Glittering Paths

It has long been believed that various gemstones have mystical powers. Some grant protection in a soul's journey through the afterlife, while others may empower the body, rendering one nigh invincible. But harmony, as always, is key--a poor balance and your spirit is thrown off.

RULES

This game consists of six gemstones:

> Ruby, which is a red square,

> Garnet, which are a red hexagon,

> Jasper, which is a red octagon,

> Sapphire, which is a blue circle,

> Lapis, which is a blue triangle,

> Aquamarine, which is a blue pentagon.

As such, there is a red player who is assigned the red gemstones, and a blue player who is assigned the blue gemstones.

There are 3 rounds in the Death Match, which each take place on a rectangular board that initially has all spaces filled with gemstones. It is guaranteed that all rubies are rotationally opposite of sapphires and vice versa, and similar for garnets and lapis, and jasper and aquamarine. Furthermore, jasper and aquamarine do not appear in the first two rounds.

At the beginning of the round, the board is revealed, and the first player to submit a legal move will make that move. Afterwards, players alternate turns.

A move involves forming a path. A path is a sequence of gemstones on the board that match the following constraints:

1. The path does not repeat a cell.
2. The path has odd length, and has at least three cells.
3. The path must start on a gemstone matching the player's color. Afterwards, the path alternates between not matching that gemstone and matching it, so every other cell on the path matches the starting gemstone.
4. Every sequence of three adjacent cells on the path must form a right angle.

When a player makes a move, they earn points equal to the number of cells on the path matching the starting gemstone, divided by the maximum number of cells on the path matching any other gemstone. Upon making this move, all gems used in the path are removed from the board. Players’ point totals are rounded to two decimal places after every move.

For the first move only, players have two minutes; if neither player makes a move in that time then one player is randomly chosen as the starting player. Afterwards a player has one minute to make their move. If you fail to make a move in the allotted time, you skip your turn. If both players skip their turns twice in a row, the round ends. (If both players agree, the round can end earlier.)

As mentioned before, there are three rounds of the DM, which each take place on boards of roughly equal area. Players’ point totals are summed, and the player with more points at the end of all three rounds wins the DM. If there is a tie, then the Death Match Opponent is the winner.

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Allowed Tools: You may use a spreadsheet or image editing tools to draw lines. You may not use any automated formulas in the DM.