This is the first post in a series responding to Alexis's comments on my Secret Roll post. I don't have time to write up a full reply today, so I'll just get this out there as a grounding for my thoughts.
Let me also preface this by saying I'm nowhere near an expert in Game Theory. I've done some light reading on the subject. My notes here come from reviewing Rosenthal's The Complete Idiot's Guide to Game Theory (2011).
There are four basic states of information in Game Theory: perfect, imperfect, incomplete, and asymmetric.
Perfect Information: all players are aware of all moves made by all other players up to that point of the game. For example, in chess, you can see the board, all the pieces, and every move you have made and every move the opponent has made is done openly.
Imperfect Information: One or more players know the possible moves that could be made, but don't know the exact move that has been made until after they make their move. Rock-Paper-Scissors is an example. You know what move you will make. You know possible moves your opponent may make. You won't know the outcome until the moves have been made already.
Incomplete Information: One or more players has imperfect information and also cannot be sure what sort of player they are up against, what strategies they favor, or the value the other player(s) place on outcomes. Poker is a good example of this, as a good poker player will try to hide their preferred strategies to more effectively bluff.
Asymmetric Information: One player has perfect information while the other player(s) has incomplete information. This sounds to me a lot like the typical DM/player distinction.
Rosenthal suggests that imperfect information games are the most interesting theoretically. "[T]he truly interesting games involving human interaction are games of imperfect information" (p. 84). However, game theorists can turn games of incomplete/asymmetric information into games of imperfect information by using a "call to Nature" or assigning a probability to each possible unknown move or unknown strategy choice in these situations.
It seems like Alexis is saying D&D works best when it's an imperfect information game. Players know the moves that they and the DM have made, but don't know the outcome until the dice are rolled. But once they are rolled, we're in a situation of perfect information until the dice need to be rolled again.
What I'm suggesting is that occasionally, incomplete or asymmetric information situations, where the player is forced to make a Call to Nature to determine the best strategy, can be a good thing.
Rosenthal, E.C. (2011). The complete idiot's guide to game theory: The fascinating math behind decision-making. New York: Alpha Books.