This is the second part of my series that focuses on the third street of Stud High. In the first part, I talked about third street in general and in this part I'll be looking at different hand categories and how to play them in various situations.
Rolled-up Trips
This is the strongest starting hand in Stud High. We will be dealt these very rarely, only 0.24% of the time. These hands do well both heads-up and in multiway spots.
Obviously, the more opponents we have the better the chance that someone will outdraw us, but these hands are fairly good at retaining their equity in multiway pots as well. For this reason, it's advised to not reveal the strength of our hand too early (for example, on a Q-J-3-A-K-2 board with an Ace open, a King flatting, and us having (3,3)3, where we also want to play hands like three flushes). I will talk about this concept in parts 4 and 5.
Split Pairs
We are going to be playing these hands the most often. The chance of getting a split pair (not accounting for dead cards) is 11.29% and this is also true for our opponents. If an Ace raises and we don't take into account any dead cards, our opponent is going to have a pair of Aces 11.29% of the time.
This situation doesn't exist however since there need to be at least two players to play a hand. In an eight-handed game, if there are seven different cards out (7-7-8-T-J-Q-K dead cards and we have an Ace for example), the probability of a split pair of Aces increases to 13%. But in case there is one additional Ace among the dead cards (A-A-K-Q-T-J-8-7 board), the probability drops to 8%.
As a basic principle, folding (or at least playing more cautious) is advisable when there is a card out that we also have as a pair. As with everything in Stud High, this is still highly dependant on the situation. If we assume we have the highest pair, then this is less of a problem and playing dead split pairs is also a good move if we think we have a high percentage chance to win the antes.
In general however, it's a fairly common mistake not to pay attention to the dead cards.
In an extreme example, dead cards could result in a small pair being a favorite over an overpair.
(2,3)2 rainbow has 34% equity vs. (A,K)A no dead cards.
However, (2,3)2 rainbow has 50.8% equity vs. (A,K)A rainbow with dead cards of AAKKK.
A Split Pair of Jacks
The board on third street is Q-J-K-A-J-3.
The Queen opens and we have split Jacks with a 6 kicker. The Queen raised from an early position so he is fairly likely to have a pair of Queens, but when he doesn't (and instead has a hand like (7,7)Q or a three-flush), there is still a chance that the Ace or King will wake up with a split pair. This means that our equity very often decreases against our opponents' ranges because of the dead Jack.
There's a saying in Stud High that goes "It's a race to two pair" and it should be well remembered. It's basically a simplified way of saying that we want to be playing hands that have the potential to make at least two pair by the river. A hand like (8,2)2 rainbow with an 82QK dead board is very weak. In contrast a (3
2)2 on an 88QK board is completely different, because our two pair/trips outs are live and we have the chance to make a straight or flush too.
If we start with (J,6)J, the chances of making trips or better by the river is exactly 18% (8.11% for a full house and 9.89% for trips) and the chance to make any two pair is 41.9%. It’s 18.53% to make precisely JJ66.
If the board is favorable for us in an eight-handed game and there are no Jacks or Sixes out, the probabilities increase (dead cards: 2,3,4,5,7,8,9).
The probability to make trips or better is 20.85% (9.77% full house and 11.08% trips). The probability to make any two pair is 41.65% (JJ66 exactly: 20.61%).
The chance to make any two pair decreases slightly while the chance to make JJ66 exactly increases. This is because the different ranks of cards, for example with a (J,6)J2K3 we will make two pairs less often, because the 2 and 3 are out, but the chance to make JJ66 increases.
As you can see, the differences are marginal even when the dead cards are favorable to us, we make trips or better 20.5% of the time instead of 18%. However, if there is both a Jack and Six out, the chances drop to 11.15%.
Dead cards: 2,3,4,5,6,7,J
Full house or better: 4.62% Trips: 6.53%
Let's look at a chart that summarizes every possibility.
Backdoor Equities with our Split Pair
Since we get four more cards, any hand we start out with has the chance to make runner-runner flushes or straights. It might look small at first glance, but the difference between (J,6)J rainbow and (J,6)J two-flush hands is significant and can be the turning point whether we play that hand in a marginal spot or not.
(J,6)J rainbow
Probability to make a flush: 0.69%
Probability to make a straight by the river: 0.96%
J6
J
Probability to make a flush: 3.34% (almost five times more than (J,6)J rainbow)
In spots like this, a hand like (J,T)J with a two-flush is the best hand to have because it can make both straights and flushes
*You might have noticed that when looking at the comparison of (J,6)J rainbow and (J,6)J two-flush that with the latter we make straight less often, despite the fact that our hand is the same. This is because on rare occasions we can make both a flush and a straight with our hand and the flush is stronger than the straight (for example (J
6
)J-7-8-9-5)
**The difference between (J,6)J two-flush and (J,T)J two-flush (from 3.34% to 3.26%) is there because I only looked at flushes and 0.08% of the time we will be making a straight or royal flush with (J,T)J two-flush.
To sum it up, there is a big difference between a hand like (J,6)J rainbow and (J,T)J two-flush. If the board is Q-J-3-A-K for instance, and the Queen raises from early position, (J,6)J rainbow should be folded, while a (J,T)J two-flush will usually be playable because of the backdoor equity.
How and When to Play Split Pairs
This is a very complicated and long topic so I will try to focus on the basic principles. There are a lot of factors to take into account when deciding whether a pair is playable.
Here are some things to consider.
- Try to have an overcard kicker (for example: Q-4-J-K-2 board, Queen opens, we have 4A-4 rainbow, which is a good enough hand to continue, but 4J-4 should be a fold)
- Extra equity (two-flush, two-straight) is worth a lot (for example: Q-4-J-K-2 board, Queen opens, (4,5)4 two-flush can be played if we assume the Queen opens wide and even more so if our two-flush outs are live)
- How live our hand is
A good rule of thumb is to fold middling split pairs if there are three or more higher door cards in play after us. For example: 6-Q-K-J-5-2 board, we have (6,4)6 two-flush, this hand should be folded. But if we change our hand to (6,A)6 rainbow, it becomes playable, because the overcard kicker is worth more than the two-flush (the best hand from these would be a (6,A)6 two-flush).
Playing split pairs against raises from higher door cards should only be done when at least one of the following conditions is met:
- Our opponent raised from a steal position - Our hand is completely live - We have extra equity (two-flush, two-straight, like (6,A)6 rainbow or (6,5)5 two-flush against a King open)
Wired Pairs
Having a wired pair means having a completely hidden pair like (2,2)K or (A,A)4. These hands often have better playability than split pairs. We will have greater fold equity when we pair our door card, because opponents are likely to put us on trips and we can also get more value from our hand when we do make trips like (8,8)2,8 because they are hidden, unlike split pairs. The probability of improving our hand is the same, but because the strength of our hand is hidden, we have better playability in marginal spots where split pars will be folded.
However, it’s worth noting we can’t make a hidden two-pair hand before the river when starting wired pair. Whereas, a split pair can make to hidden split pairs immediately.
The chances of getting a wired pair is lower than the probability of getting a split pair, because both of our hole cards have to be the same rank, while with a split pair only one of the holecards has to match our doorcard.
With zero dead cards, the probabilities are the following:
Chance for any split pair: 11.29% Chance for any wired pair: 5.65% (each split pair accounts for 0.47%)
So if our door card is a 2, we will have (A,A)2 just 0.47% of the time (not taking into account any dead cards. Obviously if 3,4,5,6,7,8,9 are dead, this will increase).
In the next part, I will take an in-depth look at three-flush and three-straight hands.
