A quicky script to make a vincent stacked area plot with the results of the threes simulation [this blog post](http://datascopeanalytics.com/what-we-think/2014/03/14/are-you-really-any-good-at-threes).

threes_plot.py

# standard library
import sys
import random

# 3rd party
import numpy as np
import vincent

N_SAMPLES = 10000

# read from stdin
score_distribution = [int(line) for line in sys.stdin]

# what is the expected random-swiper high score, given the number of
# games played?
vincent_data = {
    'index': [],
    'y1': [],
    'y2': [],
    'y3': [],
}
for n_games_played in range(1, 21):

    high_score_distribution = []
    for i in range(N_SAMPLES):
        high_score = max(random.choice(score_distribution)
                         for j in xrange(n_games_played))
        high_score_distribution.append(high_score)

    # calculate sizes needed for stacked area
    lower = np.percentile(high_score_distribution, 5)
    size = np.percentile(high_score_distribution, 95) - lower
    top = 1400 - (lower + size)

    # do this to get in correct vincent format
    vincent_data['index'].append(n_games_played)
    vincent_data['y1'].append(lower)
    vincent_data['y2'].append(size)
    vincent_data['y3'].append(top)

# make the chart
stacked = vincent.StackedArea(vincent_data, iter_idx='index')
stacked.colors('PuOr')
stacked.axis_titles(x='games played', y='high score')
stacked.to_json('stacked.json', html_out=True, html_path='index.html')