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Since most moves in Catan are public knowledge, one could count cards and keep track of the opponents' hands at all time. However, it seems that there are a few obstacles to doing this.
Have any of you had success in card counting?
In particular, how do you get around obstacles like under the table trades, discards when a 7 is rolled, and randomized robbing?
I've tried counting cards while playing Catan, and I've really found it a needless distraction. It really isn't worth the effort to know that Player X has exactly 4 Ore, a Grain and a Sheep in their hand. It gets much too confusing too quickly, especially when you throw in robbing and trades.
Instead, I focus only on counting my most scarce resource. Since that's almost always the one I would try to steal or trade for, that information is valuable enough to make the effort for. There are relatively few of that good in circulation, so keeping tabs on them as people buy, trade, and build with them is much easier.
I am a big believer in counting cards I keep rough track of what people have a lot of and what is scarce and not in the game. It expedites trading and makes sure I get the most value for my cards. I win far more than I lose so I figure it works pretty effectively.
It is a disruption that is too difficult to be useful. It could be counter productive because it diverts attention from other important details.
It is often obvious when one of your opponents is about to do something. You can infer what cards players have based on the trades they offer, and their reactions to dice rolls. Observing your opponents yields more valuable information than attempting to memorise their cards.
I do track cards when there is a rare resource or a player is about to win. A player with eight points on the board and two army cards, for example. The player may need one ore to buy what could be a third army card, so it's worth keeping track of cards.
I do count development cards. It is easy to tell what development cards other players have. There are five victory point cards, for example, and usually players hold on to them for much of the game.
You can gather information using deduction: Given the development cards you have, ones that have been played, and how many remain, you can make high fidelity guesses and estimate the probability of pulling out a card you need.
Recently two development cards remained in the game and I knew that both were victory point cards, which allowed me to win the game.
I track how many of each resource has been picked up. Its quite quick and easy using your roads/settlements/cities as counters. You can be pretty sneaky about it too. Its always nice to know what is out there when you get a monopoly.
Counting cards is very useful. Yes, it can't be done perfectly, but you can do it decently. You generally know when you have incomplete information, and can adjust your play accordingly. When playing in person, you can keep an eye on discards, which are the hardest to keep track of because of the volume. Even if you don't catch every card, you can make educated guesses about what the player's goals are with the remaining cards. I find that players often exhaust their hands, and you can reset counting from there. You don't need to keep an exact count in your head each turn, just the last few rolls and builds and knowledge of what the player had previously. Sometimes you'll guess wrong about the cards after a discard or a steal, but the risk is pretty small, and the benefits are great.
Generally, I would say that having a clear idea of what other players have allows you to manipulate the game to your advantage. If everyone else also has a decent idea of what other players have, it might not be quite as useful.
