Atropos!

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Rules

Size
413
7
Left:
(Left plays first.)
Human
Random
Very Easy AI
Easy AI
Medium AI
Tricky AI (slow)
Hard AI (very slow)
Right:
Human
Random
Very Easy AI
Easy AI
Medium AI
Tricky AI (slow)
Hard AI (very slow)

If you are unsatisfied because the game doesn't actually end with the creation of a three-colored triangle, try the Misère version.

Check out other combinatorial games.


A Brother's Fate: The first game of Atropos

King Poleus and Queen Pilana of Thebes were blessed early in his marriage with twin sons: Thaleus (elder by mere moments) and Reagos. Directly after the taxing birth, Philana prayed to the three Fates, Clotho, Lachesis and Atropos, for the continuing health of her newborn boys, then fell asleep while the midwife placed them, crying, into the nearby cradles. She awoke in the middle of the night, the doctors, midwives, and Poleus gone, replaced by the presence of a stranger in her room. Philana's heart stopped; the oldest woman she had ever seen stood poised over her twin sons. The ancient was dressed in gray robes, nondescript save a large pair of scissors held in place around her waist by a rope belt.

``Your prayers will be answered,'' began Atropos, Sister of the Shears, ``though only for one of your sons. He shall grow to an old age and reign long over Thebes, while the other shall not outlive your husband. This boy," Atropos pointed to one of the two cradles, ``will die early in his life in an act of defiance."

Philana looked at her sleeping sons, but could not recall which of the two boys was Thaleus and which was Reagos. Who had Atropos pointed to? Before she could call for the midwife, Atropos raised her hand and Philana' eyelids dropped. When she awoke, the Fate was nowhere to be seen. Had her vision been no more than a dream? The midwife had moved the cradles across the room, and was holding one of the boys near the bed. Philana considered asking which boy had been in the doomed cradle, but realized she did not want this morbid knowledge and kept the vision to herself.

By the time the twins turned 10, King Poleus' health began to decline. Before they had reached 17, he was completely bed-ridden. Uninterested in ruling the kingdom, Thaleus nevertheless accepted the reality of the situation. His father would die, and he would assume the throne. His brother, however, disagreed with this plan.

``Thaleus is a poor warrior and the people of Thebes have no love for him,'' Reagos complained to his mother, pacing briskly around the room. ``He spends his time in solitude and study, never amongst the citizens. I am skilled in battle and in the hunt and beloved in Thebes. Our city would rather have me upon the throne."

``Have you told your brother?" Philana asked, fearful of her son's aggressive tone.

``He refuses. He claims the state will collapse without the eldest son as king. I have talked to father's infantry---something Thaleus never has bothered to do..." Reagos paused, looking away from his mother. "It seems most of them would follow me in rebellion."

Philana paled. ``You cannot start a war!"

``I will not turn Thebes into a battleground!" Reagos said. ``That does not mean I will let Thebes fall apart from the inside!" He left the room before the Philana could ask any more questions. Atropos' words came back to her, and she feared her son was contemplating an assasination. Looking for advice, she fled to the dying king's bedside.

Thaleus was sitting on Poleus' bed when Philana entered, chatting with his father. Although she loathed telling either of her sons about the curse the Fate had laid on them, she revealed Atropos' decree to both the king and his eldest son. Thaleus became immediately quiet, but the weakened Poleus spoke. ``I am not long for this world. Perhaps we can convince the Fates to settle this matter in another way. It would be dangerous for all of Thebes to have the blood of one of our sons on the hands of the other.''

Philana agreed and prayed again to the three fates, begging them to reconsider. That night, Atropos appeared in another vision. ``In order to spare your country a violent conflict, we shall let your sons play a game for their lives'' Atropos began. ''They shall place figures of me and my two sisters upon this grid.'' The Fate showed the queen a triangular board of circles, the edges of which had already been populated with miniature old ladies, carved from soap. Sure enough, one edge of this boundary had alternating likenesses of Clotho and Lachesis. Another edge had figures of Lachesis and Atropos, while the third had Clotho and Atropos. ``They will follow each other's plays around the board, but if one of them creates a small triangle with me and each of my sisters in the circles, his life shall be forfeit.'' Philana nodded slowly, too frightened to speak. She realized a flaw in the ancient's plan, however. What if neither of her sons created such a triangle and managed to fill the entire board?

``Your sons will play tomorrow, before Reagos has a chance to commit his crime. You will find a board for them to use along the road to Delphi.'' With this, Atropos vanished. Certain that both of her sons would now survive, Philana slept soundly.

The queen convinced her two sons to ride east to Delphi the next morning. Once the three were outside Thebes, she explained the situation and the game to them both. She had hardly finished when spotted something not far ahead. A large stone table stood beside the road, as it ran along a set of high cliffs overlooking the sea. An old woman with large shears tied to her cloak stood next to the table. The royal family stopped, but before approaching Atropos, Philana spoke to her sons. ``Please play carefully,'' she begged. ``The only way you can both survive is to fill the entire board without creating a triangle of all three Fates.'' Reagos was reluctant to agree, but convinced his mother that he would not try to force Thaleus to create such a triangle. The elder brother remained silent, as if already calculating his plays.

The three approached the triangular table. Soap miniatures stood in attention along the border of the game board, exactly as Philana had dreamed. Three stone bowls outside the board held the extra figures. ``Thaleus, you may play first,'' Atropos said as the twins sat down on opposing stone chairs. Thaleus selected a soap Lachesis from a bowl and played it safely in the middle of the board. Reagos picked another Lachesis from outside the game board and played adjacent to his brother's move. The younger son was going to play passively, as his mother wished.

Atropos smiled and watched the two slowly fill up the middle of the board, then begin to wind their way around the boundary. When there were only two remaining spaces on the board, Thaleus placed a miniature Atropos---the only safe play for that location---leaving exactly one space. As he removed his hand, the older brother realized the flaw in their plan. The last space was surrounded by two neighboring Atropos, two neighboring Lachesis and two neighboring Clotho figures. Any figure placed would create a deadly triangle.

Reagos studied the board for only a moment before coming to the same realization as his brother. He glared at the real Atropos, who had removed the giant shears from her belt. ``Make your play, Reagos,'' she said, stepping between the two brothers.

Before Reagos could make a move, Thaleus stood up and swept the pieces off the table and into the sea. Knowing he was no match for Atropos, the Inevitable, the elder brother threw himself off the cliff, following the game pieces onto the deadly rocks.

As he fell, Atropos and the table disappeared. Although Thaleus died instantly, the soap sisters drifted across the seas, causing rough waters to froth and bubble wherever they go.

Copyright Kyle Burke 2015. Thanks to Niky Riga and Michalis Potamias for help editing this myth.