prompter: I've recently started playing the turn-based strategy game Into the Breach. I have read online that the game is considered to have 'perfect information'. What is meant by 'perfect information' in this context?

assistant: A game with 'perfect information' refers to the fact that each player has all the available information through the entire duration of the game. A classic example of such a game is chess. Into the Breach is very similar to chess, in that regard, because it continuously shows the location and state of the all the units for both the player and the opponent.

However, it is debatable whether Into the Breach qualifies as a game with perfect information, because some information is still hidden from the player. An example of this is enemy units that spawn in later turns of the game. It is not clear to the player when or where these enemies will appear.

prompter: Thats an interesting point, but I don't think I fully understand. 

We know where the enemy unit will spawn one turn before they spawn in, why is this a violation of perfect information? I'll know where they spawn after all.

assistant: 'Perfect information' in this context means that the player has full knowledge of the current game state. There is no information about the game that is hidden from the player.

An example of a game with perfect information is chess. In chess, both players know position of every piece on the board and all the possible moves for both sides.
An example of a game with imperfect information is poker. In poker, the players do not know the cards in other players' hands or in the deck. Therefore the players cannot make fully informed decisions and have to rely on probabilities.

prompter: Is into the breach a game with perfect information?

assistant: Into the Breach is a game with almost perfect information, other than the state of it's Random Number Generators. Any game with random mechanics typically makes use of Random Number Generators, which cannot be predicted or revealed to the player. Considering that Into The Breach makes use of such a mechanism, it cannot be said to have perfect information. However, most other information is revealed to the player, unlike the cards in the deck in poker.

assistant: In the context of the game "Into the Breach", 'perfect information' means that the player has complete and full visibility of the game state and all elements that are relevant to make decisions. This means that all possible actions, outcomes, and consequences of each action are known and visible to the player, allowing for informed decision-making. The term is used to differentiate the game from others where information is hidden or unknown to the player, making it more challenging to make decisions.

Here is an example of code that implements a simple card game with perfect information in Python:

css
Copy code
import random

suits = ['hearts', 'diamonds', 'spades', 'clubs']
ranks = ['2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K', 'A']

deck = [(rank, suit) for suit in suits for rank in ranks]
random.shuffle(deck)

players = ['player1', 'player2']
hands = {player: [] for player in players}

for player in players:
    for _ in range(5):
        hands[player].append(deck.pop())
        
print("Hands:")
for player in players:
    print(player + ": " + str(hands[player]))
    
# The game state is now completely known to both players
# and no information is hidden
In this example, both players have perfect information about the state of the game because all the cards in the deck have been dealt and both players know what cards they have in their hands.

assistant: In the context of Into the Breach, "perfect information" means that all information about the game state, including all future possible moves and their consequences, is available to all players at all times. This means that players have full knowledge of the game state, including the positions of all units and obstacles, and can make informed decisions based on that information.

prompter: Does this mean that Into the Breach is a game of perfect information?

assistant: Yes, Into the Breach is considered to be a game of perfect information. The game's mechanics, design, and rules ensure that all players have full knowledge of the game state and can make informed decisions based on that information.

assistant: A game is broadly considered to be perfect information if the players have complete information about the state of the game at all times.  To be more explicit this means:

1. Complete information: All players have access to all information about the current state of the game, including the positions of all pieces and all previous moves made by their opponents.
2. No hidden information: There is no hidden information or chance events that would give an advantage to one player over another. For example poker is not valid since not all cards are visible by all players.
3. Determinism: The outcome of each move is determined by the rules of the game and the player's decisions, not by chance events such as random number generation. 

To the best of my knowledge  Into the Breach is deterministic and apart from AI strategy does not have hidden information. This makes it likely it is a perfect information game but I can not say for sure. If you can confirm the conditions above are true or give me some more information I will be happy to assist you further.

assistant: Yes, even though there is a lot of strategy involved all information is available to all players at all times. Chess is another example of a perfect information game. Compare this to a game like Starcraft or League of Legends. In Starcraft each player has hidden information, in League each team does.

assistant: Depends.

Does the game feature a line of sight mechanic? Are the enemies able to conceal information, such as laying down hidden traps? These would disqualify it from being a Perfect Information game.

Does the game feature randomly generated damage? If so, is the probability distribution known to the player? Can the player see the results of the PRNG roll before executing a turn? This might also disqualify it, although some academics consider chance games with known probability distributions to be valid for analysis as Perfect Information games.

Are turns executed simultaneously? If so, information required to formally reason about the current turn is hidden.