Euchre

Goal of the game

Two teams of two face off: you and your partner (sitting across from you) against two opponents. The first team to reach 10 points wins the game.

The cards

The game uses 24 cards (9, 10, jack, queen, king, ace). Everyone receives 5 cards and the next card is turned face up in the centre. In the trump suit the order is: the right bower (the jack of the trump suit), the left bower (the other jack of the same colour), ace, king, queen, 10, 9. The left bower is part of the trump suit in every respect. In the other suits: ace, king, queen, jack, 10, 9.

Choosing the trump

• First round: starting with the player to the dealer’s left, each player may order up the suit of the turned-up card, or pass. If someone orders it up, the dealer picks up that card and discards one.
• Second round: if everyone has passed, the card is turned face down and each player may name a different suit. If everyone passes again, the cards are redealt (or, depending on the option chosen, the dealer is stuck and must choose).
• The player who chooses the trump may decide to go alone: their partner then lays down their cards.

Play

• The player to the dealer’s left leads. You must follow suit (the left bower counts as a trump); otherwise you may trump or discard.
• The highest trump, or failing that the highest card of the suit led, wins the trick.

Scoring

• The team that chose the trump takes 3 or 4 tricks: 1 point.
• It takes all 5 tricks: 2 points (4 points if the maker went alone).
• It takes fewer than 3 tricks: it is “euchred” and the other team scores 2 points.

About the AI

Levels 1 to 3 bid and play according to expert rules of increasing rigour (hand strength, team play, master cards). Levels 4 and 5 use Monte Carlo determinization: the AI generates many distributions of the hidden cards consistent with what it has seen (cards played, revealed voids, the card picked up by the dealer), solves each one exactly with an exhaustive search and chooses the bid or the card that earns the most on average. It never sees your cards, nor those of its partner.