TFT Rolldown Odds

import random

# Rolls we're tracking
rollsUntilFound = {
    "Hecarim": [],
    "Sejuani": [],
    "Nautilus": [],
    "Thresh": [],
    "All": []
}

# The full simulation
totalSimulations = 1000
for i in range(0,totalSimulations):
    # Define the base champ pool
    champPool = {
        "Brand": 22,
        "Hecarim": 22,
        "Kennen": 22,
        "LeBlanc": 22,
        "Nautilus": 22,
        "Sejuani": 22,
        "Sett": 22,
        "Soraka": 22,
        "Syndra": 22,
        "Thresh": 22,
        "Trundle": 22,
        "Varus": 22,
        "Viktor": 22
    }

    # Define current champs purchased
    currentChampsBought = {
        "Hecarim": 0,
        "Sejuani": 0,
        "Nautilus": 0,
        "Thresh": 0
    }

    # Remove champs currently purchased from pool, and remove some number of other champs
    for champ in champPool:
        if (champ in currentChampsBought):
            # Remove the champs I'm currently holding from the total pool
            champPool[champ] -= currentChampsBought[champ]
        else:
            # Remove some number of other champs from the pool
            champPool[champ] -= 0

    # Calculate num champs remaining
    totalChampsRemaining = 0
    for champ in champPool:
        totalChampsRemaining += champPool[champ]

    # Do rolls until all are found
    numRolls = 0
    threeStars = 0
    while (currentChampsBought["Hecarim"] != 9 or
        currentChampsBought["Nautilus"] != 9 or
        currentChampsBought["Sejuani"] != 9 or
        currentChampsBought["Thresh"] != 9):

        numRolls += 1

        # Roll 5 times and then increment
        for i in range(0,5):
            rollChance = random.randint(1,100)
            if (rollChance > 40):
                continue # didn't roll 40% chance

            # Now roll from remaining champs
            champRoll = random.randint(1, totalChampsRemaining)

            # Find which champ was rolled based on "weighted champ pool"
            foundChamp = ""
            for champ in champPool:
                champRoll -= champPool[champ]

                if (champRoll <= 0):
                    foundChamp = champ
                    break

            if ((foundChamp in currentChampsBought) and (currentChampsBought[foundChamp] < 9)):
                currentChampsBought[foundChamp] += 1
                champPool[foundChamp] -= 1
                totalChampsRemaining -= 1

                if currentChampsBought[foundChamp] == 9:
                    rollsUntilFound[foundChamp].append(numRolls)
                    totalChampsRemaining -= champPool[foundChamp]
                    del champPool[foundChamp]

    rollsUntilFound["All"].append(numRolls)

print("Finished simulation")
# print(rollsUntilFound)

for champ in rollsUntilFound:
    avg = 0
    for rerolls in rollsUntilFound[champ]:
        avg += rerolls
        # Could calculate other things like standard deviation, percentile rolls, etc here
    avg = float(avg) / float(totalSimulations)
    print ("Avg to find " + champ + " = " + str(avg))