Tuesday, March 07, 2006

Blind Games

I've always been fascinated by games that involve bluffing and I've always been more fascinated by 'blind' games. I define a 'blind' game to be one where there is some state in the game that a player can choose not to reveal. Instead the player claims what that state is. The other player can choose to accept or reject this state of affairs, but if it is rejected then the actual state is revealed and one or other player is 'punished' as appropriate. (Eg. blind chess isn't 'blind'.)

Consider this trivial game: you deal a pack of cards to N players. The players take turns and the winner is the first one to get rid of all their cards. A turn consists of discarding a set of cards that all have the same number or rank. This game isn't very interesting.

But now apply the 'blind transform' to this game with the 'punishment' of picking up all of the discards. The players play cards face down and make some claim about what cards they are laying down. If someone challenges this claim you have a look and mete out the punishment. A trivial game has now been turned into a mildly entertaining game. It can be turned into an excellent game by means of the 'ethyl transform' - playing whle drunk. But moving on...

One of my favourite games years ago, when I could talk people into playing it, was "Blind Le Truc". It's Le Truc but with all of the cards played face down but players claiming what the cards are. In tis case the punishment is losing a trick. Even played 'sighted' this game is full of bluff. Playing it blind brings it to a whole new level. Players can play against each other for extended periods of time playing what is practically an imaginary game going through all the motions of Le Truc without ever seeing a card. It's a lot of fun. Well, I think so anyway.

Even the most trivial of games can become interesting. Eg. each player is given an entire suit of a deck of cards. Each round a player places one card in the middle. Whoever places the highest card in the centre wins that round. Play continues until nobody has any cards left and the winner is whoever won the most rounds. After applying the blind transform, with round losing as punishment, this game is turned into something fun, at least for a few minutes.

Poker is also a blind version of a trivial game.

How amenable are these games to analysis? That last game is pretty simple. Suppose two players each have only 3 cards. What is the optimal way to play?

You can also apply the blind transform multiple times. It's more interesting if the nth application has a tougher punishment than the (n-1)th. In that case it corresponds to raising the stakes for being caught, or accusing someone of, 'cheating'.

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