Homeostasis

In this Main Match, the five players will be divided into 3 teams - two members of Team Positive, two members of Team Negative, and a solo player, representing Team Neutral. Each team will be trying to influence a mathematical equation in order to make the value as high as possible, if they are on Team Positive, as low as possible, if on Team Negative, or close to 0, if on Team Neutral.

Core Mechanics

This Match will be conducted live, over the course of three rounds. Each round will create a mathematical expression with a final result. The sum of the results of these three rounds will be the final score for the Match. Each round will consist of 11 auctions, to determine which cards will go where. The 10 cards, and the 10 slots that they can go in, are depicted below:

Initial Round

Each player will receive a private copy of these ten cards, and may choose to purchase one or more cards to save. The cost of saving cards is (X - 1)² Garnets, where X is the number of cards purchased. So, purchasing 1 card is free, but purchasing 4 cards will cost 9 Garnets. These cards are saved for future use. They will also receive 100 chips, to be bid in auctions.

Round Structure

Each round consists of 11 Auctions. First, the auction order of the ten cards will be determined. The player with the most chips remaining will go first, and in the event of a tie, the player with the most Garnets will go first. The first player will select one of the 10 cards, and decide in what position in the bidding order that card will be bid on. Then the second player will make a choice, and so on. After the fifth player has made a choice, they will then promptly make a second choice, and the players will continue making choices in reverse turn order, finishing with the 2nd player making the 9th and final choice. When it is your turn to place a card in the bidding order, if you take more than 1 minute, your decision will be made at random.

Once the order has been determined, bidding will begin. The first player in the auctioning order will be the first bidder for the first auction, with subsequent auctions beginning with the final bidder of the previous auction. In each auction, the bidder will bid chips on any of the ten slots, or pass. The first bidder must bid at least 1 chip. Subsequent bidders may bid on any one slot, including a slot that already has been bid on - in this way, the players may pool their bids. They may not make a bid that causes a tie between two slots. A player may pass if they do not wish to make a bid, which rules the player out for making bids later in this auction. If four players pass, the auctioned card will be placed in the winning slot. All bid chips are discarded, and this process will repeat for all 10 cards.

Final Auction

After all cards have been placed, an 11th auction will occur. Each player will secretly bid at the same time. In the event of a tie, the tied players will rebid, continuing until the tie is broken. Only the winning player will spend their bid chips and be able to place any of their saved cards, either at the beginning, or end of the expression. The player does not need to play all their saved cards, but may if they wish.

Then, the auctions end. Each player will have a chance to interfere with the expression, by placing a pair of brackets. Each team may only do this once during the game, and the pair of brackets may be placed anywhere. The players will have 1 minute to request the placement of a pair of brackets. If a player does there will be a further minute in which each player who can place brackets may do so. This will continue until 1 minute elapses with no brackets placed, or no player can place brackets. Then, the expression will be evaluated.

Evaluating the Expression

First, if a pair of brackets surrounds only numbers, or only operations, all such numbers or operations will be removed from the expression.

Second, if there are multiple numbers or operations in a row, without a bracket in between, the leftmost number or operation will remain, and all others will be discarded.

Third, if the first or last card in the expression is an operation, a 0 will be inserted either before or after that card, respectively. Further, if a bracket contains an operation with a missing operand, the operand will be assumed as 0: (+2) will be read as (0+2), for example. However, if this would result in a division by 0, the 0 will be replaced with a 1.

Finally, if a number is directly before a non-removed bracketed section, there will be an assumed multiplication - 2(1 + 3) is read as 2 x (1 + 3). If the number is after, it is discarded.

The resulting expression will be evaluated per the Order of Operations, to create a final result.

Example

Without any brackets, this expression would be read as thus:

2 x 1 + 3 / 1 = 5

However, brackets could interfere with this equation in many possible ways. Some of these are shown below:

2x12(+)-33/1 would become 2 x 1 - 3 / 1 = -1 2x(12+-3)3/1 would become 2 x (1 + 3) / 1 = 8

(2)x12(+)-33/1 would become 0 x 1 - 3 / 1 = -3

The final result will be added to the current total score for the Match, which begins at 0. Then, a new round will begin, with the player with the most chips beginning to set the auction order.

Finishing

Once the three auctions have been completed, the result of the Match will be determined by the end total score for the Match, which is the sum total of the three expression results.

If the final total is greater than 4, or less than -4, the Neutral player will be the Elimination Candidate. In the former case, the two members of Team Positive will each receive a Token of Life and 3 Garnets. In the latter case, the members of Team Negative will instead each receive a Token of Life and 3 Garnets.

If the final total is greater than 1, and less than 4, each member of Team Positive will receive 1 Garnet and 1 Token of Life. The Neutral player will also receive a Token of Life, meaning Team Negative will be the two competitors in the Death Match. If the final total is instead greater than -4, and less than -1, Team Negative will win Tokens of Life, and Team Positive will go to the Death Match.

If the final total is greater than, or equal to, -1, and less than, or equal to, 1, the Neutral Player will win. The Neutral Player will receive 6 Garnets and 2 Tokens of Life. They will also choose an Elimination Candidate amongst the other four players.

Accordingly, the teams of two are in opposition to each other, while the Neutral player has murky loyalties, and must play accordingly to secure a grand victory.