Previously I wrote about a strategy for heads-up Coup, but it’s a better game with more than two players and that’s how most people play. The rules can be found here.
I got into an interesting endgame situation the other night. The game had started out with many players, but was down to just two, me and my brother. I have two coins and one influence remaining. My face down card is an assassin, which he knows is likely the case based on previous turns. My brother also has one card remaining, which I believe is probably an ambassador. He has one coin. I didn’t record which other cards were exposed, but that should be an important piece of the puzzle as well. It’s my turn.
I take one coin, intending to assassinate him next turn. He uses his ambassador to trade cards with the court deck. I already thought he had an ambassador, so I don’t challenge. Naturally I watch closely as he draws his two cards. He quickly and, it seems to me, confidently, chooses one of the new cards and shuffles the other two back in.
At this point I realize I need to seriously consider changing my plan. Since he believes I have an assassin he clearly recognizes my intention to assassinate him on my turn. It seems pretty clear that he decided to dig for a contessa and my read is that he found it. If the top two cards hadn’t contained a contessa, he might have looked disappointed. What’s even more telling though is his timing. If he sees a contessa his choice is obvious since that was his plan, but if neither card was a contessa, he’d probably need to stop and think about a new plan for winning the game. So I think it’s very likely that he has a contessa and if I try to assasinate he will block.
So what else can I do? I can take foreign aid (2 coins) twice and easily win the race to coup him. This plan can be foiled if he has a duke, assassin, or captain. Nonetheless, I’m pretty confident in my read and take foreign aid. He pauses to think for awhile and takes foreign aid as well. I take foreign aid again, bringing myself up to 7 coins. He tries to assassinate me but I assume this is a desperation bluff and challenge, and he indeed has the contessa.
In this case it worked out but how good was my strategy? It seems weird to open myself up to losing to 3 different cards (duke, assassin, captain) with the foreign aid plan when the obvious assassination plan would only lose to contessa. With no other cards revealed, he finds a contessa about 45% of the time, so I can guarantee myself a 55% chance of winning just by assassinating and challenging.
The simple assassination strategy has a 55% chance of winning. What if I went for an all-foreign aid strategy? Even if he does nothing to prepare for this, it would still do worse than the assassination strategy, since when he fails to find a contessa he usually finds one of the three other cards that foil the foreign aid plan, and that happens more than half the time. If he knew I was going to foreign aid it would be even worse and he could beat me almost every time by finding a captain, duke, or assassin.
Clearly all-assassination is better than all-foreign aid, but could a mixed strategy be better than either? I don’t think so, because as we’ve seen, even if he goes all-out to stop the assassination plan, foreign aid still has a lower expectation. So it seems to me with best play by both sides, I have to assassinate, and the game simply comes down to whether he finds a contessa. In the actual game I went with a read that allowed me to deviate wildly from the generally correct strategy.