'''
Created on Jul 11, 2014

@author: Brett Paufler
Copyright Brett Paufler


Creates Game Objects for Alternate Games

    50-50 (coin toss)
    

'''

import scipy.misc

import sympy
import decimal



from lotto_class import prizeLevel
from lotto_class import lotteryGame

#import math

def blackjack():
    '''returns a 1 layer deep
        blackjack or 21 game    
    '''
    a = lotteryGame()
    a.name = 'blackjack'
    a.fileName = 'blackjack twenty one'
    a.price = 1
    a.prizes.append(prizeLevel())
    a.prizes[0].prize = 2
    a.prizes[0].odds = 1.00 / 0.4636
    a.prizes[0].returnPerDollar = float(a.prizes[0].prize)/a.prizes[0].odds
    return a


def coinToss():
    '''returns a 1 layer deep
        50-50 (coin toss) type game    
    '''
    a = lotteryGame()
    a.name = 'coinToss'
    a.fileName = 'simple 50-50 coin toss type game'
    a.price = 1
    a.prizes.append(prizeLevel())
    a.prizes[0].prize = 2
    a.prizes[0].odds = 2
    a.prizes[0].returnPerDollar = float(a.prizes[0].prize)/a.prizes[0].odds
    return a


def craps():
    '''returns a 1 layer deep
    craps style game, betting on the cum line (pass)
    '''
    a = lotteryGame()
    a.name = 'craps'
    a.fileName = 'craps near even money on the pass line'
    a.price = 1
    a.prizes.append(prizeLevel())
    a.prizes[0].prize = 2
    a.prizes[0].odds = 1 / 0.492929
    a.prizes[0].returnPerDollar = float(a.prizes[0].prize)/a.prizes[0].odds
    return a

def roulette():
    '''returns a 1 layer deep
        roulette game, betting straight up on a number
        American Style (0-00)    
    '''
    a = lotteryGame()
    a.name = 'roulette'
    a.fileName = 'simple 35to1 roulette straight up'
    a.price = 1
    a.prizes.append(prizeLevel())
    a.prizes[0].prize = 36
    a.prizes[0].odds = 38
    a.prizes[0].returnPerDollar = float(a.prizes[0].prize)/a.prizes[0].odds
    return a


def casinoGames():
    '''returns a list of all the standard casino games
    '''
    return [coinToss(),craps(),blackjack(),roulette()]


def letItRideBROKEN(g, n=2):
    '''taking a simple game (any of the above) as input
    reconfigures odds and prize if all winning bets 'ride'
    for the given number of iterations
    
    g = lotteryGame object with 1 prize level
    n = number of times to let it ride
    
    letItRide(1) returns the original object
    letItRide(2) returns odds for two straight wins, 
        all money left on the table
    
    TODO - WOULD NEED TO IMPLEMENT A .copy function to work
    a = g, g = a, writing over the passed value
    '''
    #print n
    a = g
    a.prizes[0].odds = g.prizes[0].odds ** n
    a.prizes[0].prize = g.prizes[0].prize ** n
    #g.printLotteryGameData()
    return a

def simpleGamblersRuin(g, s, f):
    '''given a simple game g (one prize level)
    returns the chance (1/odds)
    that player will win f before they lose s
        That is the odds a player will with bankroll s=start
        will increase their money to f=finish
        while making $1 bets
       
    game = lotteryGame Ojbect (only first prize level is evaluated)
    s = starting cash
    f = desired finish cash goal
    returns probability (1/odds) (0.00 to 1.00) of this happening
    
    prob = (1 - (q/p) ** s)  / (1 - (q/p) ** (s+f)
    where p = g.prizes[0].odds
    
    Formula From (BOTH):
    https://www.math.umass.edu/~lr7q/ps_files/teaching/math456/Week4.pdf
    http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GR.pdf
    '''
    s = float(s)
    f = float(f)
    p = float(1.00 / g.prizes[0].odds)
    print p
    q = 1 - p
    if q == p:
        prob = s / (f)
        print "Fifty Fifty Math"
    else:
        t = (1 - (q/p) ** s)
        #print t
        b = (1 - (q/p) ** (f))
        #print b
        prob = t / b
        #print prob

    return prob
#grindOdds = gamblersRuin   
#print gamblersRuin(coinToss(), 3, 6 )
#print (2 ** 2) / 3.0
#print grindOdds(coinToss(), 3, 6 )


#print 1.0 / simpleGamblersRuin(craps(), 500,525) 
'''
game = blackjack()
game.printLotteryGameData()
game = craps()
game.printLotteryGameData()
game = coinToss()

game.printLotteryGameData()

print "RIDE ON COMMENCING"
game = roulette()
game.printLotteryGameData()
rideOn = letItRide(game,3)
print rideOn.printLotteryGameData

print "Grind Odds"
'''
#print grindOdds(coinToss(), 10)
#print grindOdds(craps(), 10)


def funRoulette(C, p, w):
    '''
        The iterative part of the Gambler's Ruin for non- 1to1 bets
        hardwired for roulette
        
        w = number of chips = 35
        p = 0.475
    '''
    decimal.getcontext().prec = 100
    C = decimal.Decimal(C)
    p = decimal.Decimal(p)
    w = decimal.Decimal(w)
    q = decimal.Decimal(1-p)
    
    r = (C-1)/(w+1) + 1
    print "r equals %d" % r
    MC = decimal.Decimal(0)
    print "MC = %.100f" % MC
    for i in range(0, int(((C-1)/(w+1) + 1)), 1):
        i = decimal.Decimal(i)
        #print "i %d" % i
        neg = (-1)**i
        cC = int(C - i*w - 1)
        #print "Icw1 = %d" % cC
        combo = decimal.Decimal(scipy.misc.comb(cC, i, exact=True))
        #print combo 
        #TODO PERHAPS CHANCE THIS BACK
        '''
        PERHAPS HERE
        '''
        pq = (p*(q**w))**i
        #print "pq = %.100f" % pq
        #print neg

        MC += neg * combo * pq
        print "MC = %.100f" % MC
    
    MC = abs(MC)
    print "funRoulette returning %.100f" % MC   
    return MC
    
    
    #return 1


def gamblersRuin(p,w, j, C):
    '''
    
    
    1. j is the initial capital of the gambler, j>=0,
    2. C is the ultimate fortune which the gambler wants to accumulate, C>=j>=0,
    3. w is the number of chips the gambler may win in every single game, w>=1,
    4. p is the probability of winning w chips in a single game. In every single game
        the gambler is either winning w chips, with probability p, or losing one chip,
        with probability q = 1 - p. After a series of single games, the game terminates
        when,
    5. either the total fortune of the gambler for the 2rst time reaches or exceeds C
        chips, or
    6. his fortune drops down to 0 chips.
    
    P(C,j) = 1 - q**j (FM(C-j))/FM(C)

    
    'http://ac.els-cdn.com/S0304414902001060/
    1-s2.0-S0304414902001060-main.pdf?_tid=f17a7f10-0d61-11e4-9dd9
    -00000aacb35f&acdnat=1405567684_41bce5d2b0c8eb5623c3ed85c5a99c0e'
    '''
    decimal.getcontext().prec = 100
    p = decimal.Decimal(p)
    q = decimal.Decimal(1 - p)
    C = decimal.Decimal(C)
    j = decimal.Decimal(j)
    w = decimal.Decimal(w)
    #edge cases, no chance if have no money
    #a certainty if start with more money than goal
    if j <= 0:
        print "No Funds Automatically Loses, returning 0"
        return 0
    if j >= C:
        print "Funds exceed Target, returning 1"
        return 1
    
    if abs(p-q) <= .0000000001:
        fF = j/C
        print "odds close to fifty-fifty, j/C = %.100f" % fF
        return fF

    top = funRoulette((C-j),p,w)
    bot = funRoulette(C,p,w)
    qj = (q ** j)
    Pcj = decimal.Decimal(1) -  qj * top / bot
    Pcj = abs(Pcj)
    print "top = %.100f" % top
    print "bot = %.100f" % bot
    print "qj = %.100f" % qj
    
    print "PcJ = %.100f" % Pcj
    return Pcj

#gamblersRuin(p=0.0263157894737, w=35.0, j=5, C=50)

#roulette odds = 0.0263157894737
#print scipy.misc.comb(14,3)
#print 5.0/38.0
#if 1 == 1.00:
    #print "We have a match"
    


def mC(p, q, w, C):
    '''
    '''
    

    r = int((C-1)/(w+1))
    pqw = p * (q**w)
    mc = []
    for i in range(0, (r+1), 1):
        cC = C - i*w - 1
        cD = scipy.misc.comb(cC, i, exact=True)
        n = (-1)**i
        mc.append(n * cD * pqw**i)
    rV = abs(sum(mc))
    print "Running mC for %.5f  %.5f  %d  %d :RETURNING %.100f" % (p,q,w,C,rV)
    return rV

def gR(p, w, j, C):
    '''
    '''
    #print "gR Called with  %.5f  %d  %d  %d" % (p, w,j, C)
    if 2 * C > 25:
        precision = 2 * C
    else:
        precision = 25
    
    decimal.getcontext().prec = precision
    p = decimal.Decimal(p)
    q = decimal.Decimal(1-p)
    w = decimal.Decimal(w)
    j = decimal.Decimal(j)
    C = decimal.Decimal(C)
    print '\n\n'
    if j <= 0:
        print "j = %d, No Chance Returning 0" % j
        return 0
    if j >= C:
        print "j >= C (%d >= %d), A Certainty, Returning 1" % (j, C)
        return 1
    if abs(p-q) < .0000000001:
        print "Fifty-Fifty returning j/C"
        return j/C
    
    t = decimal.Decimal(mC(p,q,w,(C-j)))
    print "t  = %.100f" % t
    b = decimal.Decimal(mC(p,q,w,C))
    print "b  = %.100f" % b
    tb = decimal.Decimal((t / b))
    print "tb  = %.100f" % tb
    qj = decimal.Decimal(q ** j)
    print "qj = %.100f" % qj
    tq = decimal.Decimal(tb * qj)
    print "tq = %.100f" % tq
    pF = decimal.Decimal(1 - tq)
    print pF
    print "gR Called with  %.5f  %d  %d  %d :RETURNING %.100f" % (p, w,j, C, pF)
        
    return pF

  
p = 1.0 / 38.0
print "Roulette 10 to 1500"
#print gR(p, 35,10, 1500)
print "Roulette 10 to 1500"
    
'''
r1-1000=0.00014531113491820637976, odds=6881
r10-1000=0.0014733204939778766014, odds=678.7389

r1-1500=0.00003032796164555663731, odds=32972.8720871
r10-1500=0.00030749747745157266, odds=3252.0591983

r1-2000=0.0000065143704886973528, odds=153506.774252
r10-2000=0.0000660496909047261146517796, odds=15140.1162716
'''

print 1 / 0.00030749747745157266