Abaku Rulebook

Table of Contents

Table of Contents

• Setup
• Start of the Game
• Rules for Creating Examples
• Rules for Placing Tiles
• Scoring
  • Basic Principles
  • Bonus Spaces
• Joker
• Exchanging Tiles and Passing a Turn
• Challenging a Move
• End of the Game
• Winner
• Game Variants and Extended Rules
  • Selected Variants
  • Alternative Scoring
• Aids
  • Strategy and Tactics
• Components
• Spin Abaku (a variant using double-sided Abaku spin tiles)
• Abaku Online

Setup

Unfold game board A, give each player one rack, and mix all the tiles together in the bag. Each player draws one tile from the bag. Whoever draws the highest number goes first. Return the drawn tiles to the bag and each player draws 5 new tiles — this time secretly. You may begin.

There are two board layouts: Game Board A and Game Board B.

Start of the Game

The starting player opens the game by placing the first example on the playing area. It must be placed so that one tile lies on the center space. The center space is a bonus space (see Scoring — Bonus Spaces). On later turns, the other players attach further examples to the tiles on the board, in clockwise order.

Rules for Creating Examples

1. In Abaku we use only whole positive (natural) numbers. The result of an example must also be a whole positive (natural) number. (invalid) 4 − 8 = −4; 0.5 × 8 = 4; 8 ÷ 5 = 1.6 (valid) 8 − 4 = 4; 40 ÷ 8 = 5; 5 × 16 = 80

2. Mathematical signs between numbers are only implied. Examples are expressed as continuous strings of digits. The digit string 8412 represents the example 8 + 4 = 12.

3. An example is read horizontally from left to right, or vertically from top to bottom. The result of an example must always be on the right, or at the bottom. (invalid) 17 = 23 − 6 (valid) 23 − 6 = 17, or 23 − 17 = 6, or 7 + 16 = 23, or 16 + 7 = 23, etc.

4. In examples we use the following arithmetic operations: addition (+), subtraction (−), multiplication (×), division (÷), squares and cubes, and square (√) and cube (3√) roots of whole positive numbers.

5. A 0 may not be used as a standalone number in an example. The result of an example may not be 0. It may only be used as part of a multi-digit number. (invalid) 0 × 5 = 0; 0.5 × 8 = 4; 5 + 0 = 5 (valid) 10 − 5 = 5; 5 × 8 = 40; 10 ÷ 5 = 2

6. Every example must contain exactly one arithmetic operation. (invalid) 2 × 2 + 3 = 7; 12 ÷ 6 ÷ 2 = 1 (valid) 4 + 3 = 7; 12 ÷ 6 = 2

7. All (old) tiles placed on earlier turns may be freely included in new examples on later turns.

   The original example 1 + 2 = 3 becomes, once the turn ends, simply a row of tiles reading the digits 1, 2 and 3. On later turns, these tiles can be used in various ways:

   • 3 − 1 = 2 — the new tile is attached on the left; the player used two old tiles.
   • 2 × 3 = 6 — the new tile is attached on the right; the player used two old tiles.
   • 3 × 12 = 36 — new tiles are attached on both sides; all tiles of the original row are part of the example.

Rules for Placing Tiles

a. Tiles you place on the playing area can no longer be moved, changed, or removed on later turns. They stay on the board until the end of the game (the joker tile is an exception — see Joker).

b. Tiles must be placed in the same row or column. Tiles may not be placed diagonally.

1 × 6 = 6 and 6 − 3 = 3 are valid examples on their own, but the new tiles (highlighted) were not placed in a single row or column; the move is invalid.

c. All newly attached tiles must be part of the same single example, and must always include, or be adjacent to, at least one old tile already on the board (except for the example that opens the game).

8 − 6 = 2 and 6 ÷ 2 = 3 are valid examples on their own, but the new tiles (highlighted) do not form any single example that includes both of them together; the move is invalid.

2 + 3 = 5 — one of the old tiles (3) is part of the new example; the move is valid.

2 × 6 = 12; 7 − 1 = 6 — one of the tiles in the newly created example (6) forms another valid example with the adjacent old tiles (7, 1). The move is valid.

d. By suitably combining newly placed tiles with tiles placed earlier, you can create several different examples at once. For every newly formed group of tiles (digits) that includes at least one newly placed tile and for which you can find a valid example, you score points (see Scoring).

The combination of tiles 8412 forms only one example: 8 + 4 = 12.

The (well-chosen) combination of tiles 1248 forms three examples: 12 − 4 = 8; 2 × 4 = 8; 2² = 4.

e. Newly attached tiles must form valid examples with all adjacent tiles.

The example 3 − 1 = 2 is valid. The newly placed tile (1) creates a valid example with the adjacent old tile: √1 = 1. The move is therefore valid.

The example 3 − 2 = 1 is valid, but one newly placed tile (2) does not form a valid example with the adjacent old tile (1). The move is therefore invalid.

f. The digit 0 is an exception to the previous rule. A 0 may, but need not, form valid examples with adjacent tiles. If the 0 is the only newly placed tile that is adjacent to tiles already on the board, it must form a new example with them.

5 × 2 = 10; 6 − 2 = 4; 2² = 4 — the newly added 0 is part of a valid example (2 × 5 = 10). At the same time it is adjacent to two old tiles (2, 7). It forms no valid example with them, but the move is valid anyway.

2 × 5 = 10; 10 − 8 = 2 — the newly added 0 is part of a valid example (5 × 2 = 10). At the same time it is adjacent to two old tiles (8, 2). It forms a valid example with them (10 − 8 = 2). The move is valid.

Scoring

Basic Principles

1. Record the score after every turn. Read the examples you created on your turn out loud.

2. For every tile that is part of a newly created example, you score 1 point. This applies to every example newly formed as part of the turn.

   56783 — this turn created three examples: 5 + 68 = 73 (5 tiles — 5 points), 56 ÷ 8 = 7 (4 tiles — 4 points), 9 − 3 = 6 (3 tiles — 3 points). Total scored on the turn: 12 points.

3. An exception applies when exactly the same combination of digits forms several different examples at once (for example, the digits 9, 8, 1 could be read either as 9 − 8 = 1, or as 9² = 81). In that case, you score points for only one of these combinations/examples.

Bonus Spaces

1. If, on your turn, you place a tile on a bonus space, you score extra points. Bonuses can apply either to a single tile or to a whole example.

   • A tile bonus multiplies the point value of the tile placed on the space by 2× or 3×.
   • An operation (example) bonus multiplies the point value of every example that includes the tile placed on the space by 2× or 3×. The starting space multiplies the score by 2×.

2. A bonus space only counts on the turn in which a tile is placed on it. If an example lands on both types of bonus at once, you first multiply the tile's value, then the example's value.

   The tile 4 lies on a 2× operation bonus, and the tile 2 lies on a 3× tile bonus.

   • 4 × 3 = 12 → (2× operation bonus) 1 + 1 + 1 + (3× tile bonus 1) = 12 points
   • 4 − 3 = 1 → (2× operation bonus) 1 + 1 + 1 = 6 points
   • 3 − 1 = 2 → 1 + 1 + (3× tile bonus 1) = 5 points
   • Total: 23 points

3. If you manage to place tiles on more than one operation-bonus space at once, the bonus values are multiplied together before the score is added (for example, two ×3 bonuses within one example give a combined bonus of ×9).

Joker

1. The joker (a blank tile) is placed on the board following the standard rules of the game. When you place the joker, you must state out loud which digit (0–9) it represents.

2. On later turns, the joker on the board represents only a blank space, which may not be used in a further turn and to which no new tile (1–9) may be attached. The joker must first be replaced by an ordinary tile.

   A player determined that the joker (?) in this case represents the digit 2, and thereby created two examples: 2 ÷ 2 = 1; 2 + 3 = 5; the move is valid.

   Replacing the joker: a player replaced the joker (?) with the digit 1. It forms a new example with all adjacent tiles, 2 − 1 = 1 and 13 − 5 = 8; the move is therefore valid.

3. A player may keep a replaced joker for later turns, or use it again immediately within the same turn.

   Replacing and immediately reusing the joker: a player replaced the joker with the digit 1, and at the same time attached the joker again (6), stating that the joker now represents the digit 6. This created the examples 2 − 1 = 1; 13 − 5 = 8; 61 − 3 = 58; both the reuse of the joker and the move are valid.

4. Scoring: the joker earns you 1 point, just like any ordinary tile. However, a joker remaining on a player's rack at the end of the game costs that player a 10-point penalty.

Exchanging Tiles and Passing a Turn

If, on your turn, you cannot or do not want to play, you may either exchange tiles or pass your turn. You may exchange 1–5 tiles. First set the tiles to be exchanged aside, and only drop them into the bag after drawing the same number of new tiles. On this same turn you may not place tiles on the board — the exchange itself counts as your turn.

Warning! If you pass three times in a row, and in the meantime at least one of your opponents places an example while tiles still remain to be drawn from the bag, you lose the game.

Challenging a Move

If you decide to challenge the validity of a move, you must do so before the next player begins their turn. If you prove the move was invalid, your opponent scores no points for that turn, takes the newly placed tiles back onto their rack, and deducts one point from their score for each of those tiles. If, however, it turns out the move was correct and the mistake was on your side, you lose your next turn.

End of the Game

1. No tiles remain in the bag, and one of the players places the last tile from their rack. The player who placed the last tile additionally scores one point for every tile remaining on each of their fellow players' racks. The other players each deduct one point from their score for every tile remaining on their own rack.

2. No player is able to place an example, even after everyone has passed twice. Every player deducts one point for every tile remaining on their rack.

3. A player concedes the game.

Winner

The winner is the player with the highest total score once the game ends.

Game Variants and Extended Rules

You can adjust or extend the rules of Abaku to suit your own needs. You may also choose from the following options.

Selected Variants

Agree in advance to allow:

• only addition and subtraction
• only multiplication and division
• all operations except powers and roots
• examples placed diagonally on the board
• the result of an example on the left or at the top
• your own house rules

Alternative Scoring

a) Scoring for advanced players

Use the actual numeric value of the tiles used. For example, creating the example 6 + 8 = 14 earns a total of 19 points (6 + 8 + 1 + 4). This scoring method can also be used when playing with the joker (see Joker); in that case the joker has the value of the digit it was used for. A bonus space likewise multiplies the actual numeric value of the tiles and examples placed on it. The actual value of the tiles is also used when adding or subtracting points for tiles remaining on a rack at the end of the game. A joker remaining on a rack at the end of the game then costs a 30-point penalty. This scoring type is used in the online version of the game, where the software scores automatically.

b) "Tile and operation" scoring (recommended)

For every tile that is part of a newly created example (or examples), you score a point. Add 2 points for every example created during the turn.

12 ÷ 3 = 4; 1 + 2 = 3 — scoring: 7 tiles / 7 points + 2 operations / 4 points = 11 points

c) "Operation" scoring

Score only one point for every example created during the turn. The numeric value of the tiles and bonus spaces are not counted.

9 + 33 = 42; 9 ÷ 3 = 3; √9 = 3; √4 = 2 — scoring: four examples = 4 points

d) Abaku for One

Can't find a suitable opponent? Or want to practice? You can play against yourself and try to reach the highest possible score. Or you can try placing tiles to cover as much of the board as possible while leaving as few empty spaces as possible. Or build magic squares. Or something else? For this you can use Game Board B.

Aids

For the game itself, or for verification, you may use a calculator or other available aids. The decision to use them is up to you and an agreement between the players, and should be made before the game begins. In standard tournament play, aids are used only by the referee.

Strategy and Tactics

• Bonuses: Using them effectively has a major effect on the outcome of the game (for example, it is more advantageous to attach the combination 936 with the 9 on a 3× tile bonus than on a 2× operation bonus).
• Combinations: Combine numbers so that they form as many further examples as possible with each other and with tiles already on the board.
• Placement: Place tiles on the board so that they create as few opportunities as possible for your opponent to make an advantageous play. In short — don't needlessly feed the bonus spaces.
• Blocking: If you cannot currently make use of a bonus space, consider whether you can block your opponent's access to it (this applies especially to blocking possible 3× bonuses).
• Zero: Placing the digit zero sometimes causes problems for beginners. Exchange it, or watch more experienced opponents, and you'll find that a zero can sometimes even double your score (for example: 38 + 2 = 40; 3 × 8 = 24 / 55 − 15 = 40; 55 − 1 = 54).
• Fortune favors the prepared: Don't rely on a large lead you might have at the halfway point of the game, but don't lose your head if the situation is reversed either. One excellent move or a lucky hand can often turn the situation around. Don't give up. Both strategy and tactics grow quickly along with your arithmetic skill. Count on it.

Components

• 1 joker (blank tile)
• 1 game board
• 1 short rules booklet
• 1 cloth bag for the tiles
• 4 wooden racks
• 100 wooden tiles (10× each digit from 0 to 9)
• 1 large cloth bag for the whole game

The game is for 1 to 4 players aged 5 and up. To record your score, you can use the free Abaku scoresheet (partiář), available for download from the official site.

Spin Abaku (a variant using double-sided Abaku spin tiles)

1. Played according to the rules of Abaku, using tiles printed on both sides.
2. The difference is that one player (or pair of players) plays with black tiles, and the other player (or pair of players) plays with red tiles.
3. Players draw tiles from a single bag and turn them face-up to their own color in their rack, as previously agreed.
4. A player places their tiles on the board with their own color face-up. As in the rules of Abaku, every new placement of a player's tiles must include, or connect to, at least one tile already on the board.
5. The player turns over, into their own color, every opposing tile already on the board that they used, according to the rules of Abaku, on their turn. The turn then ends.
6. End of game: players count up their total score, and then count the number of tiles of their own color lying on the board (not on the rack) at the moment the game closes. The difference in the number of tiles won is added to the overall result.

Abaku Online

Want to play Abaku online? The rules of the game and its variants can be individually configured there.

For the general public, the app is: abakuplay.com For schools specifically (teachers and pupils), the app is: abakulab.com