Several years ago, when I was a university professor, one of the homework problems I assigned to students in the beginning programming class was to simulate the game of chuck-a-luck.

Chuck-a-luck has three dice. You place a bet on one of the six dice numbers (1, 2, 3, 4, 5, 6) then roll the three dice. If your selected number appears on all three dice you win $3. If your number appears on two of the three dice you win $2. If your number appears on one of the dice you win $1. If your number doesn’t appear on any of the three dice you lose $1.

Left: The Wikipedia article on chuck-a-luck shows the exact calculation of the house advantage for chuck-a-luck. Right: The game often uses a birdcage-like device to roll the three dice.

Even for such a simple problem there are many different design possibilities.

Chuck-a-luck is no longer played in casinos because the house advantage is very large — about 7.87%, meaning for each dollar bet, you’d lose almost 8 cents on average.

Dice in fashion. The red dress is very nice, but the earrings, shoes, and glasses are somewhat dicey I think.

Demo code:

# chuck_a_luck.py

import numpy as np

np.random.seed(3)
b = 5  # number bet on
bank_start = 0
bank = bank_start
bet = 1  # bet amount
plays = 1_000_000

print("\nPlaying chuck-a-luck %d times " % plays)
for i in range(plays):
  matches = 0
  d1 = np.random.randint(1,7)  # from 1 to 6
  d2 = np.random.randint(1,7)
  d3 = np.random.randint(1,7)

  # print(d1)
  # print(d2)
  # print(d3)

  if d1 == b: matches += 1
  if d2 == b: matches += 1  
  if d3 == b: matches += 1

  if matches == 0: bank -= 1 * bet
  elif matches == 1: bank += 1 * bet
  elif matches == 2: bank += 2 * bet
  elif matches == 3: bank += 3 * bet
print("Done \n")

print("final bank = %d " % bank)
net_gain = bank - bank_start
print("net gain = %d " % net_gain)
avg_gain = net_gain / bet  # avg gain per dollar bet
avg_gain = avg_gain / plays
print("average gain per dollar played = %0.4f " % avg_gain)