import marimo

__generated_with = "0.1.58"
app = marimo.App()


@app.cell
def __():
    import fractions
    return fractions,


@app.cell
def __(fractions):
    _transitions = {i: fractions.Fraction(6 - abs(i - 7), 36) for i in range(2, 13)}

    assert sum(_transitions.values()) == 1

    def probabilities_from_1_to_n(n=39):
        probabilities = {i: fractions.Fraction() for i in range(-11, 0)}
        probabilities[0] = fractions.Fraction(1)
        for i in range(1, n + 1):
            probabilities[i] = sum(probabilities[i - k] * v for (k, v) in _transitions.items())
        for i in range(-11, 1):
            del probabilities[i]
        return probabilities
        
    return probabilities_from_1_to_n,


@app.cell
def __(probabilities_from_1_to_n):
    sorted(probabilities_from_1_to_n().items(), key=lambda p: -p[1])
    return


@app.cell
def __(fractions):
    _transitions = {i: fractions.Fraction() for i in range(3, 19)}

    for i in range(1, 7):
        for j in range(1, 7):
            for k in range(1, 7):
                _transitions[i + j + k] += fractions.Fraction(1, 216)

    assert sum(_transitions.values()) == 1

    def probabilities_from_1_to_n_3d(n=39):
        probabilities = {i: fractions.Fraction() for i in range(-17, 0)}
        probabilities[0] = fractions.Fraction(1)
        for i in range(1, n + 1):
            probabilities[i] = sum(probabilities[i - k] * v for (k, v) in _transitions.items())
        for i in range(-17, 1):
            del probabilities[i]
        return probabilities
    return i, j, k, probabilities_from_1_to_n_3d


@app.cell
def __(probabilities_from_1_to_n_3d):
    sorted(probabilities_from_1_to_n_3d().items(), key=lambda p: p[1])
    return


@app.cell
def __():
    return


if __name__ == "__main__":
    app.run()