from random import randint

def divideBy2(decNumber):
    remstack = []

    while decNumber > 0:
        rem = decNumber % 2
        remstack.append(rem)
        decNumber = decNumber // 2

    binString = ""
    while len(remstack) > 0:
        binString = binString + str(remstack.pop())

    return binString

def sevensea2roller(rolls):
    dn = len(rolls)
    binary = [0]*dn
    result = 0
    unusedd = rolls[:]
    actived = [0]*dn
    maxv = 0
    curv = 0
    for i in range(2**dn):
        a = str(divideBy2(i))
        unusedd = rolls[:]
        actived = [0]*dn
        for j in range(1,len(a)+1):
            binary[-j] = int(a[-j])
        actived = [a*b for a,b in zip(rolls,binary)]
        if sum(actived) >= 10:
            unusedd = [a-b for a,b in zip(unusedd,actived)]
            while 0 in unusedd:
                unusedd.remove(0)
            if len(unusedd)>0:
                curv = 1 + sevensea2roller(unusedd)
            else:
                curv = 1
        maxv = max(maxv,curv)
    return maxv


#print(sevensea2roller([10,10,3,4,5]))

rolls = 10000 #this is the number of times the dice are rolled to calculate the distribution
dice = 5 #this is the number of dice rolled.
results = [0]*(dice+1)
atleast = [0]*(dice+1)
nums = [0]*(dice+1)

for i in range(rolls):
    rolledd = [0]*dice
    for j in range(dice):
        rolledd[j] = randint(1,10)
    a = sevensea2roller(rolledd)
    results[a] = results[a]+1

for i in range(len(results)):
    results[i] = results[i]/rolls
    nums[i] = i

atleast[-1] = results[-1]

for i in range(2,len(atleast)+1):
    atleast[-i] = results[-i]+atleast[1-i]

print('Chance of getting exactly/Chance of getting at least:')
print(nums)
print(results)
print(atleast)
print('Expected value:')
print(sum([a*b for a,b in zip(nums,results)]))