Median game
Rules
“Median game” is a card game or card game family where, in each round, players try to place the card which is the median (hence the name). The objective is to win the most rounds. The game can be played with 2 or more players, though is best played with 3 players.
The game is played with a standard deck of cards. It could in principle be played with a larger or smaller deck. Aces are high. Each player is dealt some number of cards. 5 is a good choice. Increasing the number of cards leads to less round-by-round randomness/luck, and decreasing it leads to more randomness. Players can see their own cards and can't see each other's cards, but can show them if they would like.
This is the gameplay for an odd number of players:
- One player places a card face-down on the table. In the first round, it is the dealer, and in the following rounds, it is whoever most recently won a round.
- The other players can discuss and strategize however they would like, including with the player who went first.
- The other players each place a card face-down on the table.
- The cards just played are revealed.
- If there is a unique median card (e.g. there are 3 players and the cards were 5, 8, J), the player who placed it wins the round, takes all the cards from this round and from the “pool”, and sets them face-down in front of themselves.
- In case of a tie (e.g. there are 3 players and the cards were 5, 5, J), the cards just played are set to the side face-down in the “pool”.
- If there are enough cards remaining in the deck for all players to draw one card, all players draw one card.
- Repeat the above steps until the players have no cards left.
- After all rounds have been played, the player with the most rounds won is the winner. The number of rounds won by players can be checked by looking at how many face-down cards each player has in front of themselves
For an even number of players, the rules are the same, except the player going first in each round announces before the round starts whether the winner will be the “high or low median”. For example, if there are 4 players, the player going first will announce whether the winner will be the player who places the second-highest or second-lowest card.
For 2 players, the game surprisingly still works, and the “high or low median” simply becomes the highest or lowest card of the two. This gives the player going first an extreme advantage in each hand (for instance, a player with an Ace will easily win a hand by going first and calling high). So you can choose to just alternate who goes first, or have the previous hand's loser go first.
Strategy
It may seem that the outcome of the game is entirely random. Consider the following points:
- There are people who can consistently beat others at Rock Paper Scissors.
- The player who goes first in each round has a significant disadvantage. Ignoring ties, each player, if placing a random card, should have a 1/3 probability of winning the round (if there are 3 players). However, if the players not going first place two cards very close to each other, it is highly unlikely that the first player will have the middle card (and impossible, if the other players place consecutive cards). For example, suppose player A just went first. Now, players B and C both agree to place cards which are “very low”. Unless player A also went “very low”, player A has no chance of winning the round.
- If the players not going first trust each other, and have matching cards, they can agree to tie up one or more rounds to ramp up the “pool,” then win a round, thus netting many cards for one of them.
The game ends up being about trust and deception.
About
Median game was created in late 2023 by me and my friends North and Katie. We were inspired by the completely pointless game “War” and our desperation for a simple and fun three-player card game.
Credit for the realization that the even-player variant works for two players when alternating who goes first is due to my friend João Vitor.
