How to play Goofspiel

Goofspiel, also known as the Game of Pure Strategy (GOPS), is a two-player bidding game played with ordinary cards. One suit is the prizes, and each player holds a complete suit to bid with. A prize is turned up, both players secretly choose a card, and the higher card wins the prize. There is no luck in your own hand at all: both players start with exactly the same thirteen cards.

What makes Goofspiel a game of skill is that it is all about judgement and reading your opponent. Every card can be used only once, so a King spent on a small prize is a King you will not have later. You need to decide which prizes are worth fighting for, which to give away cheaply, and how to stay hard to predict. Mathematicians and game theorists have studied it for decades because it is so simple to learn and so hard to play perfectly.

How to play on skill.games

When the game opens, the settings appear first: choose a difficulty and tap PLAY. You hold the 13 hearts at the bottom of the screen. The computer, called the Bot, holds the 13 spades face down at the top. The prize, a diamond, is shown large in the middle.

• Bidding: tap a heart to lift it, then tap it again or tap BID to commit. You can also drag a heart upwards to bid it at once, or drag it sideways to reorder your hand.
• The reveal: both bids slide in face down, then turn over together. The higher card takes the prize, which flies to the winner's pile.
• No peeking: the Bot chooses its bid the moment the prize is turned up, before you choose yours, and its fan is shuffled, so nothing on screen gives its choice away.
• Used cards: cards both sides have already played are shown as faded markers, so you can always see what is left.
• Carried prizes: after a tie, waiting prizes peek out above the new one, with a badge showing what is at stake.
• Menu: the button in the top-left corner pauses the game. From there you can resume, start a new game or turn the sound on or off.
• Saving: an unfinished match is saved. Next time, tap CONTINUE to carry on where you left off.
• Results: at the end you see the score, prizes taken and ties, plus your wins, losses, draws, win rate and streaks at that difficulty.

Rules

Setup. Three suits from a standard deck are used. You hold the hearts from Ace to King, the Bot holds the spades from Ace to King, and the thirteen diamonds are shuffled face down as the prizes.

Card values. Ace is 1, numbered cards are worth their number, Jack 11, Queen 12 and King 13. This applies both to bids and to prizes, so the diamonds are worth 91 points in total.

A turn.

1. The top diamond is turned face up.
2. Both players choose one card from their hand as a bid, at the same time and in secret.
3. The bids are revealed. The higher card wins the prize and its points.
4. Both bid cards are discarded; they cannot be used again.

Ties. If both bids are equal, nobody wins the prize. It stays in the middle and goes, together with the next prize, to whoever wins the next bid. Several ties in a row can build a large pot. A tie on the thirteenth and last prize scores for nobody.

Winning. After all thirteen prizes have been played, the player with more points wins. Equal points is a draw.

Strategy tips

• Know the target. There are 91 points in the deck, so 46 guarantees a win. You do not need to win every big prize, only more than half the value.
• Match your cards to the prizes. A good starting rule is to bid roughly in proportion: a high card for a high prize, a low card for a low one. It keeps your strength where the points are.
• Concede cheaply. When you decide not to fight for a prize, give up your lowest card. Throwing away an Ace or 2 on a small prize costs you almost nothing.
• Win by one, not by five. If you expect the Bot to bid a 9, a 10 wins just as well as a King. Overbidding wastes strength you will need later.
• Track both hands. Both players start with the same cards and every played card is public. When the Bot has already used its King, your Queen is the strongest card left.
• Ties are worth fighting for. A carried prize makes the next bid more valuable. Be ready to spend a strong card when the pot has grown.
• Stay unpredictable. On the higher levels the Bot learns from your bids. If you always bid the same way, it will notice and undercut you, so mix up your choices.

Difficulty levels

• Easy: the Bot often bids a random card. The rest of the time it picks a card close to the prize's value, with plenty of variation.
• Normal: the Bot bids in proportion: the higher the prize ranks among the prizes still to come, the higher the card it plays from its own hand, pushing a little harder on the bigger prizes. It only rarely bids at random.
• Hard: the Bot watches how you bid during the match and builds a picture of your style. Before each bid it plays out many possible futures against that picture and chooses a strong card, with a little variety.
• Crazy: the Bot treats each prize as a guessing game and mixes its bids so they are hard to read. It remembers your bidding style across the matches you play in one visit and exploits it, and when four cards or fewer remain it calculates the rest of the match exactly.