hand that would have been best. As is most often the case, simulation equities don’t always tell the entire story and playability aspects must also be considered.

A-2-3 is the best possible drawing hand but much rougher tri hands such as 6-7-9 also have 50 percent equity against a K♦ Q♣ J♥ 10♠ badugi. However, this does not mean we should often be contesting the pot with hands like 6♦ 7♣ 9♠ as these hands perform quite ineffectively against better three-card badugis. The reason for this is that in Badugi the best drawing hand is also the best made hand.

For example, with one draw to go the A♦ 2♠ 3♣ is around an 81 percent favorite regardless if it is up against 2♦ 4♣ 5♠ or 6♦ 7♣ 9♠. Still we would much rather have the 2♦ 4♣ 5♠ in this matchup as it can make very strong badugis while the 6♦ 7♣ 9♠ is capped at a nine. When we make a very strong badugi we can lead out and often three-bet the river for value, however, if we bet a rough nine badugi and get raised we would only have only a call.

And when our opponent’s holding is unknown it’s certainly preferable to have the 2Diamond Suit 4Club Suit 5Spade Suit as it has a reasonable chance to be the best hand even when faced with aggression from an opponent. For example, suppose you open 2Diamond Suit 4Club Suit 5Spade Suit from the cut-off and are re-raised by the button. The vast majority of players will re-raise when they have ADiamond Suit 2Spade Suit 3Club Suit or slightly worse hands such as ADiamond Suit 3Club Suit 6Spade Suit and are correct to do so. The 2Diamond Suit 4Club Suit 5Spade Suit is around a 77 percent favorite over ADiamond Suit 3Club Suit 6Spade Suit which is slightly lower than 80 percent because the latter hand has the possibility of making the best hand when it draws either the 2Spade Suit or 4Spade Suit. This is referred to as “reducing your incomplete.”

Many turn situations in Badugi are close, for example when holding a five high tri or a smooth six we may not know where we stand. In these somewhat murky situations we should tend to bet if we are the aggressor and when we aren’t we should most often continue on in the hand due to current and possible implied odds. Folding the best hand is a big equity mistake and even when holding the second-best hand we may have a few extra outs available by reducing our incomplete.

The turn situation is much clearer if we happen to be in the hand with a rough holding such as 5Diamond Suit 7Club Suit 8Spade Suit. Here we have very little chance of holding the best hand and reducing our incomplete will almost never help. In addition, if our opponent made a badugi on the second draw we can easily be drawing dead. Always continuing on with weak three card badugis is a sizeable leak especially if the pot isn’t that big.

The best drawing hand also being the best made hand is a unique feature of Badugi; in 27TD the last card means everything and thus the equities with just one draw to go run much closer. For instance, in 27TD the best possible draw of 2-3-4-7 is only around a 55 percent favorite over a much inferior 3-5-6-8. This means we should continue on the turn more often in 27TD even if your draw is mediocre.

How A Badugi Is Obtained Greatly Impacts Its Strength

We are dealt a badugi around 6.3 percent of the time which is approximately the same probability of being dealt a pocket pair in hold’em. It is very rare to be dealt a very strong badugi from the jump; in fact more than 50 percent of initial pat badugis are either queen or king high. Thus, if someone is pat on the first draw and has all badugis in their range (given their playing style and/or position at the table) their median holding is a queen badugi.

Contrast this situation with a player drawing one to the ADiamond Suit 3Club Suit 6Spade Suit. In this case ten different hearts (2Heart Suit, 4Heart Suit, 5Heart Suit, 7Heart Suit, 8Heart Suit, 9Heart Suit, 10Heart Suit, JHeart Suit, QHeart Suit, KHeart Suit) will make a badugi and each of these cards is equally likely to be obtained. Five of them will make an eight badugi or lower while the other five make higher badugis. Thus, when someone acquires a badugi via drawing one their median holding is an eight or nine which is a much stronger holding than the average initial pat badugi.

And when someone draws two to a smooth holding such as ADiamond Suit 2Club Suit and makes a pat right away on the first draw their median badugi strength is a rough ten.

These concepts are among the most important you will learn in badugi. The manner in which a badugi was acquired greatly impacts your opponent’s range and correspondingly impacts many of the decisions we will make on the later streets.

On the surface badugi appears to be a very simplistic game in which whoever runs the best will scoop the chips. Luck does indeed play a large role in any particular hand; however, there is certainly a great deal of skill and nuance in this variant. ♠

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 haneyk612@gmail.com.