michiexile / single-sided-dice

Simulator scaffold to test solutions to question about using single-sided dice to simulate single die posed by futurebird on Twitter

Simulator scaffold for single sided dice question

@futurebird on Twitter writes:

Strange dice! Set of 6, each has 1 number. Can you think of a way to use all 6 together like a normal die?
To clarify the challenge is to roll all 6 together and *easily* produce the same probability distribution of a 6-sided die?

With this package you can test possible solution attempts.

Write a function in Python that responds with either a dice value, or a list of dice to reroll. The simulator keeps rerolling as requested up to a parametrized reroll count, and then collects the results.

Your function should take a list of objects, and return either a list of integers, or a single integer. The objects handed to the function are named tuples with fields:

• position, a pair of integers uniformly drawn from [0,200]x[0,200]
• value, single integer in [0,6]. The value is 0 if the value field is facing the table and the option hidden-visible is set.
• direction, either one of 'up', 'down', 'side', 'north', 'east', 'south', 'west' or an integer in [0,359].

The simulator takes options controlling the input to the model. The parameter options should be a dict with some of these keys set:

• 'position': boolean. If True, the position field is included for the function
• 'values': string, one of 'up-other', 'up-side-down', 'up-4-down', 'up-360-down', controlling what values are assigned to the direction field
• 'hidden-visible', uses the 0 value for the value field

The simulator does a chi-squared test for fit to the uniform distribution, and returns the chi-squared coefficient as well as the probability of a chi-squared variable being at most the computed value, providing a measure of goodness of fit for the simulated approach.

As an example, the code includes the possible solution of rerolling all non-blank results until only one result is non-blank, and if so use that result as the response.

    def decision(ss):
        full = [j for j in range(6) if ss[j].direction != 'down']
        if len(full) != 1:
            return [j for j in range(6) if j in full]
        return full[0]

running this, produces (for instance) the results

    converged trials: 47.5% 475
    histogram
	  [0.16631578947368422, 0.17473684210526316, 0.1705263157894737, 0.15789473684210525, 0.15368421052631578, 0.17684210526315788]
    chi2: 0.002575069252077564    cdf: 1.7882230765945254e-08