Expression Black & White

Psychology + Mathematics DM: Expression Black & White

In Expression Black & White, players construct equations to gain the most points... but don't construct the most obvious ones, or your opponent can take your points instead.

Tiles

Each player receives two copies of each tile numbered from 1 to 12. They also receive 3 copies of each symbol (+, -, , /). Even numbered tiles (2, 4, 6, 8, 10, 12) are black, while odd numbered tiles (1, 3, 5, 7, 9, 11) are white. The symbols + and * are black, while the symbols - and / are white. These tiles are called number tiles and symbol tiles*, respectively.

There are 12 rounds in a bout. Associated with each round is a pair of global tiles, which are one number and one symbol tile. All 12 pairs of global tiles will be revealed before the start of the game; there will be a three-minute planning phase after this and before the first round of the game.

The player with the Advantage decides who goes first in the first bout. Afterwards, the player who won the previous round will go first.

One Round

In a single round, players each submit a five-symbol expression, using the two global tiles, and two number tiles and one symbol tile that they hold. These three tiles are used up. The other player is then told of the colors that were used. (They are not told, however, of what the tiles exactly are, or which ones are the global tiles.)

Because players take turns, Player 2 will be told the colors of Player 1's expression before they play their tiles.

After both players have played, the expressions will be evaluated. The player who created the expression that evaluates to a number closer to 10 will be the winner of the round. In the case of a tie, the player that played second in the round is the winner. The winner of the round earns one point.

I will announce the winner of the round, and then we will enter part two of a round, the guessing/revealing phase.

Guessing and Revealing

The losing player in a round has the opportunity to earn some points. They may guess up to two numbers and one symbol that their opponent used (other than the global tiles). A guess is correct if the tile was chosen to be used and incorrect otherwise.

A player gains 2 points for a correct number guess and loses 1 points for an incorrect number guess.

A player gains 1 point for a correct symbol guess and loses 1 points for an incorrect symbol guess.

(Guessing is not compulsory; a player can guess any amount between 0 and 3 tiles. It is not allowed to guess the same number twice.)

All guesses and whether they are correct is announced. Points are calculated accordingly. Guesses will be submitted in private, so that they can occur at the same time as the revealing.

If the losing player did not have any correct guesses, the winning player must reveal one of the tiles they chose to use. They should submit which one they would like to reveal while the other player is guessing. Afterwards, I will reveal this tile.

This process occurs 12 times. At the end, players will be out of tiles, and we move to the final guess stage.

Final Guesses

In the Final Guess stage, each player will guess the tiles that their opponent used in each round. Players should submit, for every round, what tiles they believe their opponent used in that round. (The ordering of the tiles does not need to be found; only the numbers and symbols used.) Players gain 2 points for every correct guess; an incorrect guess does not lose points.

Double Game + Endgame

This game will be played twice. In Bout 2, the player who didn't start Bout 1 will start.

At the end of both games, scores for each game are summed up. The player with more points wins. If points are equal, the player who guessed fewer correctly in each Final Guess wins (this is the player who had a higher sum of points going into the Final Guess). If points were equal then, the player who won more rounds overall wins. If there is still a tie, the player with the Advantage wins.

Timing

Players have three minutes for the planning phase and five minutes for the Final Guess.

Players have 45 seconds to submit their tiles, and 1 minute to submit their guess or reveal.

Players have 3 minutes of reserve time, but this reserve time only counts for tile submissions. If a player runs out of time on the Final Guess or in a guessing phase, they submit no guesses. If a player runs out of time in deciding what to reveal, their symbol is revealed by default.

If a player runs out of reserve time they automatically lose.

Advantage

The player with the Advantage decides who starts first in Round 1 of the first bout, and wins the final tiebreaker.

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Clarification: Parentheses do not exist; multiplication and division occur before addition and subtraction, as they would in a normal expression.

Clarification: For Bout 1, the player with the Advantage decides who goes first after the planning phase.

Amendment:

Minor typo:

Afterwards, the player who won the previous bout will go first.

Should be

Afterwards, the player who won the previous round will go first.

Clarification: In the Final Guess, a player must get all three tiles used in a round to earn points for that guess.