Sunday, 9 December 2007

hidden information

When I pondered the mechanisms for randomness in boardgames (and cardgames), another topic came to me and I thought it would be interesting (well, at least to me) to explore the mechanisms for hiding information in boardgames. When I say hidden information I mean information that is known to one or more players but unknown to one or more other players. I am not referring to information that noone knows.

So, what kind of information is hidden in games? (maybe I should call this secret information) Money (e.g. St Petersburg, Modern Art), available strength or power or choices (Tigris & Euphrates, San Juan, Ingenious, Reef Encounter), identities (Werewolf, Citadels). Having hidden information in a game increases unpredictability, because you don't know what hand your opponent has, and you have to guess based on known information, or how he/she behaves. Sometimes you make moves which are not directly beneficial to you in order to confuse your opponents about your true intentions. You bluff. Bluffing is crucial in Poker. Having hidden information adds some chaos in games, and spices things up a bit. Sometimes it is necessary to prevent a game from becoming a tedious mathematical exercise, to avoid analysis paralysis. Sometimes it is the core of the game. Werewolf would not be a game at all if the villagers know who the werewolves are. In Citadels, the core of the game is choosing characters. When the hand of cards reach you, you can tell what are missing, and you'll know what characters the players before you may have chosen. After you choose a character, you pass the remaining cards to the next player, and he or she will have slightly less information to work on (one card less). When you choose a character, you can think about what information you are releasing to the next player, and how he or she will react to that. However I have not gone to that level of depth of play myself. I just think of what bad things they can do to me if I don't take so-and-so card, or what good things they can do to themselves if I don't take another so-and-so card. In Vinci, where victory points are open information, sometimes people complain that this causes analysis paralysis in the final round when all players are trying to calculate all the possible combinations of moves that can increase their own score and decrease their opponents' scores.

Some types of information are hidden in some games but not in others. E.g. money. In Medici, money is open information. In fact money = victory points because the winner is determined by how rich you are. Everyone knows exactly how much everyone else has. You know who is leading and who you need to be wary of. In St Petersburg, money is hidden, so sometimes you really are not sure how much money your opponents have and whether they'll be able to afford the craftsmen / buildings / nobles / upgrades available on the board.

There are also situations where some information is known to more than one player but not to others. There are some games with very interesting combinations of hidden / open information and how information is communicated. In Cluedo and Mystery of the Abbey, which are both deduction games where players gradually collect small pieces of information and use an elimination process to find the murderer, each player starts with a roughly equal amount of information. During the course of the game, the players try to extract information from others, while also trying to release as little information as possible to others. As the game progresses, it becomes harder and harder to remember what information you have released and to which opponent, or what cards each opponent is holding (so that you can avoid asking the wrong question which will only give you information that you already know). In Lord of the Rings, a cooperative game, with the Sauron expansion, the hobbits will not know what cards Sauron is holding. They also cannot see what cards each other is holding, although they want to communicate this information to one another so that they can plan together to beat Sauron. However, Sauron is right there at the table listening to any information exchange. This poses a tricky challenge to the hobbits.

Some games have more hidden information, some have less, or none. Theoretically, games with little or no hidden information will tend to require more skill and are more challenging to master. Think of Chess, Go, the GIPF series. Games with more hidden information will tend to be more chaotic and tend to be lighter games. E.g. Ca$h 'n Gun$, Poison. However, in practice, having much or little hidden information is not really a big factor in determining whether a game is heavy or light. The more dominant factor is randomnes / luck. Blokus is an open information game. You can see exactly what pieces your opponents have left. Yet Blokus can be played in a very relaxed way. It can be played with much thinking and planning too. I guess it is very much up to the players. Coloretto is also an open information game, but is a light game. This is because of the luck / randomness introduced by the card draw. Monopoly is also open information (I think). Gulo Gulo and Villa Paletti are open information games, but you'd hardly associate them with Chess. On the other hand, Tigris & Euphrates has hidden information, i.e. your hand of 6 tiles, which is often crucial when it comes to the wars or the civil wars (more layman terms for the official terms used in the game - external and internal conflicts). Yet it is quite a deep and challenging game.

What are the mechanisms for hiding information?

  • Cards - This is probably the most handy way of hiding information. You can hold many cards in your hand, even for games like Ticket To Ride where you will often have many many many cards. Just imagine playing Ticket To Ride using tiles instead of cards. It would be a nightmare. For almost all card games, cards are used as a mechanism for hiding information. There are exceptions, like Coloretto.

    Cards are the most convenient way of hiding information. This is Mystery Rummy: Jack the Ripper

  • Tiles - Scrabble, Mahjong, Ingenious, Acquire. For some, you have a rack on which to put the tiles. Tiles are often required to be of a certain shape, so that they can fit onto the board. Otherwise using cards would probably be a more convenient and cheaper way of hiding information. Pieces in Lord of the Rings - The Confrontation can probably be considered tiles. They stand up with the text side only visible to the controlling player.
  • Tokens - Order tokens in A Game of Thrones are placed face down on the board. The backs of the tokens show which player they belong to, but other players will not know the order placed. Aladdin's Dragons also uses tokens in a similar fashion.

    A Game of Thrones. The command tokens are the round ones seen on the map (face-down, only showing the player colour and icon), and also on the lower right of the photo (face-up, showing the actual commands).

  • Blocks - I'm mainly thinking of block war games like Hammer of the Scots, Rommel in the Desert and Crusader Rex. Your blocks have information only on one side, the side facing you. You only reveal your blocks when you are about to start a battle. Blocks are also a nifty way to keep track of information, i.e. the strength of your troops. Near the four edges of a block are different numbers of pips, indicating the strength level of the block. The block stands upright, and the edge on top incidates the strength level of the block.

    Crusader Rex, a block war game.

  • Screens - Tigris & Euphrates, Aladdin's Dragons, Reef Encounter, Keythedral, Modern Art, Samurai, Samurai Swords. Many of Richard Breese's games feature screens. One advantage of screens is they can be used to hide different types of components - cubes, tokens, tiles, coins. They provide an area where you can just drop these components, without needing to arrange them neatly like Scrabble tiles or cards to make sure they are not visible to others. You can just carelessly drop them behind your screen. The bad thing is if you are too careless and tip over your screen... oops!
  • Time / Memory - The (not unlimited) capacity of the human brain in memorising and tracking information is a mechanism for "hiding" information. When playing Tigris & Euphrates, technically you can watch and track what cubes your opponents collect. But it is so tedious that people just do not bother. Instead, you just get the general feeling that a certain opponent has many cubes of so-and-so colour but not many of another colour. In Modern Art, you can track how much money everyone has, because every everyone knows who paid whom how much and for which painting at every auction. But how many people actually do that? In many games, victory points get this type of treatment too. There is some tracking of victory points, but you are not exactly sure who is in front and who is trailing. In Carcassonne, you do track your points throughout the game, but the farmer scoring at game end usually has a big impact, and there is also scoring for incomplete features at game end, so sometimes you can't be sure exactly who is winning. This helps to discourage detailed calculation. Most people prefer not to bother and just play from the gut. In Through the Desert, you can track and calculate the scores of everyone at any one time. This is a open information game too. There is no score track provided, but you can calculate the scores if you want to. But most people don't bother. You just use your general gut feel to tell you who is doing well and who isn't. That's the beauty of the laziness of the human brain.

One game mechanism that is related to hidden information is blind bidding. E.g. players secretly bid an amount of money for a particular privilege, like being the start player for the round. Some people don't like blind bidding. I don't hate it, but I'm not particularly fond of it either. I guess it makes me feel a lack of control, and makes me feel I have to make a blind guess. There is blind bidding in Modern Art (bidding for a painting, of course), Aladdin's Dragons (bidding for the right to use a location), Die Macher (turn order), Felix: The Cat in the Sack (in this case, "blind" in the sense that you don't really know what you're getting), Samurai Swords (turn order), A Game of Thrones (the right to claim the throne, fiefdom, espionage, and contribution to protect the realm from the wildings).

After writing this blog entry, I realise that the amount of hidden information has little correlation to whether I like a game of not. I had thought I'd prefer games with less hidden information.

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