Deuce to Seven Triple Draw Lowball: Examining Open Ranges, Equities, and Positional Considerations

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

Thus far in our Deuce to Seven Triple Draw Lowball (27TD) discussions we have looked at the different starting hands and the corresponding positions at the table where an open should be profitable. The next item on the agenda is to determine how to best react with various holdings when an opponent has already entered the pot for a raise before us.

However, before getting to that it will be most useful to first examine what a standard solid opening range looks like in regards to its approximate breakdown between pat hands, one card draws (D1), two-card draws (D2), and three-card draws (D3). Another interesting aspect to consider is what approximate percentage of the time a player holds a deuce given the position from which they opened.

Having familiarity of “hot/cold” equities is also very useful as is the understanding that the ability to realize equity is a very important factor that should not be neglected. If we need to improve in order to stay in the hand then we may be a bigger underdog than we may have imagined. Lastly, when making a decision whether or not to play we cannot ignore the impact of position.

Examining an Open Range

As detailed in previous issues the suggested default open ranges by position for one- and two-card draws are as follows:

One-Card Draws (D1s) Two-Card Draws (D2s)
UTG Six Max Hijack Cutoff Button UTG Hijack Cutoff Button
2347 2356 3468 3478 3678 234 246 347 345
2357 2368 3457 3467 4568 237 258 348 367
2345 2456 3568 3578 4678 247 268 278 468
2457 3458   3567   235 256 358 378
2367 2378       257   357 467
2467 2478       245   457 568
2346 2578       238   458 346
2358 2678       236   368  
2567         267      
          248      

We can also open pat eights or better from any position (approximately 0.7 percent of hands), some unbreakable pat nines from the cutoff and later, and premium three card draws (2-3, 2-4, 2-5, and 2-7) from the button. This is a tight but solid opening range and it produces the following various statistics for the UTG and HJ positions:

UTG Opening % 15.8%   HJ Opening % 20.7%  
Deuce % 94% Deuce % 95%
% Opens % Opens
Pat 0.7% 4% Pat 0.7% 3%
D1 5.1% 32% D1 6.0% 29%
D2 10.0% 63% D2 14.0% 68%
D3 0.0% 0% D3 0.0% 0%
  15.8% 100.0%   20.7% 100%

As we can see when someone is following a solid pre-draw strategy their opens from the first two positions will almost always contain a deuce. The lone deuce-less hands are D1s such as 3-4-5-8, 3-4-6-8, 3-5-6-8 and sometimes 3-4-5-7. This range is quite strong; UTG and Hijack opens will either have a pat eight or better or a D1 around 36 percent and 32 percent of the time respectively.

Cutoff and button open statistics for a solid opening range are as follows:
CO Opening % 30.1%   BU Opening % 45.3%  
Deuce % 69% Deuce % 63%
% Opens % Opens
Pat 0.9% 3% Pat 0.9% 2%
D1 7.2% 24% D1 8.1% 18%
D2 22.0% 73% D2 29.0% 64%
D3 0.0% 0% D3 7.3% 16%
  30.1% 100%   45.3% 100%

From the later positions we can observe that the percentage of the time a deuce is accounted for is much lower as is the probability that a player is either pat or drawing one as a percentage of their overall range.

If a player is very loose and plays mediocre holdings from all positions their statistics are going to look much different than those above. As in any poker variant it is crucial to pay attention to what hands people are playing from each position. Do they respect position and understand the importance of the deuce? Are they playing the rougher D1 holdings such as 3-6-7-8 from any position? When do they begin to open their D3s?

Sampling of Pre-Draw Matchups and Realization of Equities

In a battle of two cards draws the situation is often very close; however, a premium D2 versus a marginal or steal D2 usually has around 55-60 percent equity:

237 51% 237 53% 237 56% 237 59%
247 49% 348 47% 378 44% 457 41%

When you are dealt a pair or trips your equity situation is much better especially if it is a rank that your opponent needs to fill his hand. As you can see below it can turn your holding from an equity underdog to a favorite:

237 54% 237 51% 237 47%
268 46% 268(6) 49% 268(66) 53%

A two-card draw versus a one-card draw is a definite underdog:

237 38% 237 41% 237 46% 237 42%
2457 62% 2348 59% 2378 54% 2568 58%

The situation for the two card draws is even worse than depicted above as these are “hot/cold” equities assuming both hands go to showdown. However, that will not always be the case as the D2 usually has to improve to continue after the second draw which makes the one card draw a larger favorite.

How much the D2 needs to improve will be discussed in future installments but generally in a reraised pot we must have at least a one card draw to a nine or ten low in order to continue after the second draw. And we can only consider calling this light when our opponent is not already pat. According to “hot/cold” equities the 2-4-5-7 is around a 62 percent favorite over 2-3-7; however, in actual game play its winning percentage is probably closer to 75 percent.

A D3 is almost always an equity underdog to a D2; however, the differences are not that significant:

23 43% 23 46% 23 47% 23 50%
247 57% 268 54% 378 53% 346 50%

A D3 will also realize its equity less often than his opponent’s D2 and while this disadvantage is not as pronounced as a matchup between a D2 and a D1 it is still a consideration. We are always going to defend the big blind against a steal raise with a hand like 2-4 but we should be very cautious in defending worse holdings such as 2-8 and 3-8.

One of the main advantages of defending with a holding such as 2-4 is that when you improve you are often drawing to strong hands thus having implied odds on your side. With worse D3s there are less strong hands to make so even when you do get lucky and improve dramatically it can still end up costing many chips. Since we are often drawing more cards and also ceding position, we should not get lured in by pot odds and defend mediocre D3s.

It’s also important to not over defend against a strong range. As we would expect a D3 is in really bad shape against any D1 both in terms of equity (see below) and the ability to realize whatever equity it has.

23 28% 23 33% 23 33% 23 35%
2457 72% 2568 67% 3568 67% 3678 65%

It should be relatively clear that a D3 doesn’t perform that well against a solid player’s early position opening range. This range is somewhat heavy in pats and D1s and even when our opponent is drawing two our equity is still often in the low 40s. While we are getting good odds to defend from the blinds it will be difficult to reap a profit over the long term as we are out of position and will struggle to realize our equity.

Impact of Position

Having position in 27TD is a clear advantage because there are various benefits that the in-position player has that will allow him to win a greater than his equity share of the pots. For example, in position we have the option of staying pat with weaker hands when our opponent is still drawing which we would not have been able to do from out of position. Or we can possibly use the power of acting last by raising with a weak pat or drawing hand in an attempt to get your opponent to either break a pat holding or fold outright.

Position also allows us to “freeze” an opponent. Freezing is a situation on the turn where we may be a slight favorite to hold the best pat, however, we just call a bet for the dual purpose of saving money when we have the worst hand and to also not encourage villain to break his hand where we he may be then drawing live to the pot.

For example, suppose two players were both drawing one on the second draw and the first player leads out highly representing a pat hand. In this situation the second player should just call if he made a hand such as 8-7-6-3-2 as this will ensure that his opponent stays pat with rougher eights, nines, or possibly worse holdings.

There are more advantages to position; these are but just a few examples. So how much is position worth? That’s tough to say and no one probably knows an exact answer but it wouldn’t surprise me if it added 5 percent or more to the probability of winning the hand. For example, if two players are initially dealt the same D2 their equities at the onset would both be 50 percent but it wouldn’t surprise me if in position player ended up winning 55 percent of the pots or more.

In 27TD the pots can get quite large quickly thus once we choose to enter a pot we are often enticed to chase until the end. This makes our decisions on the first betting round very important because one bad call can easily lead to a series of very marginal or losing calls on future streets. In the next installment on 27TD we will start to put the information we learned in this issue to full use as we discuss how to react with various holdings when an opponent has opened the pot ahead of us. ♠

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].