#!/usr/bin/env python
"""
 Craps simulation
 See for example http://en.wikipedia.org/wiki/Craps
 
 Chap 9, Exercise 7, pg 292 of Zelle's "Python Programming"

 Jim Mahoney, Oct 24 2006 
 for the Intro Programming class


 --- output (on a PowerBook, with test games and all defaults ) ----
 
   thirty:Desktop$ ./craps.py 
   Testing 5 games 
   
   === game 1 ===
     first roll is 8
     roll 2 is 8
     which makes the point and wins.
   
   === game 2 ===
     first roll is 10
     roll 2 is 7
     which is a seven-out and loses.
   
   === game 3 ===
     first roll is 9
     roll 2 is 3
     roll 3 is 5
     roll 4 is 6
     roll 5 is 7
     which is a seven-out and loses.
 
   === game 4 ===
     first roll is 9
     roll 2 is 9
     which makes the point and wins.
   
   === game 5 ===
     first roll is 8
     roll 2 is 2
     roll 3 is 9
     roll 4 is 8
     which makes the point and wins.
   
   Calculating the odds of winning at craps...
     number of games simulated  =    10000
     number of games won        =     4887
     odds of winning are        = 0.489 +- 0.010 at 95% confidence
   thirty:Desktop$ 


 --- output (on cs, without tests, with 1e6 simulated games) ----

   mahoney@cs oct_25.attachments$ time ./craps.py 
     Calculating the odds of winning at craps...
     number of games simulated  =  1000000
     number of games won        =   492328
     odds of winning are        = 0.4923 +- 0.0010 at 95% confidence

     real       0m29.382s
     user       0m29.372s
     sys        0m0.004s
     mahoney@cs oct_25.attachments$ 

"""

from math import sqrt
from random import randint

def roll():
    """ Return the result of rolling one 6-sided die.   """
    return randint(1,6)

def game(verbose=True):
    """ Play a game of craps.
        Return True or False for a win or a loss.
        If 'verbose' is set (by default it is),
        then print out a description as well. """
    first_roll = roll() + roll()
    if (verbose):
        print "  first roll is", first_roll
    if (first_roll in (2,3,12)):
        if (verbose):
            print "  which craps out and loses."
        return False
    elif (first_roll in (7,11)):
        if (verbose):
            print "  which wins outright."
        return True
    else:
        roll_number = 1
        while True:
            roll_number = roll_number + 1
            next_roll = roll() + roll()
            if (verbose):
                print "  roll", roll_number, "is", next_roll
            if (next_roll == first_roll):
                if (verbose):
                    print "  which makes the point and wins."
                return True
            elif (next_roll == 7):
                if (verbose):
                    print "  which is a seven-out and loses."
                return False

def test_games(n_games=5):
    """ Run a bunch of verbose games  """
    print "Testing", n_games, "games "
    print
    for i in range(n_games):
        print "=== game", i+1, "==="
        game(verbose=True)
        print

def calculate_odds(n_games=1e4, verbose=True):
    """ Calculate the odds of winning by running a number of games
        (1000 games by default).
        Return the measured odds as the fraction wins/n_games.
        If 'verbose' is True (the default), then print the odds too."""
    if (verbose):
        print "Calculating the odds of winning at craps..."
    (wins, games) = (0, 0)
    n_games = int(n_games)
    while (games < n_games):
        games = games + 1
        if ( game(verbose=False) ):
            wins = wins + 1
    odds = 1.0 * wins / n_games
    # sigma_1 = estimated standard deviation of odds of a single game
    # sigma_n = estimated standard deviation of odds from n games
    # statistics say true value is in +-2*sigma with 95% probability.
    sigma_1 = sqrt( odds * (1.0 - odds) ) 
    sigma_n = sigma_1 / sqrt( 1.0 * n_games )
    if (verbose):
        print "  number of games simulated  = %8i" % n_games
        print "  number of games won        = %8i" % wins
        print "  odds of winning are        =" + \
                " %.4f +- %.4f at 95%% confidence" % (odds, 2*sigma_n)
    return odds

## un-comment the next line to see the verbose test games.
# test_games()         

# We need about a million games to get enough statistics to show
# that the odds of winning are really less than a half.
# On cs (with a 2Hgz dual core AMD64 cpu) this takes about half a minute.
calculate_odds(n_games=1e6)