Casino Number Guessing Game: Rules, Strategy, and Mathematical Analysis
This guide explains the classic "Number Guessing Game" commonly found in casinos and Indian gaming culture, including rules, probability analysis, and optimal strategies. The game is designed for educational purposes only and does not encourage real gambling.
1. Game Rules
Objective: Guess a randomly generated number between 1 and 100 within 7 attempts.
Feedback: After each incorrect guess, the system tells you if the number is "Higher" or "Lower."
Reward: Win a prize (e.g., ₹5000) if guessed correctly. No prize for incorrect guesses.
Example Flow:
System picks a secret number (e.g., 42).
Player guesses 50 → "Higher."
Player guesses 25 → "Lower."
Continue until correct or out of attempts.
2. Mathematical Analysis
Probability of Winning
Single Attempt: 1/100 ≈ 1% chance.
Optimal Strategy: Use binary search to minimize attempts.
Best Case: Guess correctly on the 1st try (1/100).
Worst Case: Guess correctly on the 7th try (1/100).
Average Attempts: ~3.5 (log₂100 ≈ 6.6, rounded to 7).
Expected Value (EV)
Assumption: Prize = ₹5000, no cost to play.
EV = (Probability of Winning × Prize) - (Probability of Losing × Cost)
= (1/100 × 5000) - (99/100 × 0) = ₹50 per play.
House Edge
If players pay ₹100 to play:
EV = ₹50 - ₹100 = -₹50 (50% house edge).
3. Optimal Strategy
Binary Search: Start with the midpoint (50) to halve the remaining range.
Adjust Based on Feedback:
If "Higher," focus on the upper half (51-100).
If "Lower," focus on the lower half (1-49).
Example Path:
Guess 50 → "Higher" → Next guess 75 → "Lower" → Next guess 62 → ... Continue until found.
4. Code Implementation (Python)
import random
def casino_guessing_game():
secret = random.randint(1, 100)
attempts = 0
low, high = 1, 100
while attempts < 7:
guess = (low + high) // 2
attempts += 1
print(f"Attempt {attempts}: You guessed {guess}")
if guess < secret:
low = guess + 1
elif guess > secret:
high = guess - 1
else:
print("Congratulations! You won!")
return
print("Game Over. The number was:", secret)
# Play the game
casino_guessing_game()
5. Cultural Considerations (India)
Legal Compliance: Ensure adherence to Indian gambling laws (e.g., no online real-money gambling in most states).
Ethical Design: Avoid targeting vulnerable populations. Use it as a math learning tool instead.
Monetization: If converting to a real game, partner with licensed casinos or use virtual currency.
6. Advanced Variations
Multi-Round Mode: Win incremental prizes for consecutive correct guesses.
Dynamic Ranges: Allow players to choose ranges (e.g., 1-1000).
Probability-Based Rewards: Offer higher prizes for fewer attempts.
Final Note: This game demonstrates principles of probability and critical thinking. Always prioritize responsible gaming!
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