Doorcards in Seven Card Stud - Stud Strategy

January 2, 2008

When playing 7 card stud, it’s important to pay attention to the other cards that are out. If you are starting with a pair of Queens in the hole, you need to be wary if any Kings or Aces are out. And even when your Queens seem to be the highest pair out, what does it mean when the player across the table pairs his doorcard 8? This article will talk about those two situations and dispel two common misconceptions.

Watching out for higher doorcards

Imagine that you are dealt [QQ]4 to start. Looking around the table you see that no one has an Ace, but there are two players with King doorcards. Good news right? Since there are two Kings out, that means it there must be less chance that either one of them has a pair of Kings since now they would need to have one of just two remaining Kings in the hole, instead of three. Many people accept this as intuitively correct, but I’m a technical player, so I’d like to do the math.

Let’s first figure out the likelihood of a single opponent with a King doorcard having a pair of Kings. We will always know what 10 cards from the deck are when playing at a full (8 person) stud table – our three cards plus the other seven door cards. If one of those seven cards is a King, then we know there are three Kings left in the 42 unseen cards. Therefore the chance of our opponent having another King in the hole with his first card is 3/42. Then if the first card isn’t a King, the second card has a 3/41 chance. Working that out we get:

So you only see one King doorcard, there is a 14.5% chance that player has at least a pair of kings.

Now if two opponents have a King door card the math goes:

So, your opponents have a 9.6% chance of having – each! Between the two of them there is a 19.2% chance that one of them has a pair of Kings. Now we know that two Kings out is more dangerous for your Queens than just one!

When your opponent pairs his doorcard

Here’s one I’ve read in many places, including some books written by stud pros: when your opponent pairs his doorcard two times out of three he will have trips (and therefore you should fold anything but monster hands). The logic behind this is simple – if your opponent has stated with a pair, two of the three possible card combinations give him trips.

Those three cases are:

[XY]X – X
[YX]X – X
[YY]X – X

Two of those three cases give the player three of a kind, and the other gives him two pair (we’re assuming he started with a pair). That simple logic leads players to assume the odds of the opponent having trips is two out of three. However it fails to examine the likelihood of each case occurring.

In this situation the math is pretty simple. When your opponent has a split pair (split meaning one of the pair cards is down, and the other is the doorcard) that means there are two more of those cards in the deck, so he has two chance to trip up. When your opponent has a wired pair (the hole cards are paired) that means that there are three other cards out that will pair his single doorcard.

So two of our starting hands (where the pair is split) each have two chances to pair the doorcard and give trips – four chances in all. The single case where the pair is wired has three chances to pair the doorcard and give the player two pair. Of the seven possible scenarios, four yield trip and three yield two pair.

So now we see that instead of a 2/3 chance that a paired doorcard means trips, the actual chance is 4/7. That is 57% instead of 67% - in both cases it’s still the most likely scenario, so watch out when your opponent pairs his doorcard!
The fact that you can see some of your opponent’s cards, and from that glean information as to his potential holdings, is just one of the many factors which make stud card games (Stud Hi, Stud Hi/Lo, and Razz) different from flop games (Hold’em, Pineapple ,and Omaha).If you are looking for a room where there is enough action for Stud at various limits you can try Full Tilt Poker or Poker Stars. Both of these rooms see enough traffic to keep this game active.

Good luck at the tables!

Frez

Frez is Bonus Internet Poker’s writer on strategy and theory in most poker games. He has been playing poker for over 5 years between a mix of online and live games. If you would like advice or to have Frez look over a hand that you have question about you can email him here. Your questions will be posted on the site and/or monthly newsletter. frez @ bonusinternetpoker.com

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