Success in Coup depends on the cold, hard skills of probability and deduction along with the fluffy, social skills of deceiving and lie detection. It’s about choosing which roles to pretend to be while challenging at the right time. To keep this short, I will mostly stay away from talking about the social skills and focus on the math. Check out the video immediately below or continue on for the text version.
Unlike most games, there isn’t much of a middle game because games of Coup are so short. I am characterizing high-level strategy in terms of Early Game and Late Game. Overall, you can feel free to claim to be anyone you wish in the early game because the only people who will likely challenge you are those with a pair of the character you are claiming. Once you get into the late game, players have much more information about the characters remaining, so you need to be careful about making false claims about your character.
In the early game, you want to be the Duke so you can gain the coin advantage. The Assassin can be nice to knock opponents down in influence early and the Contessa can help to block early assassination attempts as well. If you are none of these, you may want to take the Ambassador action and exchange your cards with the Court Deck.
Do not take foreign aid in the early game. There will likely be many others claiming to be the Duke and taking 3 coins so it will not be much of a risk to also claim to be the Duke to block your foreign aid.
In your first few turns, pretend to be the Duke, even if you are not. Getting 3 coins per turn will be extremely helpful later in the game. It will not be worth it for your opponents to challenge you unless you do it every single time. It does make you a bit of a target if you have more coins than anyone else, so do not be afraid to use them early to assassinate someone.
The best late game character is the Captain to steal and block others’ stealing and control the cash flow. The Contessa can also be nice if someone attempts to assassinate you and the Assassin can be good for a final assassination for 3 coins instead of 7. If you are not one of these after the first player is exiled, you may want to take the Ambassador action to exchange cards with the Court Deck.
Once you get into the late game when there are 1-2 opponents remaining, taking foreign aid can force others to give you information or allow you to get 2 coins each turn. 2 coins and information may be more valuable late game than getting 3 coins with the Duke.
Stealing with the Captain gets to be far more valuable in the late game as your number of opponents decreases. If you have a single opponent, taking 2 coins from them means +2 for you and -2 for them, resulting in a 4 coin swing in your favor, and likely securing an uncontested Coup in a matter of turns.
If you and an opponent each have 1 influence, it comes down to who will be able to get up to 7 coins first. You usually have three options here: steal with the Captain, tax with the Duke, or assassinate with the Assassin. If you do not have any of these characters, you better start faking it as the Captain or the Duke until you have the coin advantage or you will lose.
After you play a bit with the same group, you will run into a situation where someone always says they are the Duke. Should you challenge them? Well, maybe you have a good read on them and can tell when they’re lying, but let me explain the odds. When you are given your initial hand, you have seen two of the fifteen cards. If none of them are the Duke, the chances that this opponent’s Duke claim is honest is 6/13 = 46.15%. I don’t know about you, but I wouldn’t want to bet my influence on almost a flip of a coin. BUT, if you have a Duke card in your hand, the chances that they are also the Duke falls to 4/13 = 30.77%. This becomes more reasonable to challenge them on it. If you have a pair of Dukes, it drops to 15.38%.
As the game progresses past the initial hand, you’re on your own. There are only 15 cards in the whole Court Deck, so you can do some quick probability calculations every time someone takes a character action to get a feel for the likelihood that they are telling the truth. Use that, along with past character actions and any tells they may have to help make your final decision about when to challenge.
If you have 2 influence, NEVER:
Falsely claim to be the Contessa when you are being assassinated.
Challenge an Assassin who is assassinating you. (unless you have perfect information that they are not the assassin)
If you are wrong about either of these two, you are exiled. You will be ridiculed and then left to sadly sit and watch the rest of the game with an embarrassed look on your face. It’s far better to just accept the assassination and live to fight another day.
A corollary to this is that you can pretend to be an assassin and assassinate someone with 2 influence and your opponent is less likely to challenge it.
Use pairs to your advantage. When your opponents claim to be a particular character, they do not expect someone to have 2 of them, so this is a good time to challenge them. Just keep in mind that there are only 15 cards in the deck so there is still a good chance they have the other character card unless it is already face-up. Also, if someone is closely watching your claims, you can try to trick them by continuing to claim you are someone even after you lose an influence, especially if you make it look like you acted very quickly and possibly overlooked the fact that you lost that character when you lost your influence. If you do not see any opportunities to use your pairs to your advantage, you may want to use the Ambassador action so you can get two different characters.
It is very unlikely someone will challenge whether you are the Ambassador because it doesn’t immediately hurt them and is not guaranteed to help you, so feel free to falsely use this action if you do not like your current hand.
Once player A steals from player B using the Captain and player B allows it, anyone else can safely steal from player B. This means that you need to be careful when you allow anyone to steal from you because others may pile on and it means you should feel free to get in on that action if someone else allows it.
After you have played with the same group for a few games and they improve their bluffing skills, you will want to begin making most of your decisions on perfect information, or at least deducing which information is highly likely to be correct based on the face up cards, the cards in your hand, and their past claims. People get harder to read with practice.