#!/usr/bin/python
# calculate the probabilities of suit match for "royal match" bet

import random

maxdecks=100000
maxdealt=50 # number of cards dealt into deck
bet=25 # starting bet



#===================================================================
# calcprob
#
# probability of royal match win, given 'nsuitcards' cards left of
# a particular suit in a deck of 'ncards' cards, and possibility
# of K/Q pair indicated by 'royal'
#
# this assumes 1 deck and 3-1/10-1 payout
#
def calcprob(nsuitcards, ncards, royal):
    # royal match K/Q
    if royal == 1:
        prob1 = 2.0/ncards    # first card
        prob2 = 1.0/(ncards-1)    # second card has only 1 possibility to get match
        rmprob = prob1*prob2
    else:
        rmprob = 0
    payout = 11
    royalmatchreturn = rmprob*payout

    #print "Probability of royal match is ", rmprob, " with payout of ", royalmatchreturn

    # 2 cards of any suit match (non-K/Q)
    prob1 = float(nsuitcards)/ncards;
    prob2 = ((nsuitcards-1.0)/(ncards-1.0))
    mprob = (prob1*prob2)
    mprob -= rmprob
    payout = 4  # 3-1 odds
    matchreturn = mprob*payout

    #print "Probability of non-royal match is ", mprob, " with payout of ", matchreturn


    if royal == 1:
        treturn = (matchreturn+royalmatchreturn)
    else:
        treturn = (matchreturn)
    #print "Total return is ", treturn, " (",nsuitcards,",",ncards,")"
    return treturn


#=============================================================
# countsuits()
#
# Count the number of cards in each suit, returned as 4 item list
#
def countsuits(deck):
    nsuitcards = [0,0,0,0]
    for i in range(0,4):
        for j in range(0,13):
            if deck[i*13+j] == 0:    
                nsuitcards[i] += 1
            #print "deck[",i*13+j,"] = ",deck[i*13+j]
    return nsuitcards
    

#===============================================================
# calcprob2
#
# Count the expected return of royal match with current deck.
# K/Q are considered to be the first 2 cards in the suit
#
def calcprob2(deck):
    royal = [1,1,1,1]
    nsuitcards = countsuits(deck)
    ncards = sum(nsuitcards)
    prob = 0.0;
    # determine if royal can happen
    for i in range(0,4):
        # treat first 2 cards in suit as K/Q
        if deck[i*13] or deck[i*13+1]:
            royal[i] = 0
        prob += calcprob(nsuitcards[i], ncards, royal[i])

    # calculate probs
    return (prob)

#=================================================================
# playdeck()
# 
# calculate return after removing 1 random card from the deck up
# to 'ndealt' cards
#
# deck[] is a list of all cards in the deck.  we'll assume they're
# in order, first 13 cards same suit, next 13 same suit, etc...
#
def playdeck(ndealt):
    deck = []
    prob = []
    global bet
    for i in range(52):
        # reset deck    
        deck.append(0)

    for i in range(ndealt):
        #print i, " cards dealt, (", countsuits(deck),")"
        prob.append(calcprob2(deck))
        #print "Probability is ", prob(i)

        # deal out a card
        while 1==1:
            rand = random.randint(0,51)
            if deck[rand] == 0:
                deck[rand] = 1
                break
###########
    #
    # Here we apply our counting strategy
    #
    # bet when red/black count swings larger than 5

#    nsuitcards = countsuits(deck)
#    redblack = (nsuitcards[0]+nsuitcards[1]) - \
#        (nsuitcards[2]+nsuitcards[3])
#    if abs(redblack) >= 6:
#        bet *= prob[ndealt-1]

###########
    return prob

    
#=====================================
# Begin
#=====================================


#
# Play a bunch of decks and average probabilities
#

totprob = []  # list of probabilities n cards into deck
favdecks = [] # number of favorable decks, listed by number cards dealt

totprob = playdeck(maxdealt)   # initial probabilities
for i in range(maxdealt):
    if totprob[i] > 1.0:
        favdecks.append(1)
    else:
        favdecks.append(0)

for ndecks in range(1,maxdecks):
    prob = playdeck(maxdealt)
    # integrate current deck into average over all decks
    for i in range(maxdealt):
        totprob[i] += (prob[i]-totprob[i])/ndecks
        if prob[i] > 1.0:
            favdecks[i] += 1
    

# print averaged probabilities

f = open('dealtvsfavdecks.txt','w');
f.write("# cards dealt | expected payout | number of favorable decks |" \
        " % decks that are favorable\n")
print "Average of", maxdecks, "decks"
for i in range(maxdealt):
    line = "%i %f %i %f\n" % (i, totprob[i], favdecks[i], \
            float(favdecks[i])/maxdecks*100)
    f.write(line)
    print i, "cards dealt, payout = %.6f" % totprob[i], ",\t", favdecks[i], \
            " fav decks (", float(favdecks[i])/maxdecks*100, "%)"
f.close()


# now, if we were to recognize all favorable decks and only play them...