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In card games and board games, “HTI” means hidden but trackable information.
I think there are two kinds of HTI.
The problem is when the designer believes it’s the second kind but it’s the first kind in practice.
Someone with a really good memory will do a lot better in No Thanks, Jaipur, Gin, or Traders of Osaka because you basically get X-ray vision which will help you try to predict your opponent’s play, a key part of all of those games.
Memory games can exist and be fun. That’s fine. Even when the game isn’t intentionally designed as a memory game, but it becomes a memory game because the designer makes this mistake, it can still be a fun memory game.
Trick-taking games and ladder-climbing shedding games definitively have a memory component to being played well. You can’t see which tricks have gone but if you remember them, that can help you gradually learn more and more (by process of elimination) which cards are remaining in the opponent’s hand.
What’s fun about these trick-taking games is that they have a nice learning curve. You go gradually from “uh, has the ace of spades gone yet”, i.e. keeping track of a handful of cards, to over time being able to remember all the cards. The more you can remember, the better you do.
This is different than the “X-ray vision” type HTI where if you can remember everything, you get massively rewarded. If you can’t remember everything, it just comes back to bite you. You’ll get tripped up trying, straining, hoping to remember but even a single missing piece in your mind spells doom. That’s exhausting rather than fun. We want a challenge curve, not a hard wall.