Exploring game theory with a simple card game (GOPS)

By Paras Mittal
Published January 2, 2026
Updated January 2, 2026

I recently discovered GOPS. It's a fascinating and simple card game. It's my new favorite card game. Unlike nearly all card games, this game is not luck based.

I've described the rules below. Try playing with a friend. Otherwise, try this. However, the AI can be predictable.

I prefer the carryover variant.

Game of Pure Strategy (GOPS)

Also known as Goofspiel.

GOPS is a two-player card game in which players compete by bidding for prizes. Unlike most card games, players act simultaneously rather than taking turns, and both players hold identical resources. The outcome is determined entirely by the players' decisions.

In game theory, GOPS is a multi-stage simultaneous-move game with complete information and imperfect information: both players know the rules and each other's available cards, but neither knows the other's bid until both are revealed.

Card Ranks

Each card has a rank from 1 to 13:

A card's rank determines both its value as a prize and its strength as a bid.

Setup

1. Take a standard 52-card deck and separate the deck into four suits.
2. Designate one suit as the prize suit. Shuffle it and place it face-down as the prize deck.
3. Each player takes one of the remaining suits as their bidding hand (13 cards, held so only they can see them).
4. Discard the fourth suit; it is not used.
5. Each player has an empty, face-up score pile where they will place prizes they win.

Gameplay

The game consists of 13 rounds. Each round proceeds as follows:

1. Turn the top card of the prize deck face-up. This is the current prize.
2. Each player privately selects one card from their bidding hand and places it face-down. This is their bid.
3. Once both players have placed their bids, the bid cards are revealed simultaneously. The player who played the higher-ranked bid wins the current prize and places it in their score pile. Both bid cards are then discarded face-down.

After resolution, the next round begins with a new current prize.

Resolving Ties

If both players bid the same rank, a tie occurs. Both bid cards are still discarded. Choose one rule before play begins:

Discard rule: The current prize is discarded. Neither player scores it. The next round proceeds normally.

Carryover rule: The current prize is not awarded. Instead, it remains in the center and is added to the prize for the next round. The winner of the next round takes both prizes. If consecutive rounds end in ties, the pot continues to grow until a player wins a round and collects all accumulated prizes. If the final round ends in a tie, any prizes remaining in the center are discarded.

Game End

The game ends after all 13 rounds. Each player sums the ranks of the cards in their score pile. The player with the higher total wins. If both players have equal totals, the game is a draw.

The maximum possible score is 91 (the sum of ranks 1 through 13). Under the discard rule, the two players' scores may sum to less than 91.

Sources: inventor