import string, random
#scroll to the bottom of the page to calculate
# the general idea of this code is to brute force the probability
#its not very fancy code, but it gets the job done

# what it does it calculates how many legends based on a large number of rolls
# it calculates singles rolls first, and finds how many egg hatches are "wasted" if a pack had been bought
# it then calculates the probability of not getting a dupe on the "wasted rolls"
#it then evaluates if pack offers more legends or not
# this is based on the inclusion or rare egg hatches to the pack hatches
#all the probabilities are adjusted based on how many legend/myth of each banner/rare egg you already have

#READ THIS
#the code may take a bit to run, if it takes too long, decrease the number of eggsToHatch on line 32 by a factor of 10, 
#but try to keep it over as high as possible
#vice versa, you can also increase it for slightly better accuracy
#the code is meant to take into account you stopping when you get a featured leg/myth
# to change this to stopping when ANY legend is reached uncomment lines 54, 55, and delete the extra right parenthesis


def shouldRollSingleOrPack(numBannerLegOwned, numBannerMythOwned,
                                  numRareEggLegOwned, numRareEggMythOwned,
                                  numEggLegOwned, numEggMythOwned):
    probOfNewLegOrMyth = (.05 - numBannerLegOwned*.0075 - numBannerMythOwned*.0075 
                                - numEggLegOwned*.0005 - numEggMythOwned*.01/60)
    probRareEggNewLegOrMyth = .44 - numRareEggLegOwned*.4/34 - numRareEggMythOwned*.04/15

    singleCount = 0
    singleSaved = 0

    singleLegends = 0
    legendLastSeen = 0

    eggsToHatch = 1000000

    while eggsToHatch > 0: #hatch number of eggs given as singles
        roll = random.random()
        foundLegend = (roll < probOfNewLegOrMyth)
        singleCount += 1
        if (foundLegend):
            singleLegends += 1
            singleSaved += (10 - (singleCount - legendLastSeen)%10) # calculate how many eggs saved compared to using pack
            legendLastSeen = singleCount
        eggsToHatch -= 1

    packLegends = singleLegends
    
    singleCount += singleSaved
    saved = singleSaved
    bannerMultiplier = .0075*(4 - numBannerLegOwned - numBannerMythOwned)/probOfNewLegOrMyth
    nonBannerLegMultiplier = .0005*(35 - numEggLegOwned)/probOfNewLegOrMyth
    nonBannerMythMultiplier = (.01/60)*(15 - numEggMythOwned)/probOfNewLegOrMyth
    #print(probOfNewLegOrMyth, (probOfNewLegOrMyth - .0075*bannerMultiplier  
    #                        -.0005*nonBannerLegMultiplier - (.01/60)*nonBannerMythMultiplier) )
    while saved > 0: # calculate eggs that would be used if hatching pack with adjusted probability (no dupes wanted)
        roll = random.random()
        foundHatchLegend = (roll < probOfNewLegOrMyth)
        foundPackLegend = (roll < probOfNewLegOrMyth - .0075)
                #*bannerMultiplier  -.0005*nonBannerLegMultiplier - (.01/60)*nonBannerMythMultiplier) 
                            # accounts for leg/myth already seen -->
                            # and averages probability loss from egg in same pack based on it
        if (foundHatchLegend):
            singleLegends += 1
        if (foundPackLegend):
            packLegends += 1
        saved -= 1
    
    packRareEggs = singleCount/10/5
    legendsPerRoll = singleLegends/singleCount
    legendsPerPack = (packLegends)/(singleCount/10)
    legendsPerRareEgg = packRareEggs*probRareEggNewLegOrMyth/(singleCount/10)
    packPlusRareEggs = (packLegends + packRareEggs*probRareEggNewLegOrMyth)/(singleCount/10)
    
    if (legendsPerRoll > packPlusRareEggs /10):
        return f'try a single bc legendsPerRoll = {legendsPerRoll} , packPlusRareEggs/10 = {packPlusRareEggs/10}'
    else:
        return f'save up for a pack bc legendsPerRoll = {legendsPerRoll} , packPlusRareEggs/10 = {packPlusRareEggs/10}'
    
#for example:
#inputs in this order: numBannerLegendOwned, numBannerMythOwned,
#                      numRareEggLegendOwned, numRareEggMythOwned,
#                      numEgg (non banner) LegendOwned, numEgg (non banner) MythOwned
print(shouldRollSingleOrPack(0, 0, 26, 10, 12, 3))
print('')

# delete the three apostrophes at the top and bottom to uncomment the code

'''
print("here are the trials i coded")
print('0 banner mons previously owned, 0 rare egg mons owned, 0 reg leg eggs owned')
print(shouldRollSingleOrPack(0, 0, 0, 0, 0, 0))
print('')

print('0 banner mons previously owned, 1/4 rare egg mons owned, 1/4 reg leg eggs owned')
print(shouldRollSingleOrPack(0, 0, 8, 2, 8, 3))
print('')

print('0 banner mons previously owned, 1/2 rare egg mons owned, 1/4 reg leg eggs owned')
print(shouldRollSingleOrPack(0, 0, 17, 4, 8, 3))
print('')

print('0 banner mons previously owned, 1/2 rare egg mons owned, 1/2 reg leg eggs owned')
print(shouldRollSingleOrPack(0, 0, 17, 4, 17, 4))
print('')

print('0 banner mons previously owned, 3/4 rare egg mons owned, 1/2 reg leg eggs owned')
print(shouldRollSingleOrPack(0, 0, 26, 5, 17, 4))
print('')

print('0 banner mons previously owned, 3/4 rare egg mons owned, 3/4 reg leg eggs owned')
print(shouldRollSingleOrPack(0, 0, 26, 5, 26, 5))
print('')

print('0 banner mons previously owned, all rare egg mons owned, 3/4 reg leg eggs owned')
print(shouldRollSingleOrPack(0, 0, 34, 15, 26, 5))
print('')




print('1 banner mons previously owned, 0 rare egg mons owned, 0 reg leg eggs owned')
print(shouldRollSingleOrPack(1, 0, 0, 0, 0, 0))
print('')

print('1 banner mons previously owned, 1/4 rare egg mons owned, 1/4 reg leg eggs owned')
print(shouldRollSingleOrPack(1, 0, 8, 3, 8, 3))
print('')

print('1 banner mons previously owned, 1/2 rare egg mons owned, 1/4 reg leg eggs owned')
print(shouldRollSingleOrPack(1, 0, 17, 4, 8, 3))
print('')

print('1 banner mons previously owned, 1/2 rare egg mons owned, 1/2 reg leg eggs owned')
print(shouldRollSingleOrPack(1, 0, 17, 4, 17, 4))
print('')

print('1 banner mons previously owned, 3/4 rare egg mons owned, 1/2 reg leg eggs owned')
print(shouldRollSingleOrPack(1, 0, 26, 5, 17, 4))
print('')

print('1 banner mons previously owned, 3/4 rare egg mons owned, 3/4 reg leg eggs owned')
print(shouldRollSingleOrPack(1, 0, 26, 5, 26, 5))
print('')

print('1 banner mons previously owned, all rare egg mons owned, 3/4 reg leg eggs owned')
print(shouldRollSingleOrPack(1, 0, 34, 15, 26, 5))
print('')
'''