#!/usr/bin/env python
# coding: utf-8

# # Chutes & Ladders
# 
# This is a fun evening exploration to teach myself how to code
# Python by asking the question "What does the distribution of
# games of Chutes & Ladders look like by number of spins to win?"
# 
# If you're new to Jupyter or Python you might find this interesting.
# 
# There's quite a long tail distribution - if you get very unlucky,
# the game might last well over 200 spins, but if you're super lucky
# you could get it in 7. :)
# 
# - David E. Weekly <david@weekly.org>

# In[33]:


# We'll be lazy and code both chutes and ladders as "portals",
# first specifying the square FROM which the portal will go and
# then the square TO which the portal will take you. This allows
# both forward and backward movement. This set of coded portals
# maps the Chutes & Ladders game.

portals = {
        1  : 38,
        4  : 14,
        9  : 31,
        16 : 6,
        21 : 42,
        28 : 84,
        36 : 44,
        47 : 26,
        49 : 11,
        56 : 53,
        51 : 67,
        62 : 19,
        64 : 60,
        71 : 91,
        80 : 100,
        87 : 24,
        93 : 73,
        96 : 75,
        98 : 78,
}

# Plays a game of Chutes & Ladders, returns # spins to win
# If printGame is true, will print details of the game.
import random
def playGame(printGame):
    currentSquare = 0
    spins = 0
    while True:
        spin = random.randint(1,6)
        spins = spins + 1
        if printGame: print "you spun a", spin
        if currentSquare + spin > 100:
            if printGame: print "oh no, you can't go past 100"
        else:
            currentSquare += spin
            if printGame: print "after roll you landed on", currentSquare
        portalDest = portals.get(currentSquare)
        if portalDest is not None:
            if printGame:
                if portalDest < currentSquare: print "oh no, a chute to", portalDest
                if portalDest > currentSquare: print "oh yay, a ladder to", portalDest
            currentSquare = portalDest
        if currentSquare == 100:
            break
    if printGame: print "you won in", spins, "spins!"
    return spins

playGame(True)


# In[34]:


# Now we're going to play a whole bunch of games to get a distribution.
print "Playing games..."
gameOutcomes = [playGame(False) for game in range(100000)]
print "100,000 games completed."


# In[35]:


print "Fastest game is in", min(gameOutcomes), "spins."
print "Slowest game is in", max(gameOutcomes), "spins."


# In[21]:


get_ipython().run_line_magic('matplotlib', 'inline')
import numpy as np
import pandas as pd
from scipy import stats, integrate
import matplotlib.pyplot as plt
import seaborn as sns

print "Median game takes", int(np.median(gameOutcomes)), "spins."
print "95th %ile game takes", int(np.percentile(gameOutcomes, 95)), "spins."
sns.distplot(gameOutcomes, axlabel="spins to win", hist_kws={"histtype":"step", "alpha":1, "color":"g" })