Game Theory: Dice Complicate Things

This is a follow up post to this discussion of why some rolls should remain secret from the players, and this brief summary of information states in Game Theory.

Again, I'm far from an expert in Game Theory. If I make some mistakes, forgive me. The following is based on my understanding of the theory.

Game Theory uses mathematical models to explain, and hopefully predict, human decision making. It sets up scenarios and tries to use logic, modeling of all permutations, and probability to create these models, and many of the models show optimal game states called equilibria. A state of game equilibrium is the optimal moves for one or both players in the game.

As mentioned in the post on information in games, sometimes one or both players have imperfect or incomplete information about the game state, and so a Call to Nature (or assigning probabilities of any possible move happening) is made.

Now, Game Theory isn't designed to predict outcomes of things like common games. It's really about creating hypothetical situations to model real world decisions. So from what I've read, the Call to Nature is used as infrequently as possible. It's possible, though, if I keep studying GT, that more advanced models do include constant randomness in the game model. If so, I haven't gotten there yet.

Rolling dice is a Call to Nature. But in a GT model, it's a theoretical position discussing the possible outcomes or permutations of the model based on the probabilities assigned.

In an RPG, the dice are a Call to Nature, but they also are also an unknown. Until the dice are rolled, we can know the probability of a result, but no player or game master knows what the outcome will be until the dice are rolled.

In a pure diceless story-game, there are no Calls to Nature. Players can enjoy a state of perfect information. Every move made by every player is in the open.

In an RPG involving random number generation (by dice, card, or what have you), the game state may be perfect if the game master has no secret information that the players do not. Usually, though, the GM will know some things about the game state that the players don't, resulting in an Asymmetric state of information.

The dice, though, are the great equalizer. Players and GMs alike are in a state of Imperfect information. In a way, the dice could be thought of as a player in the game as well as the GM and players. And no one knows what moves the Call to Nature Player will make. You can't predict their strategy (unless you game with loaded dice). You can know the probability of any particular throw, but the result will always be a surprise.

How this affects things, and why keeping some of these throws secret will have to wait for another post, though. I'm out of time.