In Deuce to Seven Triple Draw Lowball (27TD), the cards you have seen can have a dramatic impact on the range of hands your opponent may hold. While in all poker games the likelihood of your opponent having a specific hand or range of holdings will change based upon observed cards, the opportunity to effectively use this information is probably more pronounced in 27TD than in any other draw variant.
In 27TD, everyone is trying to make one kind of hand (a low), as opposed to a multiple of possibilities including pairs, trips, straights, and flushes. There are only seven different ranks you can use to make an Eight-low or better and in order to make one of these good lows, we obviously need to hold at least one Seven or Eight.
Therefore, the cards we have seen can dramatically impact our opponent’s probability of holding/making a good hand, the average strength of their made lows, and also increase/decrease the likelihood they make a high pair on the last draw with which they will feel compelled to bluff.
In addition, there are situations in 27TD where we know our opponent almost always has a deuce thereby eliminating many possible combinations of possible made lows. For example, if a tight solid opponent opens from early position and takes two on the first draw, he virtually always has a deuce. He also holds a deuce if he calls an early position raise from outside of the blinds and initially draws two.
Players of this ilk are not apt to be playing holdings such as 347, 348, or 357 in these spots. However, if he was in the big blind and called a raise from either the cut-off or the button, all of these hands would be in his range.
If we know our opponent has a deuce, then he cannot make hands such as 86543 or 87543. In addition, if we hold an Eight but not a Seven, our opponent is more likely to have a Seven-low and less likely to have an Eight than he would otherwise be. And if we hold a Seven but not an Eight, the opposite would be true.
Let’s take a look at a relatively common scenario where we put all of these concepts into use.
Suppose our opponent and we were both drawing one on the second draw, we make an 85432 low, and our turn lead gets raised. Are we supposed to re-raise here for value?
In order to answer this question, we must consider our opponent’s range and how we fare against it. Since both players were drawing one on the second draw, our lead on the turn is highly representing a pat holding, yet our opponent chose to raise us anyway. In this particular situation, villain’s value range is typically any ‘86’ or better low.
With some frequency, our opponent will also have other “stuff”: some good ‘87’ lows might be included in his value range or he might be raising in an attempt to get you to break with some strong draws or a rough holding such as T8762 that unblocks nines. If he’s raising with T8752, he’s also using the principle of card removal as it’s more likely that you hold a Nine-low which one may consider breaking.
Let’s first consider how the 85423 is doing under the assumption that our opponent is only raising us with an ‘86’ or better low. If we include all possible lows and do not weight them based upon the cards we hold or whether or not our opponent has a deuce, our equity is as follows:
Most players probably consider the 85432 worthy of a turn re-raise and the result above appears to justify that. After all, we have 50% equity against our opponent’s value range and he could also be value raising some ‘87’ lows or making a move trying to induce a break. In addition, when an option is close it is usually beneficial for metagame reasons to take the more aggressive action and re-raising punishes our opponent when he is making a play at the pot.
However, the obvious problem with the calculations above is that we do not take card removal into account. We could have also arrived at the same answer simply by looking at a 27TD hand chart and noticing that we beat four hands, lose to four hands, and tie when your opponent also has 85432.
Since we hold 85432, it means that our opponent is much more likely to hold one of the ‘76’ lows more than any other pat hand. In addition, if our opponent opened from first position and initially drew two or flatted our early position raise, he most likely he has a deuce and we can then eliminate 86543 from his range.
If we take out 86543 and weight the possible combinations reflecting card removal, the adjusted estimated equity is as follows:
As we can see, we only have a 39% chance of having the best hand after taking into account all of the factors that we should.
Now let’s assume that our opponent plays this situation in an extremely aggressive manner and 40% of the time he has worse hands or draws. Of this 40%, we will assume that 30% of the time he has a premium draw with approximately 15% equity when we pat and a 10% chance he has a worse low.
Under these assumptions, our approximate equity would be as follows:
In this scenario, while we have around 59% equity, it does not necessarily mean that we have a slam dunk re-raise. A three-bet reopens the betting allowing our opponent to cap the action when he has a better hand, and most players will do so with any Seven-low. In addition, we won’t get any extra value when villain decides to raise and fold to a three-bet with a holding such as T8762.
When our opponent can (and will) re-raise with better holdings we may need as much as 66.67% equity against a range in order to profitably re-raise. We require less if our opponent will not always cap with better holdings or if they possibly four-bet with lesser hands, but in this situation it seems highly likely all better holdings will punish us. In addition, many opponents are not so aggressive that they are raising the turn 40% of the time with worst hands.
If instead, we hold 76542 things are quite different as we now block a seven and unblock eights. Now against villain’s raising range of an ‘86’ or better low (with no 86543) we have approximately 61% equity:
With the Seven-low, our hand is clearly good enough to three-bet as our opponent will sometimes be raising the turn with holdings other than ‘86’ or better lows for one reason or another. When we hold a Seven, it is around 33% more likely our opponent has an Eight-low.
In this example, the impact of card removal has shown that we have a clear three-bet with the #4 hand 76542, but only a call with #5 85432. In other situations, the cards we have seen (or not seen) may indicate that it may either be a good time to “snow” or call the river in the hopes of picking off a bluff. The very best Triple Draw players are constantly taking in all of this information and using it to optimize their play and so should you.
