strategies_against_random_2014_2015.py

"""
Quick script and data to analyse game played in class against a random strategy

The variable 'student_data' is a list composed of lists of strategies recorded by
players in class against a computer player a series of 3 mixed strategies:

    - (.2, .8)
    - (.9, .1)
    - (1/3, 2/3)

The game played is a modification of the matching pennies game:

    [[2, -2], [-2, 2]]
    [[-1, 1], [1, -1]]
"""
from __future__ import division
import matplotlib.pyplot as plt


def analyse_game(student_data, computer_data):
    for rnd in range(3):  # Plot the mixed strategies.
        x = sum(([sum([s == 'h' for s in row]) / 6 for row in [row[rnd]
                for row in student_data]])) / len(student_data)
        plt.figure()
        ind = [1, 2]
        width = .5
        fig, ax = plt.subplots()
        cax = ax.bar(ind, [x, 1 - x], width)
        ax.set_xticks([i + width / 2 for i in ind])
        ax.set_xticklabels(['$x$', '$1-x$'])

        x1, x2, y1, y2 = plt.axis()
        plt.axis((x1, x2, 0, 1))

        plt.savefig('%sstrategiesvbestresponse.png' % rnd)
        print x

        scores = []
        for row in [row[rnd] for row in student_data]:
            score = 0
            for j, s in enumerate(row):
                if s == computer_data[rnd][j] == 'h':
                    score += -2
                if s == computer_data[rnd][j] == 't':
                    score += -1
                if s == 'h' and computer_data[rnd][j] == 't':
                    score += 1
                if s == 't' and computer_data[rnd][j] == 'h':
                    score += 2
            scores.append(score)
        print sum(scores) / len(scores)

        plt.figure()
        plt.hist(scores)
        plt.savefig('%sscore_histogram.png' % rnd)


if __name__ == '__main__':

    student_data = [['hhthth', 'tttttt', 'hhhhth'],
                    ['hhhhhh', 'tttttt', 'hththt'],
                    ['hhhhhh', 'ththtt', 'ttthtt'],
                    ['hhhhhh', 'tttttt', 'hhhhhh'],
                    ['hhhhhh', 'tttttt', 'hhhhhh'],
                    ['hhhthh', 'tttttt', 'hththh'],
                    ['hhhthh', 'tttttt', 'hththh'],
                    ['hhhhth', 'tttttt', 'htthht'],
                    ['hthhhh', 'tttttt', 'hthhht'],
                    ['tthhhh', 'tttttt', 'ttthtt'],
                    ['hthhtt', 'httttt', 'tthtth'],
                    ['hhtthh', 'tttttt', 'hthhht'],
                    ['hhhhtt', 'tttttt', 'tthhtt'],
                    ['hhtttt', 'tttttt', 'hhhtth'],
                    ['hhhhhh', 'ttttht', 'hthttt'],
                    ['hhhhhh', 'ttttht', 'hthttt'],
                    ['hhhhhh', 'tttttt', 'hthhth'],
                    ['hhhtth', 'ttttth', 'thhhth'],
                    ['hhhtth', 'ttttth', 'thhhth'],
                    ['hhhthh', 'ttttth', 'htthth'],
                    ['hhhhhh', 'tttttt', 'hhhhht'],
                    ['hhhhtt', 'ttttth', 'hhthth'],
                    ['htthht', 'tthttt', 'thhhtt'],
                    ['hhhhth', 'tttttt', 'hthhth'],
                    ['hhhhtt', 'tttttt', 'hhhhhh'],
                    ['hhttht', 'tttttt', 'hhtttt'],
                    ['httttt', 'tttttt', 'hhhtth'],
                    ['httttt', 'tttttt', 'hhhtth'],
                    ['hhthht', 'tttttt', 'hhthth'],
                    ['hhhtth', 'tttttt', 'thhthh'],
                    ['thhthh', 'tttttt', 'hhttht'],
                    ['hhhtht', 'tttttt', 'hhhtth'],
                    ['hhhhhh', 'tttttt', 'hhhtth'],
                    ['hhhhhh', 'tttttt', 'thhhht'],
                    ['hhhthh', 'tttttt', 'hhhhhh'],
                    ['hhhhtt', 'tttttt', 'hhhhth'],
                    ['hhhhhh', 'tttttt', 'htthtt'],
                    ['hhthhh', 'tttttt', 'hhhhtt'],
                    ['hhthtt', 'tttttt', 'hhtttt'],
                    ['hhhhhh', 'tttttt', 'hhhhhh'],
                    ['thhttt', 'ttttht', 'hhhttt'],
                    ['thhhht', 'httttt', 'httttt'],
                    ['hhhtht', 'tttttt', 'hhhttt'],
                    ['hhhttt', 'tttttt', 'ttttth'],
                    ['hhhtth', 'tttttt', 'hthhth'],
                    ['hhtthh', 'tttttt', 'htthth'],
                    ['thttht', 'tttttt', 'ttthht'],
                    ['hhthhh', 'tthttt', 'hthhhh'],
                    ['thhhht', 'tttttt', 'thhhth'],
                    ['thttth', 'tttttt', 'htttth'],
                    ['thhhht', 'tttttt', 'hhhhhh'],
                    ['hhthht', 'ttthth', 'hhhtth'],
                    ['thhtth', 'tttttt', 'hhhhhh'],
                    ['hhhhhh', 'tttttt', 'hththt'],
                    ['hhhtht', 'tttttt', 'thtthh'],
                    ['hhthhh', 'tttttt', 'tthhtt'],
                    ['hhhtht', 'tthttt', 'hhhhtt'],
                    ['hthhtt', 'ttthtt', 'hhhtth'],
                    ['hhhhhh', 'tttttt', 'hhhhhh'],
                    ['hhhthh', 'tttttt', 'hhthhh'],
                    ['hhhhhh', 'tttttt', 'hhhhhh'],
                    ['hhthht', 'tthtth', 'hhthht'],
                    ['thhhht', 'ttttth', 'hhttht'],
                    ['htthtt', 'tthttt', 'ttttth']
                    ]

    computer_data = ['ttttth', 'hhhhhh', 'httthh']
    analyse_game(student_data, computer_data)