Quantum TicTacToe Environment Documentation

Overview

Quantum TicTacToe is a futuristic twist on the classic 3x3 Tic Tac Toe game. In this version, each player places spooky marks in a superposition of two cells. These quantum moves remain entangled until a cycle is formed, triggering a collapse into classical marks. Players must carefully manage their entanglements to outmaneuver their opponent and be the first to form three classical marks in a row.

Action Space

• Format: Each move places a spooky mark in two empty cells:

  [a,b]
  

• Examples:
  • Entangle cells 0 and 4: [0,4]
  • Entangle cells 2 and 5: [2,5]
• Notes:
  • a and b must be different and refer to empty cells.
  • Players may include extra text before/after the brackets; only the [a,b] pattern is parsed.

Observation Space

Reset Observations

At the start of the game, each player receives a detailed prompt:

You are Player 0 in Quantum Tic Tac Toe.
Your symbol is 'O', and your move numbers are always even (e.g., O2, O4).

📍 Goal: Win by forming a line of three classical marks (solidified from superpositions).

🌀 How to Play:
- On each turn, place a spooky mark in two different empty squares using the format '[a,b]'.
- These marks are entangled, and labeled like 'X1 / X1' or 'O4 / O4'.
- You cannot place spooky marks in a square that has already collapsed (solidified).

💥 Collapse Rule:
- If your move creates a cycle in the entanglement graph, it collapses automatically.
- Each spooky mark in the cycle turns into a classical mark in one of its two positions.
- Any dependent spooky marks also collapse.

⚖️ Victory:
- The game ends when a player has three classical marks in a row.
- If both players get a line during the same collapse, the one with the lower max move number wins.

Example move: '[0,4]' places a spooky mark in cells 0 and 4.

Step Observations

After each move, players receive the updated board with spooky marks, classical marks, and square indices for reference. Example:

Quantum Tic Tac Toe Board:

 [0]       [1]       [2]     
 0A / 2A   1B         2A

---+----------+----------+---

 [3]       [4]       [5]     
 0A         2A       3B

---+----------+----------+---

 [6]       [7]       [8]     
           3A       1B

Submit your move as '[a,b]' to place a quantum mark in two locations.

Gameplay

• Players: 2 (Player 0 and Player 1)
• Board: 3x3 grid
• Marks:
  • Player 0: O (even move numbers, e.g. O2)
  • Player 1: X (odd move numbers, e.g. X1)
• Turn Structure:
  • Each player places a spooky mark into two uncollapsed cells.
  • Entanglement cycles automatically collapse and may trigger chains of collapses.

Key Rules

1. Spooky Marks:

   • Each move entangles two empty cells.
   • Cells can contain multiple spooky marks until collapse.

2. Collapse:

   • Cycles in the entanglement graph cause all involved spooky marks to collapse.
   • Collapse picks one of the two entangled cells for each mark, favoring the first available.
   • Chains of dependent marks collapse recursively.

3. Victory:

   • A player wins by forming three classical marks in a row.
   • If both players win simultaneously, the player with the lower maximum move number (earlier win) gets 1 point, the other gets 0.5.

4. Invalid Moves:

   • Trying to place a spooky mark in a collapsed cell or using duplicate indices is invalid.

Rewards

Contact

For questions or issues with this environment, please reach out to guertlerlo@cfar.a-star.edu.sg.