Deuce to Seven Triple Draw Lowball: Power Ratings for Two-Card Draws

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Check out Haney’s Introduction to Triple Draw Lowball here.

Most of your starting hands in Deuce-to-Seven Triple Draw Lowball (27TD) are the two-card draws. Among 27TD players there is often a difference in opinions on how strong some of these various holdings are and from what position at the table they are playable.

For example, how strong is the 2-5-6, and is it a profitable under-the-gun open in a six-handed game? In what situations should we play 3-4-5? The deuce is an incredibly important card in 27TD and the 3-4-5 does not have one, so how valuable is this holding given that it still has three other good low cards? Finally, what about other types of hands such as 2-7-8, 3-4-6, and 4-5-8?

In a game such as limit hold’em you can conduct an empirical analysis using a database of results from one of the various tracking software packages. Since there are not that many different hand combinations, one can examine the results of winning players who have played hundreds of thousands of hands and readily observe how profitable (or unprofitable) different hands are from each position. We can then use this information to formulate pretty well-defined opening round strategies.

Software packages are available for 27TD but to my knowledge no databases of results have ever been shared publicly. If anyone has any to share it would be great to compare those results with the conclusions presented in this article. If we cannot utilize empirical studies, we must look to other ways to ascertain the value of the two-card draws.

Proposed Methodology For Ranking Hands

In an attempt to rank the various holdings, we will consider the following four factors:

• Strength of Potential Hands Made (Among eight or better lows)
• This will be used to calculate the Relative Rank Adjustment
• Number of Eight or Better Lows Possible
• 2-3-7 can make six different eight or better lows while starting holdings such as 4-5-7 and 2-4-5 can only make four and five respectively
• The latter hands make fewer eight or better lows due to straight possibilities
• Whether Or Not The Holding Has A Deuce
• Whether Or Not The Holding Has Either a Seven Or An Eight

For each of the four factors above we will compute a percentage (from 0-100 percent) and then multiply all four of them together to arrive at a final factor. The higher the resulting percentage the more value a particular two-card draw has according to this methodology.

Relative Rank Adjustment

The Relative Rank Adjustment rates holdings based on the various eight or better lows they can make ranging from no. 1 (7-5-4-3-2) to no. 18 (8-7-6-5-3). In this regard the 2-3-4 is the best holding because on average it will makes the strongest lows:

Hand Rank
7-5-4-3-2 1
7-6-4-3-2 2
8-5-4-3-2 5
8-6-4-3-2 6
8-7-4-3-2 10
Average Rank 4.8

It can make the two strongest hands in the game [no. 1 (7-5-4-3-2) and no. 2 (7-6-4-3-2)] and the worst holding among the eight or better hands is no. 10 (8-7-4-3-2) resulting in an average rank of 4.8. However, the 2-3-4 only makes five different eight or better lows because the 56 combination is a six-high straight and this slight handicap will be accounted for in the next step.

2-3-7 is generally regarded to be on par with 2-3-4 in regards to overall starting hand strength because it has the three best cards and cannot make a straight. However, it is hampered somewhat in average rank strength due to the times it catches an eight and is thus capped at an 8-7 low: In these rankings we assume that any improvement towards an eight low is kept and in game play this is almost always the case.

Hand Rank
7-5-4-3-2 1
7-6-4-3-2 2
7-6-5-3-2 3
8-7-4-3-2 10
8-7-5-3-2 11
8-7-6-3-2 14
Average Rank 6.8

As you can see the 2-3-7 will on average make slightly worse hands, however, it has the ability to make six different eight-or-better lows.

And a marginal starting hand such as 3-5-8 will yield a much lower average rank of made hands:

Hand Rank
8-5-4-3-2 5
8-6-5-3-2 7
8-6-5-4-3 9
8-7-5-3-2 11
8-7-5-4-3 13
8-7-6-5-3 18
Average Rank 10.5

Since the 2-3-4 makes the strongest hands (Average Rank of 4.8) it is considered the “gold standard” upon which to rank all of the other holdings and receives a Relative Rank Adjustment of 100 percent. To arrive at the Relative Rank Adjustments for all other holdings you would divide 4.8 by the average rank for that particular holding. For example, 2-3-7 would have a Relative Rank Adjustment of 70 percent (4.8/6.8) and 3-5-8 would be 46 percent (4.8/10.5).

Number Of Eight-Or-Better Lows Adjustment

This adjustment penalizes a hand for potentially having reduced outs due to straight draws. Starting hands such as 2-5-7, 2-4-8, and 3-7-8 cannot make a straight and thus have the ability to complete six different eight-or-better lows. These starting hands and all others where potential straights are not a factor have an adjustment factor of 100 percent.

Holdings such as 2-3-4 and 3-4-5 with straight potential are penalized. The 2-3-4 can possibly finish with five different eight or better lows thus it has an adjustment of 83 percent (5/6). Meanwhile the 3-4-5 will often pick up a straight draw and only makes four eight or better lows thus it receives a 67 percent (4/6) adjustment.

No Deuce Adjustment

Not having a deuce in your hand is a significant handicap; therefore, any starting hand that lacks one is hit with a 75 percent adjustment. This is a subjective adjustment but due to the importance of the deuce it is reasonable to discount any holding lacking a deuce by at least this much.

No Seven/Eight Adjustment

Sevens and eights are not nearly as important as a deuce are still key cards in 27TD, thus any two-card draw that does not start with at least one of these cards receives an 85 percent adjustment. Once again this is subjective; however, as you can see in the chart below once this 85 percent adjustment is applied to 2-3-4 the final percentage when multiplied by all factors is very close to that of the 2-3-7. And most experienced players would more or less agree that these two holdings are on equal footing.

Average Rank Relative
8+ Hands Rank Adj # Hand Adj No 2 Adj No 7/8 Adj
2-3-4 4.8 100% 83% 100% 85% 71%
2-3-7 6.8 70% 100% 100% 100% 70%

The 2-3-4 and 2-3-7 are the best two-card draws. 2-3-4 makes the strongest range of hands but gets penalized because the potential six high straight is worthless and it lacks both a seven and an eight. The 2-3-7 has a lower average rank but it never picks up a straight draw and already has a seven in its possession.

Power Ratings

In order to make the results easier to compare we will now assign each holding a Power Rating on a 0-100 scale. Given that 2-3-4 is the highest ranked D2 it receives a Power Rating of 100. The 2-3-7 is very close behind with a rating of 99 (70 percent/71 percent). In order to arrive at the Power Rating for other hands you would divide 70 percent by the raw percentage obtained after multiplying the four factors together.
The complete list of calculations and Power Ratings are as follows:

Average Rank Relative Power
8+ Hands Rank Adj # Hand Adj No 2 Adj No 7/8 Adj Rating
234 4.8 100% 83% 100% 85% 71% 100
237 6.8 70% 100% 100% 100% 70% 99
247 7.3 65% 100% 100% 100% 65% 92
235 5.4 89% 83% 100% 85% 63% 89
257 8.0 60% 100% 100% 100% 60% 85
245 6.0 80% 83% 100% 85% 57% 80
238 8.8 54% 100% 100% 100% 54% 77
236 6.4 75% 83% 100% 85% 53% 75
267 9.2 52% 100% 100% 100% 52% 74
248 9.3 51% 100% 100% 100% 51% 73
246 7.0 69% 83% 100% 85% 49% 69
258 10.0 48% 100% 100% 100% 48% 68
268 11.2 43% 100% 100% 100% 43% 61
256 8.0 60% 83% 100% 85% 43% 60
347 8.0 60% 83% 75% 100% 38% 53
348 9.8 49% 100% 75% 100% 37% 52
278 13.2 36% 100% 100% 100% 36% 51
358 10.5 46% 100% 75% 100% 34% 48
357 9.0 53% 83% 75% 100% 33% 47
457 7.5 64% 67% 75% 100% 32% 45
458 9.4 51% 83% 75% 100% 32% 45
368 11.7 41% 100% 75% 100% 31% 44
345 7.0 69% 67% 75% 85% 29% 41
367 10.6 45% 83% 75% 100% 28% 40
468 10.8 44% 83% 75% 100% 28% 39
378 13.7 35% 100% 75% 100% 26% 37
467 9.3 52% 67% 75% 100% 26% 37
568 11.8 41% 83% 75% 100% 25% 36
346 8.3 58% 67% 75% 85% 25% 35

Suggested Default Openings by Position in a Six Max Game

• UTG: 2-3-4 (PR 100) to 2-4-8 (PR 73)
• It’s somewhat interesting to note that the 2-6-7 is ranked below 2-3-8 and 2-3-6 and only slightly above 2-4-8. While still worthy of an open from any position, this holding should not be considered a premium two-card draw in the same class as 2-3-4, 2-3-7, and 2-4-7.
• If the game is seven- or eight-handed we should consider eliminating the bottom portion of the range from 2-3-8 and lower unless we are paired.
• HJ: 2-4-6 (PR 69) to 2-5-6 (PR 60)
• As in most limit games not many more hands added as you move from first position over to the hijack. There are still two players left to act behind you and four players overall.
• CO: 3-4-7 (PR 53) to 3-6-8 (PR 44)
• Since it does not contain a deuce but is otherwise somewhat strong the 3-4-7 holding is the logical start point for the cut-off range. 3-4-7 is certainly not a holding you want to play multi-way when it appears that many of the deuces are dead.
• BU: 3-4-5 (PR 41) to 3-4-6 (PR 35)
• 3-4-5 is a very weak holding in that it lacks a deuce as well as either a seven or an eight therefore it marks the beginning of the button steal range.
• Holdings not listed such as 5-6-7, 4-7-8, 3-5-6, 4-5-6, and 5-7-8 all have a power rating of 32 or lower and thus should be folded unless you are paired and/or the blinds appear to under defend.

Impact of Pairs

Having duplicated cards in your hand always makes your hand stronger because they somewhat reduce the probability that your opponents hold hands that may contest the pot and when they do play it may be a card they need to fill their hands. In addition, you are slightly less likely to pair up on the last draw.

When you have a pair, two pair, or possibly trips hands have the potential to be opened from an earlier position than the guidelines specified above, however, one should exercise good judgment in this regard. Paired deuces, two pair or trips is relevant but when you have but one pair that is not deuces it’s not great removal and would only change your action when the situation is otherwise very close. For example, we should not open up 3-6-8 from the hijack simply because it has a pair of sixes, however, a holding such as 2-2-5-5-6 would absolutely be an open from under-the-gun.

Although there is some subjectivity built into this exercise it is effective in comparing hands amongst themselves and solidifying the default opening standards. None of the results were too surprising thus I surmise experienced players probably have similar standards to those outlined above; however, there may still be several hands that may be shifting up or down a notch from what they may currently be doing. If you are currently opening up deuce-less holdings such as 4-5-7 from any position this is a sizeable leak that must be plugged in order to have any sustained success in the game. ♠

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].