On Wednesday night, I played a cooperative card game called The Gang for around 2 hours. The Gang is a cooperative adaptation of Texas Hold’em where players have to guess how good their hand it relative to other players.

A round of The Gang starts with players drawing 2 cards and then taking a chip to represent how strong they think their hand is. The chips have a number of stars ranging from 1 to the number of players in the game. Then there are 3 more rounds where cards are revealed, players reasses the relative strength of their hand, and then take a chip. During the 4 round, the chips players take have to correctly represent the

There are 1326 possible poker hands. A binary search to find a value in data that has 1326 items would take up to 11 iterations.

There are 6! ways that players can take chips. As a result, the way players represent chips can represent up to 9 bits of information. Players have 3 rounds to take chips before they have to take chips correctly representing the strength of their hand. This represents 27 bits of information, which is not enough to communicate the exact contents of people’s hands, even when considering the fact that the game is played with a standard 52 card deck without duplicates.

I think the fact that players have to communicate the relative strength of their hand over multiple rounds instead of simplify taking chips to communicate the exact cards in their hand is a brilliant design.