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 [email protected]

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)
```

Out[33]:

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]:

```
%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" })
```

Out[21]: