### The TiqTaqToe Dice A set of TiqTaqToe consists of $52$ dice: $25$ d4 token dice[^1], $25$ d6 token dice, and two normal d6 dice. Player 1 will mainly use the d4 dice, while Player 2 will mainly use d6 dice. Whenever a player makes a move, they will place these dice on the classic nine-square tic-tac-toe board. The token dice are not rolled but merely placed; the two normal d6 dice are the ones we'll use to roll for outcomes. Each player is given dice of five different colours: Red, green, blue, yellow, and purple, with white lettering for Player 1 and black lettering for Player 2. We will represent these in ASCII diagrams, like the one below, using lowercase letters (r, g, b, y, p) for Player 1 and uppercase letters (R, G, B, Y, P) for Player 2. ``` /\ /\ /\ /\ /\ R---R G---G B---B Y---Y P---P / 4\ / 4\ / 4\ / 4\ / 4\ | 4 | | 4 | | 4 | | 4 | | 4 | r----r g----g b----b y----y p----p R---R G---G B---B Y---Y P---P ``` These dice do not have the usual numbers ranging from $1$ to $4$ or $6$, however. Instead, (most of) the d4 dice have the numbers $1$, $2$, and $4$ printed on them, and (most of) the d6 dice have the numbers $4$, $2$, $1$, and $-2$, with the $2$ appearing twice. (The final side of each die is reserved for a symbol corresponding to the colour of the die.) ``` /\ /\ /\ /\ / 4\ -> / 2\ -> / 1\ -> / r\ r----r r----r r----r r----r R---R R---R R---R R---R R---R R---R | 4 | -> | 2 | -> | 2 | -> | 1 | -> |-2 | -> | R | R---R R---R R---R R---R R---R R---R ``` From [[TiqTaqToe with Interference|Level 2]] onwards, the players also get access to one die of the opponents shape. These dice only have the numbers $4$ and $-2$. ``` /\ /\ /\ /\ / 4\ -> /-2\ -> /-2\ -> / r\ r----r r----r r----r r----r R---R R---R R---R R---R R---R R---R | 4 | -> | 4 | -> |-2 | -> |-2 | -> |-2 | -> | R | R---R R---R R---R R---R R---R R---R ``` Five dice per colour, with five colours per player makes for $25$ dice per player, and $50$ dice in total. ``` Player 1 Player 2 /\ /\ /\ /\ /\ R---R G---G B---B Y---Y P---P / 4\ / 4\ / 4\ / 4\ / 4\ | 4 | | 4 | | 4 | | 4 | | 4 | r----r g----g b----b y----y p----p R---R G---G B---B Y---Y P---P /\ /\ /\ /\ /\ R---R G---G B---B Y---Y P---P / 4\ / 4\ / 4\ / 4\ / 4\ | 4 | | 4 | | 4 | | 4 | | 4 | r----r g----g b----b y----y p----p R---R G---G B---B Y---Y P---P /\ /\ /\ /\ /\ R---R G---G B---B Y---Y P---P / 4\ / 4\ / 4\ / 4\ / 4\ | 4 | | 4 | | 4 | | 4 | | 4 | r----r g----g b----b y----y p----p R---R G---G B---B Y---Y P---P /\ /\ /\ /\ /\ R---R G---G B---B Y---Y P---P / 4\ / 4\ / 4\ / 4\ / 4\ | 4 | | 4 | | 4 | | 4 | | 4 | r----r g----g b----b y----y p----p R---R G---G B---B Y---Y P---P r---r g---g b---b y---y p---p /\ /\ /\ /\ /\ | 4 | | 4 | | 4 | | 4 | | 4 | / 4\ / 4\ / 4\ / 4\ / 4\ r---r g---g b---b y---y p---p R----R G----G B----B Y----Y P----P ``` In addition, each player is given one normal d6 die (numbered 1 to 6), to be used when observing the board to roll for outcomes. The game can also be played with just one d6 die, but its easier with two, since you will sometimes be asked to roll two d6 dice to decide an outcome. The numbers on the dice represent *probabilities*, presented in fourths: $4$ is "four fourths", so that's $100\%$; $2$ is "two fourths", so a half ($50\%$); and $1$ "one fourth", or $25\%$. We also have the number $-2$, reflecting the fact that in the quantum world, probabilities can not only be positive, but negative as well! Not all dice are needed at every level, so how the pieces should be distributed will be explained in each chapter. The [[TiqTaqToe Player Reference]] also contains an overview. After observing a symbol by rolling to find where it should be placed, they can be drawn in using a pen or pencil, or using X/O tokens for faster replayability. If you go for the latter route, I recommend making $9$ tokens with X drawn on one side and O on the other, since in [[TiqTaqToe with Complementarity|Level 3]] the number of X and O symbols observed on the board can go all the way from zero to nine. For the purpose of this manual, the ASCII diagrams will represent observed symbols as empty triangles resp. squares. ``` /\ +---+ / \ | | +----+ +---+ ``` As for the game board, as mentioned the game is played on a usual $3 \times 3$ grid. This can be sketched up using pen and paper. Alternatively, a small whiteboard with a dry-erase marker makes for an excellent playing board. Now that you know the pieces, it is time to try your hand at the first level, so head on over to [[TiqTaqToe with Entanglement]] to learn how to play the first level! [^1]: For those new to d4 dice, they are tetrahedral—pyramid shaped—dice. When they stand, it is usually the number at the top that gives the value, though some d4 dice have the number written along the bottom of each side instead.