What is Slay the Spire?
Slay the Spire (StS) is a roguelike deckbuilder. It's a single-player game where you assume the role of one of four characters attempting to "ascend" the titular spire. Every run (a single game) starts from the same point: you get a small deck of weak cards and little else. As you progress, you can add more cards to your deck, remove existing cards and accrue other resources, such as relics, gold and potions. Encounters become gradually harder too, with enemies being more dangerous and more resilient.
StS runs are split into three acts, each act comprises 16 floors. At the beginning of every act, the player is presented with a randomly-generated map with multiple starting points.
Nodes in the map can be combat rooms (where the player fights one of the act's potential encounters), elite rooms (where the player faces off more difficult foes in exchange for greater rewards), campfires (where the player may upgrade cards or rest, restoring some HP), shops (where the player can trade gold for relics, potions, cards or remove a card), treasure rooms (where the player may open a chest to receive a relic and sometimes gold) and unknown rooms (that may randomly be a combat, shop, or treasure room, or contain an "event" with many potential effects).
The act map always includes a layer of treasure rooms, a layer of campfires before the top layer, which is the boss room for that act.

A sample map. The player can start at any of the four normal fights on the bottom. Question marks are unknown rooms, horned enemies are elites, the bags of money are shops and the icon on the top informs the player the act's bosses are Deca and Donu.
Like many strategy games, StS requires players to balance short-term value against long-term value. An example is potions: potions can be used once to perform one of several beneficial effects. To that end, they typically have an immediate value. However, because they can be used only once, strong potions should be preserved to maximize impact - except you can only carry so many potions at once, so hoarding them risks trading immediate value for nothing.
The cards offered to players also exhibit a similar tension. Some cards are strong but have delayed effects, while others have a limited potential but work immediately. For example, the card Glass Knife deals 8 damage twice to a single enemy, then becomes weaker (so it would deal 16, then 12, then 8 and so forth). 1 energy for 16 damage is a good deal, but in longer-running fights the card becomes more and more of a liability. Conversely, Noxious Fumes applies 2 poison at the beginning of each player's turn. It does nothing the turn you play it, then 2 damage, then 3, 4 and so on. It ends up dealing an amount of damage quadratic in the number of turns, but ramps up very slowly.
Combat
One of the unique features of StS is the turn structure. Every turn starts with player actions, followed by enemy actions. This means if the player's actions take the enemies out of commission, the enemies have no chance to retaliate. Enemies indicate what move they intend to make on their turn in advance. Most moves' outcomes are completely predictable, while some are subject to limited randomness (for example, an enemy may indicate it plans to summon allies. The identity of allies will not be known ahead of time, but the pool is small).
At the beginning of each combat, the deck order is randomized. Every turn the player draws five cards from the cards not drawn yet (the draw pile). Played cards go to the discard pile (for the most part), as do cards in hand when the player ends their turn. When the player needs to draw a card but the draw pile is empty, the discard pile is shuffled and becomes the draw pile. This means that while draws are random, players have some ability to predict future draws.
For example, if I have one copy of a card and I draw it early on, I know I can either play it immediately, or will have to wait, at least however many turns it'll take me to go through my draw pile, before I can see it again.
At the beginning of every combat turn, a player's energy is set to some number (initially 3, but this value can change with some relics). Playing cards requires paying their energy cost, which ranges from 0 to 3. Generally speaking, the more cards cost, the more impactful they are.
Enemies often attack the player. The player may use block cards on their turn. Unblocked damage causes the player to lose HP. Excess block (more than needed to mitigate all incoming damage) disappears at the end of the turn. HP doesn't regenerate automatically between floors.

A fight versus The Champ. The player has 16 block accrued against The Champ's attack for 18 damage. The player has 3 energy left out of the 3 they started with. The draw pile contains 2 cards, the hand has 5 (costing 1, 2, 1, 0, 1 energy respectively) and the discard pile has 14.
Tactics
The first skill StS players learn is how to optimize their sequence of plays for a given turn. Given a particular draw, amount of energy and enemy intents, the question is what cards to play, and in what order, to maximize damage dealt and/or minimize HP loss.
Because some cards have unpredictable effects (either due to randomness or due to drawing cards), a human player would first decide whether to play those cards at all, and if so, would tend to play them first and re-evaluate once the unpredictability has resolved. For example, they might play a card that deals damage to a random enemy, then when seeing which enemy was hit, choose their next plays.
Some tactical decisions can only be made in the context of looking ahead several turns. There's often a choice between taking no HP loss and dealing less damage this turn, and taking some HP loss and dealing more damage. The correct answer would depend on factors such as enemy pattern (an enemy that becomes stronger over time would push the player to aggressively trade damage with it), the contents of the draw pile (if I know next turn my expected damage is low it might impact how I play this turn) and the exact values of enemy HP (pushing an extra point of damage is worth a lot more if it means I can kill this enemy next turn).
There are also combat-level considerations. For example, it's sometimes wise to defer dealing damage in order to not cross an enemy HP threshold that would change the enemy's move set for future turns, or to allow a relic that activates every N turns to progress its counter, or to wait to draw a card with an effect that persists after combat (such as wanting to play alchemize to generate a potion). These sorts of considerations aren't about looking ahead a few turns - rather they're about looking ahead to the next fight, or to the next phase of the current fight.
Balancing Risk versus Reward
After a map node is complete, the player chooses one of the connected nodes to travel to. Choosing the path through the map is a strategic concern requiring players to balance risk and reward. A player may lock themselves into a path that's high value (many elites and campfires) but no branches, meaning if a combat goes wrong and the player loses a lot of HP, the entire run is in jeopardy. The more gold you have, the more inclined you are to path towards a shop. The weaker a player is, the more inclined they are to go for normal combat encounters, where they can get potions and card rewards to improve their deck. The act boss is known in advance, and so players continuously evaluate their chances of beating it, adjusting their resource use and pathing accordingly.
Every route to a better deck runs through combat: card rewards come from winning fights, and the gold that buys cards in shops comes from the same place.
Elite fights contain stronger monsters. These are not regular monsters with more HP or higher damage - these are enemies designed to prey on specific strategies. Some enemies punish inconsistent decks by attacking every turn. Some punish over-reliance on frontloaded damage, some punish slow decks, or small decks, or a reliance on skills to deal damage. In exchange, defeating an elite yields a relic (an item bestowing a continuous positive effect to the player), more gold than a regular fight and a card reward containing rare cards, which typically have stronger effects one can build a deck around.

A card reward screen. The player may pick any one card, or skip to pick none of them.
Correctly evaluating when to fight elites is critical to success. When done well, it allows a player to accrue resources which in turn allow them to fight more elites, potentially snowballing the strength of their build and outpacing the ramping of difficulty in higher floors. Misjudging, when not fatal, can leave a player with low remaining health, which in turn would force further combat avoidance, resulting in loss of potential value such as card rewards, relics and card upgrades.
To judge accurately, a player weighs which elite they might face, how badly their draws could go, what the map's remaining branches allow, and what their relics and potions can add.
Deck building
Cards' value doesn't exist in a vacuum. A card can be considerably better or worse depending on the relics a player has and the other cards in the deck.
For example, Blade Dance generates three Shiv attack cards. Accuracy increases the damage of Shivs. Accuracy is worthless if you have no Blade Dances, but is quite strong if you have two or three of them, since it doubles the damage of each. StS has many such synergies, more and less direct.

Blade Dance and Accuracy work better together.
A card's value also shifts in accordance with the upcoming encounters. The classical example is the act 1 elite, Gremlin Nob. This enemy gains strength whenever the player plays a skill. So, early in act 1, if an elite is coming up, attack cards are higher value and skills are lower value. Conversely, right after fighting the nob, skills appreciate in value since you can't fight the same elite twice in a row. The same concepts apply to other encounters and the act boss - each may penalize some approaches to winning combats while rewarding others.
Finally, decks need to be balanced. Encounters, elites and bosses in StS are designed to punish one-dimensional decks. For example, the Time Eater limits the amount of cards a player can play each turn, inhibiting a set of strategies around infinite combos. The Nemesis becomes near-invulnerable every other turn, messing with decks whose damage-mitigation plan is to kill all the attackers. A good player considers "lose conditions" and builds their deck around those - or attempts to avoid encountering them.
Metagame knowledge
Randomness aside, StS always tells you what a certain card will do when played. However, there's a lot of game knowledge that needs to be discovered through playing a lot. For example, StS employs a pseudo-random distribution for randomness, meaning the more a random event doesn't happen, the more likely it becomes. The chance to get a potion from a combat is 40%. If you do, the chance goes down to 30%. If you don't, it goes up to 50%. The same goes for the chances of getting a rare card, the chance an unknown room will be a combat/shop/treasure/event and so on.
The other part is enemy patterns. Enemy intents tell you what they do this turn. However, only playing repeatedly teaches you that the Gremlin Leader is more likely to attack you if it has some gremlin sidekicks alive, or that Nemesis can't use its 45-damage attack two turns in a row.
This sort of knowledge helps players hedge against the inherent randomness in the game, meaning ultimately it's exceedingly rare to die to "bad luck".
In summary: StS requires players to balance between short-term value and long-term growth, constantly re-evaluate the value of their current resources and plan ahead over hundreds of "turns" in order to defeat the titular spire. It's a challenging game with a high skill ceiling, for both human and AI agents. Unlike chess, where your poor play (or the opponent's brilliant one) is immediately apparent when analyzing the game, in StS it's hard to tell which of a dozen inter-related decisions was a mistake, since outcomes alone don't carry this signal due to the inherent variance.
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