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Who Wins from This Connect Four Position?

From the 42 cells of the board, does the first player win, lose or draw with perfect play? Learning game outcomes from positions alone is a hard test for any model.

Use caseMedia and gamesPredictionModel evaluation

The table

67,557 Connect Four positions after eight moves, with the state of every cell and the result under perfect play. It's in Welt's research catalogue as Connect-4 Board States, 67,557 rows by 43 columns, licensed MIT (PMLB collection). The catalogue measures its signal at 0.34. At 67,557 rows and 42 features the table is larger than the model limits allow, so the walkthrough evaluates and fits on a seeded sample of 2,000 rows. TabICLv2 and Kumo Tabular Medium compete.

Walkthrough

  1. Load it from the catalogue

    Find the table, read its recorded target and print the column names.

    import pandas as pd
    from welt import Client
    
    with Client() as client:
        item = client.research_datasets(q="connect-4", limit=1)["items"][0]
        info = client.research_dataset(item["id"])
        data = client.load_research_dataset(item["id"])
    
    target = info["targets"][0]
    target = target["name"] if isinstance(target, dict) else target
    print([column["name"] for column in info["schema"]], target)
  2. Pick the rows

    Set aside 20 rows to predict at the end. The models learn from a seeded sample of 2,000 of the rest, the most this table's width allows.

    known = data.dropna(subset=[target])
    new_rows = known.sample(20, random_state=1)
    table = known.drop(new_rows.index).sample(2000, random_state=7)
  3. Compare the models and predict

    The models compete on the same folds against a simple guess, then the top-ranked one is fitted on the whole table. ROC AUC runs from 0.5, a coin toss, to 1, a perfect ranking, and a lower Brier score means the probabilities can be trusted more. The last table puts each prediction next to the real answer.

    with Client() as client:
        evaluation = client.evaluate(table, target, task="classification", seed=7,
                                     models=["tabicl-v2", "kumo-medium"])
        model = evaluation.fit()
    
    print(evaluation.summary()[["name", "rank", "roc_auc_mean", "brier_mean"]])
    features = new_rows.drop(columns=target)
    print(pd.DataFrame({"actual": new_rows[target].values, "predicted": model.predict(features),
                        "probability": model.predict_proba(features).max(axis=1)}))

What you get

An outcome per positionWin, loss or draw, with a probability.
A hard testThe catalogue measures a modest signal for such a rule-bound game.
A classic benchmarkCompare with published results.

Try it

Use Open with to run the research datasets notebook in Colab, Kaggle or Jupyter and search for "connect-4", or run the code above after pip install "welt-client[parquet]".