Play to your side's strengths
The asymmetric nature of the game means that you're going to have to learn how to play as two different factions. The king and his knights are strong, capable of pushing citizens and assassins out of the way, and moving as a single, difficult to attack unit.
On the flip side of that, the strength of the assassins comes from the fact they're hidden. That gives you plenty of chances to bluff your enemy into wasting their energy on citizens rather than the killers in their midst.
If you know how both sides play, you're going to be in a better position to work out your opponent's strategies, so make sure you get to grips with both sides of the titular fight.
There are multiple different ways to win a game of Kings and Assassins, and sometimes you're going to have to pick between them on the fly. Plans go wrong, so having a backup is going to be super important here.
The king wins if he gets to his castle within the turn limit, but he'll also win if his knights capture or kill all three of the assassins. The assassins win if they manage to kill the king, but they'll also score a victory if the king isn't safely home by the end of the game.
Always be ready to try the second option if your first course of action hasn't come off as you'd hoped. Lost two assassins trying to kill the king? Keep the third safe, and royalty away from the gates, and you can snatch victory from the jaws of defeat.
Don't waste your manacles
It's tempting to manacle anyone who comes close to the king, but that's what the other player wants you to think. This is a game of bluff, double bluff, and sometimes even triple bluff. Like Poker with swords and knives instead of cards.
Think about where you'd position the assassins, think about the moves the other player has made, and don't clamp manacles on someone just because they look a bit suspicious. Everyone is suspicious, that's sort of the point.
Working out which movements are fake-outs and which ones are actual acts of aggression is half the fun. If in doubt, push a citizen back. Their reaction on the next turn will reveal the truth of them.
Protect, protect, protect?
To start with you'll want to go all out with attack, and while that can sometimes work, protecting what you've got is a much more viable strategy. Leave the king alone and he's vulnerable to attack. Sacrifice two assassins in quick succession and you're open to defeat.
But by the same token, you can feint an attack in order to draw out your assailants, or throw away two assassins in order to keep one of them safe and sound while the king flounders around trying to find them.
Knowing who to keep alive and who to throw to the wolves is one of the key skills in the game. Knowing who your opponent is trying to keep alive is the first step to becoming a master.
You can think of Kings and Assassins like a slightly weird game of chess. If you're only countering immediate threats, then you're missing the overall plan that your opponent is trying to put into place.
Take your time over each move, and think about the position you're going to end up in after the current turn, and the next one, and the one after that. Consider the permutations of your foe's moves as well.
While the game is mechanically simple, it's in the psychology where things really spark to life. Thinking ahead, and outwitting your opponent's potential future strategies, is a skill you definitely need to learn.