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Deduction · University War · Season 1

Balance Game

Four hidden digits, one scale. Every answer you get is an answer you give away.

Level 3 of 3 · Hard10 min2 playersvs AIOnline
Appeared inHidden
Mode
Full rules

How to play Balance Game

Hide four digitsGive cards A to D four different digits that add up to 20.
Ask a comparisonOne of your cards against one of theirs, or two against two. Both see <, > or =.
Answers cut both waysEvery answer tells your opponent about your cards too.
Name it to winGuess all four digits in order. Wrong passes the turn.
Read the full rules

Settings

How to play

  1. Hide four digitsGive your cards A, B, C and D four different digits from 0 to 9 that add up to exactly 20.
  2. Ask a comparisonOn your turn, put one of your cards against one of theirs, or two of yours against two of theirs. Both players see less, more or equal.
  3. Answers cut both waysThe answer is about your cards as much as theirs, so every question also tells your opponent something about you.
  4. Name their numbersInstead of asking, state all four of their digits in order. Right wins at once; wrong passes the turn.

Rules

Balance Game is a two-player deduction duel. Each player hides four digits on cards A, B, C and D, and the first to name the other player’s digits, in order, wins.

Your secret

  1. Choose four different digits from 0 to 9 that add up to exactly 20, and place them on cards A, B, C and D. For example A 9, B 1, C 4, D 6.
  2. Both players set their secret at the same time, without seeing each other’s.

There are 384 possible secrets: 16 sets of digits, each in 24 orders.

A turn

Players take turns. On your turn, do one of these:

  • One against one: compare one of your cards with one of your opponent’s, for example “my B against your C”.
  • Two against two: compare the total of two of your cards with the total of two of theirs, for example “my A+D against your B+C”.
  • Guess: state all four of your opponent’s digits, A to D. If you are right, you win. If you are wrong, the turn passes.

The answer to a question is less than, more than or equal, and both players see it. Because each answer compares your cards with theirs, your opponent learns about your secret from every question you ask, and from every question they ask too.

Our version

  • A coin flip decides who asks first (on the show, the winner of an earlier match chose).
  • Setup has a 60-second timer. If it runs out before you lock in, the random valid secret already filled in on your screen is used.
  • Each turn has a 2-minute timer. Running out passes the turn, as on the show.
  • A guess must itself be a possible secret (four different digits adding up to 20).
  • You may ask the same question twice; nothing in the rules forbade it.
  • The answers list shows your own card values next to each comparison, so you can read it at a glance.
  • Under every game you can see how many of your possible secrets your opponent still has to choose from, worked out from the answers and each secret they could hold. This is the heart of the game, so it is always on.
  • The “Possible secrets” helper (on by default, turn it off in settings) counts the opponent’s secrets that fit every answer so far and lists them once 24 or fewer remain. Tap one to fill in a guess. It is a strong aid; turn it off for the show experience.
  • Online rooms work the same way, and your opponent’s digits are never sent to your browser until the game ends.

Sources: fan wikis.

Strategy

Use your own numbers as a ruler. Your 9 against their A nearly always comes out “more”, so it tells you little. Compare with your middle cards (4 to 6) to split their possibilities roughly in half.

Every question is a trade. If you ask “my 0 against your C”, the answer is less or equal, and your opponent learns your card is very small. Prefer questions where the answer tells you a lot and them little.

Pairs reach further. A two-against-two total covers two of their cards at once and ranges from 1 to 17, so it can carve the 384 secrets into finer pieces than a single card can.

Remember the total. All four digits add up to 20, so once you know three, the fourth is fixed, and knowing A+B tells you C+D.

Guess before they do. A wrong guess costs one turn and gives nothing away about you. If your opponent is close to knowing your digits and you are down to a handful of options, a guess now can beat one more question.

Questions people ask

Can you play Balance Game online?

Yes. This page has a free version you can play in your browser against an AI at three levels, with no sign-up, or against a friend in an online room.

How many possible secrets are there?

384. There are 16 sets of four different digits that add up to 20, and each set can be laid out on A, B, C and D in 24 orders.

Can two cards be equal?

Not within one player's secret, as the four digits must be different. Your card can equal one of your opponent's cards, which is why a comparison can come out equal.

What happens if I guess wrong?

Nothing but the lost turn. The turn passes to your opponent, and that secret is ruled out for both of you to see.

What if I run out of time?

Setup lasts 60 seconds; if you have not locked in, the digits shown on your screen are used. Each turn lasts 2 minutes; running out passes the turn.

Can the game end in a draw?

No. Play goes on until somebody names the other player's four digits exactly.

Does the AI cheat?

No. The AI only works from what a player in its seat could see: its own digits and the shared list of answers.

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