A guide to some strategy fundamentals in Heart of Crown.
So you want to help your waifu become queen? Great, this guide will attempt to teach you some of the general concepts to help you succeed at Heart of Crown. Before we start, I'll assume that you have completed the in-game tutorial and maybe played a few games.
Rush: The Simplest Strategy
At its core, Heart of Crown is a race to 20/30 Succession Points. Consider a game of Heart of Crown without a supply deck. The fastest way to reach 20 Succession Points in this game would be to only buy Cities until you reach 6 coins. After that, only buy the most expensive Succession cards. Once you have 20 Succession Points in your deck, start putting them in your domain. If you follow this strategy with pretty much any princess you'll win in 17 or 18 turns, though Lulusaika and Laolily are slightly faster. This is the Rush strategy, and since this doesn't use any cards from the supply deck, you can use this strategy in any game.
Any strategy involving the supply deck must be able to beat the Rush strategy, otherwise it is not viable.
Advanced Strategy: Looking Ahead
Because of how your deck grows over the course of the game, a strategy in Heart of Crown is defined by what you want your deck to look like. The Rush strategy wants money in the Backing Phase and Succession Points in the Succession Phase and tries to get it in the simplest way possible. Making a strategy starts even before the first turn by looking at the supply set you'll be using. I recommend playing single player games with various premade sets to help come up with strategies.
When looking at a supply set, you want to have an idea of what cards to aim for, which princess you should back, and how you should back them. As an example, the Beginner supply set is very good for building a card cycling engine, or a deck that aims to draw as much of itself as possible each turn. You can use Post Horse + Trading Ship to keep the cards flowing, City Development to improve your buying power each cycle, and Wishing Well/Alchemist to filter out Apprentice Maids. Ideally you'd like to back Bergamotte in order to reuse key actions, and back her with 1-2 Cities in order to keep actions like Post Horse/Trading Ship. A Beginner set cycling strategy can win a single player game in 15-16 turns, which will beat Rush a majority of the time.
Adapting to Change
Of course, in a game with strong players, everyone will know that cycling is strong on the Beginner set and will try to use that strategy if possible. Your opponents might buy certain cards before you are able to, or important cards will not be available to everyone simply due to luck of the draw. It is therefore also important to adapt your game plan as the game goes on.
A common situation in a high-level Beginner set game is that someone will beat you to backing Bergamotte when you're trying to make a cycling deck. What then? I'm a fan of using Klam Klam as a backup strategy and changing my focus to Large Cities and Imperial Capital/Crown if it's available. You can also do things like buying Infantry Batallion and Battering Ram to try and delay the Bergamotte player from completing their engine. Or you can simply fall back on a Rush strategy and hope the Bergamotte player gets unlucky. There are many strategies you can try when things don't go your way. Having to plan and adapt to strategies is what makes Heart of Crown an interesting game.
There is a lot of Heart of Crown strategy that I haven't covered, but knowing how to make a good plan and how to change it on the fly should help you at least beat the AI. Good luck in your quest for succession!