If your definition of “hidden information” implies that chess has it then I think you will predictably be misunderstood.
Terms that I associate with (gaining advantage by spending time modeling a situation) include: thinking, planning, analyzing, simulating, computing (“running the numbers”)
Yeah I do not super stand by how I phrased it in the post. But also your second paragraph feels wrong to me too – in some sense yes Chess and Slay the Spire hidden information are “the same”, but, like, it seems at least somewhat important that in Slay the Spire there are things you can’t predict by purely running simulations forward, you have to have a probability distribution over pretty unknown things.
(I’m not sure I’ll stand by either this or my last comment, either. I’m thinking out loud, and may have phrased things wrong here)
Randomness is when the game tree branches according to some probability distribution specified by the rules of the game. Examples: rolling a die; cutting a deck at a random card.
Slay the Spire has randomness; Chess doesn’t.
Hidden Information is when some variable that you can’t directly observe influences the evolution of the game. Examples: a card in an opponent’s hand, which they can see but you can’t; the 3 solution cards set aside at the start of a game of Clue; the winning pattern in a game of Mastermind.
People sometimes consider “hidden information” to include randomness, but I more often find it helpful to separate them.
However, it’s not always obvious which model should be used. For example, I usually find it most helpful to think of a shuffled deck as generating a random event each time you draw from the deck (as if you were taking a randomly-selected card from an unordered pool), but it’s also possible to think of shuffling the deck as having created hidden information (the order that the deck is in), and it may be necessary to switch to this more-complicated model if there are rules that let players modify the deck (e.g. peeking at the top card, or inserting a card at a specific position).
Similar reasoning applies to a PRNG: I usually think of it as a random event each time a number is generated, though it’s also possible to think of it as a hidden seed value that you learn a little bit about each time you observe an output (and a designer may need to think in this second way to ensure their PRNG is not too exploitable).
Rule of thumb: If you learn some information about the same variable more than once, then it’s hidden info. For instance, a card in your opponent’s hand will influence their strategy, so you gain a little info about it whenever they move, which makes it hidden info. If a variable goes from completely hidden to completely revealed in a single step (or if any remaining uncertainty has no impact on the game), then it’s just randomness.
Interesting Side Note: Monte Carlo Tree Search can handle randomness just fine, but really struggles with hidden information.
A Player is a process that selects between different game-actions based on strategic considerations, rather than a simple stochastic process. An important difference between Chess and Slay the Spire is that Chess includes a second player.
We typically treat players as “outside the game” and unconstrained by any rules, though of course in any actual game the player has to be implemented by some actual process. The line between “a player who happens to be an AI” and “a complicated game rule for selecting the next action” can be blurry.
A Mixed Equilibrium is when the rules of the game reward players for deliberately including randomness in their decision process. For instance, in rock-paper-scissors, the game proceeds completely deterministically for a given set of player inputs, but there remains an important sense in which RPS is random but Chess is not, which is that one of these rewards players for acting randomly.
I have what I consider to be important and fundamental differences in my models between any two of these games: Chess, Battleship, Slay the Spire, and Clue.
Yet, you can gain an advantage in any of these games by thinking carefully about your game model and its implications.
If your definition of “hidden information” implies that chess has it then I think you will predictably be misunderstood.
Terms that I associate with (gaining advantage by spending time modeling a situation) include: thinking, planning, analyzing, simulating, computing (“running the numbers”)
Yeah I do not super stand by how I phrased it in the post. But also your second paragraph feels wrong to me too – in some sense yes Chess and Slay the Spire hidden information are “the same”, but, like, it seems at least somewhat important that in Slay the Spire there are things you can’t predict by purely running simulations forward, you have to have a probability distribution over pretty unknown things.
(I’m not sure I’ll stand by either this or my last comment, either. I’m thinking out loud, and may have phrased things wrong here)
Some concepts that I use:
Randomness is when the game tree branches according to some probability distribution specified by the rules of the game. Examples: rolling a die; cutting a deck at a random card.
Slay the Spire has randomness; Chess doesn’t.
Hidden Information is when some variable that you can’t directly observe influences the evolution of the game. Examples: a card in an opponent’s hand, which they can see but you can’t; the 3 solution cards set aside at the start of a game of Clue; the winning pattern in a game of Mastermind.
People sometimes consider “hidden information” to include randomness, but I more often find it helpful to separate them.
However, it’s not always obvious which model should be used. For example, I usually find it most helpful to think of a shuffled deck as generating a random event each time you draw from the deck (as if you were taking a randomly-selected card from an unordered pool), but it’s also possible to think of shuffling the deck as having created hidden information (the order that the deck is in), and it may be necessary to switch to this more-complicated model if there are rules that let players modify the deck (e.g. peeking at the top card, or inserting a card at a specific position).
Similar reasoning applies to a PRNG: I usually think of it as a random event each time a number is generated, though it’s also possible to think of it as a hidden seed value that you learn a little bit about each time you observe an output (and a designer may need to think in this second way to ensure their PRNG is not too exploitable).
Rule of thumb: If you learn some information about the same variable more than once, then it’s hidden info. For instance, a card in your opponent’s hand will influence their strategy, so you gain a little info about it whenever they move, which makes it hidden info. If a variable goes from completely hidden to completely revealed in a single step (or if any remaining uncertainty has no impact on the game), then it’s just randomness.
Interesting Side Note: Monte Carlo Tree Search can handle randomness just fine, but really struggles with hidden information.
A Player is a process that selects between different game-actions based on strategic considerations, rather than a simple stochastic process. An important difference between Chess and Slay the Spire is that Chess includes a second player.
We typically treat players as “outside the game” and unconstrained by any rules, though of course in any actual game the player has to be implemented by some actual process. The line between “a player who happens to be an AI” and “a complicated game rule for selecting the next action” can be blurry.
A Mixed Equilibrium is when the rules of the game reward players for deliberately including randomness in their decision process. For instance, in rock-paper-scissors, the game proceeds completely deterministically for a given set of player inputs, but there remains an important sense in which RPS is random but Chess is not, which is that one of these rewards players for acting randomly.
I have what I consider to be important and fundamental differences in my models between any two of these games: Chess, Battleship, Slay the Spire, and Clue.
Yet, you can gain an advantage in any of these games by thinking carefully about your game model and its implications.