Here are my strategy tips for playing the game Regicide.
Familiarize yourself with the rules, if you haven't already.
Regicide Rules (PDF)
Like many games, your best strategy is to maximize the potential of each action you take. You want to deal out damage fast to keep the game short and use less resources. Order your actions in a way that you get the most out of each of them.
The power of each suit is as follows:
Diamonds are the most powerful suit in the game. They are the only way to replenish player's hands. Since hands act as both your health and your attack options, drawing more cards will both protect you longer and increase your options.
If you run out of diamonds, you will be unable to draw new cards and lose. It cannot be emphasised enough that diamonds are your number 1 priority.
To maximize the use of diamonds, wait as long as possible to play the card. You can't draw more cards than the max hand size, so playing diamonds early will squander it's fullest potential. You want to play it at a time when players will draw more cards with it. Since damage is dealt predictably, it's not that challenging to wait until the right moment.
Clubs are the second most powerful suit. Dealing double damage is a big deal, because they will end fights quickly. The faster you can end a fight, the less resources you need to use and less damage you take. Plus, you don't take damage after a lethal strike. Using a clubs face card against an enemy of the same rank is an instant perfect kill, since their starting health is always exactly double that of their attack power.
Hearts exists solely to power draw for diamonds. You won't really need to use it that often throughout the game, since the tavern deck is pretty large. But don't slack on it for too long. If you stick to playing only the highest powered hearts or pair a companion with your attack every few rounds, you'll likely be safe. The rest can be used for health discard.
You could choose to use hearts early on. When the discard is still small, you can guarantee that you are putting back only the most powerful cards you just played to the bottom of the tavern deck, ensuring you will have them later against the Kings.
Priority of hearts should rise as the tavern deck gets smaller.
Spades are the weakest suit. For the most part, spades should be your discard fodder along with hearts. The priority of Spades will increase if one of the other higher priority suits is getting blocked. If diamonds is blocked, Spades will help you hold your cards for longer. If clubs are blocked, you can still win through attrition.
Higher value cards are, of course, higher priority. They allow you to take and deal more damage each turn.
10s and Jacks are both power 10, so they are equal priority. But it can feel more rewarding using the enemy's former allies to destroy them.
Companions can also be a good priority, since they pair easily with any other card.
Combos can be good if you already have them. It's not worth trying to draw into a combo. It's often best to use a combo early to make more room in your hand for more cards, and ensure you get use of their effects.
Remember to prioritize order of actions and damage first. Playing an 8 of clubs is likely to be a better start than comboing a 2 of Clubs and 2 of diamonds, since you will have 3 cards to draw instead of 2. But if you need that 8 to tank damage this turn, it would be better to play the combo first.
Use the Suit Priority order to help guide you on which cards you should keep and which you should toss. In general, higher ones you want to keep, lower ones you can use to discard.
The order of priority can change if you are currently facing a boss who's blocking that suit from being used. If you are facing against a Clubs, then it will be better to toss it and use a Spades instead. You'll get to draw up for the next boss when you play diamonds anyways, which is likely to give you new clubs.
Diamonds are an exception. If you have a lot, you can discard some, but you never want to throw away your last diamond. They are your lifeline. Even a 2 of diamonds may draw you to another diamonds to keep going. If everyone runs out of diamonds, you will lose.
In solo, you can consider the Jesters to be diamonds. But remember they are extremely limited in use. You shouldn't need to spend them until you either at the Kings, or you haven't drawn any diamonds. Save them.
Don't be afraid to throw away half your hand with smaller values. Those smaller values are not going to do much on your turn. Don't try to rely on getting combos. Throw them away and use diamonds to replace them with better cards.
Don't get too attached to combos you do have. It can be worth breaking them up to save yourself from discarding more of the bigger cards. Against a Jack, discarding an 8+2, then 9+2, saves you from having to discard the 8+9 together at the same time.
Companions are more valuable than other low power cards. They are easy to clear from your hand to make room for more draw power, and they give you an extra power almost for free. Often the +1 damage with any card can make it easier to get exact damage on a kill.
In general, you want to be dealing as much damage as you can each round. Start with Clubs, then when hands are about to be empty, switch to diamonds.
Attempting to get a perfect kill with exact damage is worth trying to do if you see a clear way to do it. It's not worth going too far out of your way for it, but an extra round might be. Smaller value cards can make this easier to do, but it's not worth the risk of holding onto them specifically for that if you're unsure about it. It's harder to set this up with more players due to the limited communication mechanic.
Try to avoid using a card who's power is currently being blocked. It's always beneficial to have a power used. But if you can get lethal or exact damage, go ahead and use an attack with a blocked power.
Keep track of which suits of enemies you've already faced. You'll face each one once for each rank.
If you haven't yet faced off against diamonds, try to play diamonds as your last attack against the previous boss to draw up your hand. Don't get caught off guard with no card options.
Clubs will be your best attack against everything except clubs. Switch to using spades as your primary attack.
Always make sure that you will have enough to discard for damage before making an attack. Living is more important than dealing a little extra damage.
Play aggressively. Don't worry about saving your big damage cards for later bosses. Focus on the current one and draw more cards. With hearts and diamonds, it's almost certain those powerful cards will come back. It's better they get used twice.
Yielding is an emergency maneuver that should never come up if you are managing your diamonds well (or got unlucky). Only do this if you have no way of both attacking and accepting damage.