God plays dice

Don’t worry, this is not a post about quantum mechanics. It is about randomness in games. Specifically, I want to discuss  the different kinds of randomness you can have in board and card games.

Typically, a game that works with dice is a game with randomness. In general, I do not enjoy randomness, and I am not alone in that. Still, there are games with dice that I enjoy. The reason is that there are different kinds of randomness. Broadly speaking, we can distinguish two: non-determinism, and imperfect information.

Non-determinism means that certain decisions of a game are resolved in a random manner. Imperfect information means that aspects of the game are unknown to one or more players. At first glance, one would say that only non-determinism amounts to randomness, while imperfect information does not. However, imperfect information can be the result of randomness, and that is the kind of randomness that I can enjoy!

Let me give an example of randomness: the game of Risk. In Risk, a player might decide to attack another player with a certain amount of troops. He then rolls dice to determine the damage that the troops do. His opponent defends by rolling dice. The two dice rolls determine how many troops are removed from the game. This is a typical example of non-determinism: the randomness gets applied after the decision to attack has been made.

On the opposite side of the coin we have a game such a Poker. Poker is a game of imperfect information. Each player knows his own cards, and open cards of his opponents, cards on the table, and the bids that the opponents made. They do not know the hidden cards of the opponents. Therefore, they have to make a decision in a situation with unknowns. There is no non-determinism involved, however; it is not as if the best hand will be decided by a die roll or something. The best hand is the best hand in the current situation, and the fact that part of that current situation is unknown makes the game interesting.

Some would argue that Poker has non-determinism in the dealing of the cards. That, however, is not non-determinism, even though it concerns randomness. The initial game situation is set up randomly, but that all happens before the first decision of a player. Therefore, Poker is purely a game of imperfect information.

There are no dice in Poker, but there are many games with dice that are imperfect-information games. An example is Backgammon. In this game a player rolls dice to determine his possible moves. He then decides which moves to make. The player has complete knowledge of the state of the game when he makes a decision, and the outcome of the decision is purely the result of his decision. However, whether or not it was the best decision depends on the situation in which the opponent must make a follow-up decision, and that situation will be partly decided by the rolling of dice.

To give a very simple example to distinguish non-determinism and imperfect information: suppose I have a game in which I have two pawns that move along a track. How far a pawn moves is determined by a die. Now, if the game rules specify that I should first decide which pawn to move, and then roll the die to determine how far it moves, that is non-determinism. If the rules specify that I first roll the die and then determine which pawn to move, that amounts to imperfect information. Personally, I’d say that the second game is more interesting than the first, as it may allow deeper tactics. Although I probably would still rather play Arkham Horror.

I recently stated in a newsgroup that the difference between imperfect information and non-determinism is similar to the difference between science and religion. In science, we examine in what shitty situation we are and take steps to get out of it. In religion, we place our trust in fate to get us out of shitty situations. I thought this was a fun observation but I got a warning from the moderator: I had not surmised that my (fairly innocent) remark might offend religious people.

The moderator was probably right. Still, the response brought me a slightly deeper insight in why I prefer imperfect information over non-determinism: it might be because I am a scientist. I don’t mind being thrown into a shitty situation in a game, and I don’t mind that my opponent gets into a less shitty situation. It is the situation I have to work with and which I have control over. It is a challenge to overcome, and the shittier the situation, the sweeter the victory if and when I manage to achieve it. On the other hand, winning because the dice fell favorably just feels hollow.

Well, yeah, I can relish in the knowledge that Fate was on my hand, but that means that Fate, not I, won the game. And frankly, if Fate really must win a game, I say let her pick her own game group.


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