Background
I recently read a forum post in General that explained that there is a high likelihood the RNG system is being sub-divided into categories for opening certain item containers. As an example, what this means is that the game first does an RNG roll for the type of weapon (example: one hand weapon) and then proceeds to roll for the specific weapon (example: sword, mace, dagger, etc.). This could also explain the higher chance of getting something like a shield since there is only 1 type (shield) with one specific item in that category (shield). I will use this later as a potential explanation of the relatively more common occurrence of Hlaalu Kwama Egg/Ebony Mine showing up in repeats since Hlaalu only has one type of contract card.

I want to emphasize this is a guess at what the RNG is like. A categorical RNG system could not be what most players expect and might help explain why certain events like chaining contract cards occur more frequently.

How This Applies to ToT
I suspect ToT uses the same categorical RNG system and will outline some qualitative reasons later. An example of what a categorical RNG system could be for ToT is shown here:



The interpretation of this table is that a spot in the tavern is first determined using an RNG roll for Patron. There are 4 patrons and 1 Tavern (which I count as a Patron). That is the first Sub-Probability column, each of the five has a 20% chance. Next, an RNG roll is done for what type of card it will be. I just have them listed as Card, Contract, or Agent, each with a 33% chance. Finally, among either Card, Contract, or Agent, the specific card is rolled for, with X%, Y%, Z% chance depending on how many are currently available. You'll notice the Tavern is always 100% a contract card since it has no other type.

How This Affects Playing ToT

• Just from an intuition standpoint this can be confusing. We see the animations of the cards being shuffled and we tend to assume the probabilities would be like a typical card draw. If there are 1 to 4 copies of each card within the starting 100 cards (I believe it's 100 at the start but could be wrong), we tend to associate them with initial probabilities on the order of 1/100 to 4/100. For example, the relatively common occurrence of a repeat Hlaalu Kwama Egg/Ebony Mine:
  
  Typical Card Draw Probability for Drawing the 2nd Kwama Egg/Ebony Mine (assuming 4 copies, and): 3/99 = 1/33 or once in 33 attempts, given close to a full deck.
  Categorical RNG for Drawing the 2nd Kwama Egg/Ebony Mine : [(20%)*(33%)*(3/3)] = 0.066 or 1/15 or once in 15 attempts.
  
  1/15 feels closer to what I encounter versus 1/33. These numbers will change depending on how the cards are drawn and discarded, but it gives an example of why this event could be more common for categorical RNG. Keep in mind the categorical RNG system can also have a tendency to keep the chances around 1/15, where the typical RNG system might go down to something like 1/60 as the game progresses.
  
  For those that are unfamiliar, I chose this example because repeat Hlaalu contract cards when combo'd with just one other Hlaalu card can award around 9-12 gold just from the contract cards themselves. This is an absurd amount of gold especially for the early game and can easily lead to a game winning advantage.
  
  
• From the example above, chaining contract cards is more potent and common than one might expect. This isn't just for Hlaalu that effectively only has one type of contract card. It is also for decks like Orgnum and Mora where the contract cards are similar in effect (power generation) and combo off each other.
• A patron's card type might still appear even though players are buying all the patron's cards. Think of games where Crow cards constantly show up.
• I could go on, but I'll leave the rest of it up to the reader to ponder.

Possible Reasons

• My guess is that all of ESO uses the same categorical RNG system. I don't have a background in software, but I believe this would help standardize the RNG implementation and make it easier to troubleshoot and update systems, versus having to go through each team's unique RNG configuration.
• "Truly random" RNG in ToT might lead to odd games. I haven't really investigated this but one could use some RNG simulator for numbers 1-100 (take the chosen number out and decrement by 1 each time to account for card draw to make it more accurate) and see what the game could look like.
• There might be modifiers appended to the RNG numbers to make this closer to what could be expected from shuffling cards.
• I also suspect the 5 card draw spots in the Tavern were initially there to communicate a more categorical approach (1 spot for each Patron + 1 Tavern spot). However, it may have been removed for simplicity of presentation.

Conclusion

• Again, this is a guess at the RNG system.
• A categorial RNG system is not intuitively expected and has different chances (often higher chances) of drawing certain cards. This is especially important when chaining contract cards can completely swing the direction of the game. Therefore, players have a critical need to understand what is the underlying RNG system.
• It may still be an RNG seeding issue causing the duplicates, or both.
• To prove this further would take more work than I'm willing to do for ToT.