Balancing Act

Full rules

1. Overview
2. The cards
3. Setup
4. A round
5. Your turn
6. Balanced or tipped over
7. End of a round
8. Not a word about your cards
9. Winning and losing
10. Difficulty levels
11. Tips for beginners
12. Variants

Overview

Balancing Act is a cooperative card game: you all play as one team and win or lose together. In the middle of the table stands a scale with two pans, a left one and a right one – you simply lay cards on two places. In turn, each of you puts a card onto one of the pans; its number is its weight. Whenever both pans weigh exactly the same, the scale is balanced and is emptied. But if one pan ever gets too much heavier than the other, the scale tips over and you lose a life. And when the last card of a round has been played, the scale must be balanced too. You keep your cards hidden and may not talk about them – only one card of each hand lies face up for everybody to see.

• Players: 2–4; best with 2.
• You need: one standard 52-card deck without jokers.

Balancing Act is a new game written for this site and not yet playtested. It is not based on a published game. The limits and the number of lives were set with a computer simulation (see "Difficulty levels").

The cards

The top card of a pan is the card that was put there last. Lay the cards of a pan overlapping in a column, so that every card can be read and the top card is the one nearest to you.

• A card that the Queen lifts goes to the discard pile together with the Queen. A card that the Jack shifts becomes the top card of its new pan.
• A Jack or Queen may work on either pan, the heavier or the lighter one. If only one pan holds cards, it works on that pan. On an empty scale it does nothing: just put it on the discard pile.
• An Ace used as a counterweight always balances the scale, so it never has to be remembered: the scale is emptied at once.

Setup

1. Take the four Kings out of the deck. On the Normal level, lay three of them face up beside the scale: these are your lives. Put the fourth back in the box (other levels: see "Difficulty levels").
2. Shuffle the other 48 cards and put them face down as the draw pile.
3. Leave room in the middle of the table for the left pan and the right pan, and next to them for a discard pile.
4. Choose who starts the first round.

The game has four rounds of 12 cards each. Each round has a limit – the largest difference the scale can take:

The scale gets more sensitive every round: with two players the limit is always 9 minus the round number.

A round

1. Deal: deal 12 cards from the draw pile – with 2 players 6 each, with 3 players 4 each, with 4 players 3 each. There is no drawing during the round.
2. Face-up card: everybody looks at their cards and lays one of them face up on the table in front of them. It still belongs to your hand; the others stay hidden in your hand.
3. The starting player takes the first turn; then play goes on clockwise until all 12 cards have been played. In the next round, the next player clockwise starts.

Your turn

1. Play one card – from your hand or your face-up card: - a number card or an Ace onto either pan; - a Jack or Queen: carry out its action.
2. Check the scale (see below).
3. Face-up card: if you have played your face-up card, lay another of your cards face up. You may also swap your face-up card for a card from your hand. If you have only one card left, it lies face up.

You must play a card on every turn – you may not pass, even if every card you hold would tip the scale.

Balanced or tipped over

After every card, add up both pans. The difference is how much heavier the heavier pan is.

• Balanced: both pans weigh the same. All cards on the scale go face down to the discard pile, and the scale is empty again. This is what you are aiming for.
• Tipped over: the difference is greater than the limit. Turn one King face down – you have lost a life – and put all cards on the scale on the discard pile. A difference exactly equal to the limit is still fine.
• Otherwise nothing happens, and the next player takes their turn.

End of a round

The round ends when everybody has played all their cards. If cards are still lying on the scale, it is not balanced: turn one King face down and clear the scale. An empty scale is balanced.

Then deal the next round. After the fourth round the draw pile is used up and the game is over.

Example: Anna and Ben play on the Normal level, round 1, limit 8. Anna holds 7♣ 3♦ 5♠ 9♣ J♥ A♠ and shows the 3♦; Ben holds 4♥ 8♦ Q♣ 10♠ 2♣ 6♥ and shows the 4♥. Anna starts.

1. Anna puts the 7♣ on the left pan: 7 against 0, difference 7.
2. Ben sees Anna's 3♦. He puts his 4♥ on the right: 7 against 4, difference 3. His face-up card is gone, so he shows the 2♣.
3. Anna plays her 3♦ on the right: 7 against 7 – balanced! The three cards go to the discard pile. Anna shows the 5♠.
4. The scale is empty. Ben can't start with the 10♠: 10 is more than the limit of 8, and the scale would tip over. He puts the 6♥ on the left.
5. A 9 can only be played when the difference is large enough, so Anna gets rid of hers now: 9♣ on the right. 6 against 9, difference 3.
6. Ben sees Anna's 5♠ and makes the difference 5: 2♣ on the right, 6 against 11. He shows the 10♠ – a warning that this card needs a big difference.
7. Anna plays the 5♠ on the left: 11 against 11 – balanced! She shows the J♥ and keeps the A♠ hidden.
8. Ben starts the empty scale with the 8♦ on the left: 8 against 0. A difference of exactly 8 is still allowed.
9. Anna plays the J♥ and shifts the 8♦ to the right pan: 0 against 8. Now Ben's 10♠ fits. Her last card, the A♠, now lies face up.
10. Ben's last cards are the 10♠ and the Q♣. If he lifted the 8♦ with the Queen, Anna's Ace would weigh 1 on the empty scale and his 10♠ would then tip it (1 against 10, difference 9). So he plays the 10♠ on the left: 10 against 8, difference 2. His last card, the Q♣, lies face up.
11. Anna puts the A♠ on the right pan as the counterweight: it weighs 2, 10 against 10 – balanced!
12. Ben plays the Q♣ on the empty scale; it does nothing. The round is over and the scale is empty: no life lost.

Not a word about your cards

You may not give away anything about your hidden cards: no numbers, no "I can balance that", no "put it on the left", no "don't!", no sighing, no pointing and no pausing on purpose. What lies on the table is public: you may add up the pans aloud, say the difference, the limit and the lives, and talk about the rules and whose turn it is.

Your face-up card is your only signal. Because you may swap it at the end of every turn, it says: "this is what I can use next". Make the difference equal to your partner's face-up card, and they can balance the scale.

Winning and losing

• You lose as soon as you have to turn a King face down and none is left face up.
• You win together if you have played all four rounds without losing.

You can never get stuck: every card can always be played, even if it tips the scale. But some deals are simply bad. In a computer check with all hands open, two players could play about 97 rounds in 100 without losing a life in rounds 1–3, and about 84 in 100 in the last round with its limit of 5. With three or four players it was 90–96 in 100 in rounds 1–3 and 80–90 in the last round. That's what the lives are for.

Difficulty levels

On the Expert level all your cards stay hidden, and only the pans tell you anything.

The budget: you have to survive four round ends and every tipping over. With a large limit almost everything fits; with a small one the big cards become a burden. A card of weight w can only be played on the lighter pan when the difference is at least w minus the limit. In the last round with two players (limit 5), a 10 fits only at a difference of exactly 5, a 9 at 4 or 5. There are eight 9s and 10s among the 48 cards, so play them early, while the limit is still large. The Aces, Jacks and Queens (twelve cards) are your tools for the end of a round.

In a computer simulation of 2000 games per level for two players, a bot that plans the last eight cards of each round – it guesses its partner's hidden cards and tries out every way to play the rest – won:

The simple bot only thinks one card ahead until the last six cards of a round, and tips the scale much more often. Most teams will land somewhere in between. With the limits for 3–4 players, the planning bot won 93% / 79% / 49% (Easy / Normal / Hard) with three players and 84% / 62% / 32% with four. These numbers are a first guess for a game that has not been playtested: if you win easily, go up a level; if you keep losing, go down one.

Tips for beginners

• Aim at the face-up cards. Before you play, ask: can I make the difference equal to the next player's face-up card?
• Show what you want to play next, and swap your face-up card when your plans change.
• Get rid of 9s and 10s early, when the difference is large – the limit only gets smaller.
• Keep an Ace, Jack or Queen for the end of the round. They can fix a difference that no number card can.
• Count back from the last card. With two players, the one who didn't start the round plays its last card. Plan the last few turns together – through your face-up cards.

Variants

All optional – agree before you start.

• Open hands (for learning): play with all cards face up, but still without talking.
• Two face-up cards (easier): everybody shows two cards. In the simulation the planning bot then won 80% on Normal instead of 66%.
• Steady scale: the limit stays at 7 (with 3–4 players at 8) in all four rounds.