x̄ - > Infinite Tic‑Tac‑Toe — A Storyteller's Map

Infinite Tic‑Tac‑Toe — a storyteller's map

Ah, let me paint a little tableau for you—no engines humming in the dark, no algorithms grinding, just a quiet sketch of how each policy might play upon an infinite board.

Picture it like a storyteller’s map: a handful of marks scattered across a vast, silent grid. To keep things readable, we show only a tiny window of the infinite plane—just enough to glimpse the soul of each policy.

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1. Local Expansion Policy

Each side plays tightly around the first center mark, like villagers gathering around a fire.

   - - - - -   
   - X O - -  
   - O X - -  
   - - - - -  
      

Both X and O cling to tradition, keeping their conflict close and familiar.

2. Global Positional Policy

Moves are far apart, seeds cast across the field to prepare for future harmony—or chaos.

       O

   X           O


               X
      

Here, neither insists on immediate battle; they seek influence rather than skirmish.

3. Threat‑Building Policy

X builds a fork; O rushes in with a worried brow.

   - X - X -
   - - O - -
   - X - - -
      

You can almost feel the tension: one wrong block and the floodgates open.

4. Spatial Control Policy

Each player spreads marks to deny territory, like farmers staking out land boundaries.

   X - - - X
   - O - O -
   - - X - -
   - O - O -
   X - - - X
      

A quiet, methodical contest for long‑term control.

5. Randomized / Exploratory Policy

The board begins to look like scattered raindrops—some meaningful, some simply curious.

   - - - X - -
       O
   X
            O

       X
      

A wandering style: unpredictable, slightly mischievous.

6. Reinforcement‑Learned Policy

Early moves show structure—triangles, spacing, intentional near‑misses that hint at deeper calculations.

   X - - X
   - O X -
   - - O -
   X - - X
      

There’s balance in the spacing, a calculated rhythm learned from thousands of simulated lives.

7. Hypothetical “Optimal” Policy

A whispered ideal—symmetry intact until the moment X breaks it.

       X
   O       O

       X
   O       O
       X
      

A perfectly mirrored dance, until X takes the central spine and claims the initiative.

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policy you choose:

• win‑seeking forks
• area control
• deep RL patterns
• long‑distance pincer maneuvers
• even hybrid policy mixtures

Animate a policy