Card games

We played a “perfect strategy” game today where everyone theoretically has an equal chance of winning.

The game is called 91 and the rules are below.

We also played a couple of “collaborative games” where all players work together to try and beat the cards. The two we played were German games called The Game and Hanabi.

The Game

Hanabi

Rules for 91:

Number of players: 2-7

Materials: 1 card deck for 2-3 players; 2 card decks for 4-7 players (no jokers).

Players and Cards: The game is for two to seven players, using a complete suit from a standard 52-card pack for each player plus one extra suit. Two decks are needed for four or more players. Cards rank Ace (low), 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K (high). As a prize, the Ace is worth 1 point, cards 2-10 face value, Jack 11, Queen 12 and King 13.

Setup: The cards are sorted into suits. One suit (traditionally diamonds) is shuffled and stacked face down as a prize pile. Each of the other players takes one complete suit.

Play: The top card of the prize pile is turned face up (so you see its value). Then each player selects a card from their hand with which to bid for it and places it face down (so you can’t see its value). When all players are ready, the bid cards are revealed simultaneously, and the highest bid wins the prize card. The bid cards are then discarded and the prize card is placed beside the player who won it. The next card of the prize pile is turned face up and players bid for it in the same way. If two players put the highest bit, the bid cards are discarded but the prize card remains on offer. A new prize card is turned face up and all players then make their next bid for the two prize cards together, then for three prize cards if there is another tie, and so on. If any of the players’ last bid cards are equal, the last prize card (and any others remaining from immediately preceding tied bids) are not won by any player.

Scoring: When all players run out of bid cards, the play ends. Each player totals the value of the diamonds they have won in bids (Ace=1, 2- 10 face value, J=11, Q=12, K=13) and the greater total wins the game.

Guess the average

Today we played a game where everyone simultaneously guesses a number between 0 and 100. The person who is closest to the average (mean) wins. What number would you choose?

The game is played in multiple rounds. It is interesting to see how strategies change and how the mean changes over time.

One fun variation is that the winner is the person who is closed to 2/3 of the mean – an analysis is here.