Lottery Probability Calculator
Choose Lottery Type
Lottery Parameters
Advanced Options
📊 Prize Tier Probabilities
💰 Expected Value Analysis
Raffle Probability Calculator
Raffle Parameters
Multiple Prize Scenarios
🎯 Win Probability Visualization
📋 Raffle Strategy Tips
- Bulk Buying: Multiple tickets increase your odds proportionally
- Early vs Late: Timing doesn't matter for random draws
- Prize Distribution: Multiple smaller prizes offer better overall odds
- Expected Value: Most raffles have negative expected value
Lottery Odds Comparison
Any Prize: 1 in 24.9
Any Prize: 1 in 24.0
Any Prize: 1 in 13.0
Any Prize: 1 in 6.6
🔄 Odds Comparison Chart
📊 Real-World Probability Comparisons
More Likely Than Winning Powerball:
- Being struck by lightning (1 in 1M)
- Becoming a movie star (1 in 1.5M)
- Getting attacked by a shark (1 in 11.5M)
- Becoming an astronaut (1 in 12M)
Less Likely Than Powerball:
- Flipping heads 28 times in a row
- Drawing the same card 5 times from a shuffled deck
- Guessing a random 9-digit number correctly
- Rolling double sixes 10 times in a row
Lottery Syndicate Calculator
Syndicate Setup
Member Analysis
📈 Syndicate vs Individual Comparison
⚖️ Syndicate Pros & Cons
✅ Advantages
- Better odds with more tickets
- Lower individual cost
- Shared risk and excitement
- Professional management
❌ Disadvantages
- Smaller individual winnings
- Trust and legal issues
- Management fees
- Complex tax implications
Lottery Number Generator & Analysis
Generate Numbers
Number Pattern Analysis
🔥 Number Frequency Heatmap
Advanced Statistical Analysis
📈 Probability Distribution Analysis
💸 Long-term Expected Value Simulation
🧮 Mathematical Formulas Used
Combination Formula
C(n,k) = n! / (k!(n-k)!)
Where n is the pool size and k is numbers to choose
Expected Value
EV = Σ(Probability × Prize) - Cost
Sum of all prize probabilities minus ticket cost
Binomial Distribution
P(X=k) = C(n,k) × p^k × (1-p)^(n-k)
Probability of k wins in n independent trials
Hypergeometric
P(X=k) = C(K,k) × C(N-K,n-k) / C(N,n)
Used for raffles without replacement
Learn Probability & Statistics
🎲 Basic Probability Concepts
What is Probability?
Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1 (or 0% to 100%).
- 0 or 0%: Impossible event
- 0.5 or 50%: Equally likely to happen or not
- 1 or 100%: Certain event
Independent vs Dependent
Independent: Previous events don't affect future ones (lottery draws)
Dependent: Previous events affect future outcomes (drawing cards without replacement)
📊 Combinations vs Permutations
Combinations (Order Doesn't Matter)
Used in most lotteries where [1,2,3,4,5] = [5,4,3,2,1]
Formula: C(n,k) = n! / (k!(n-k)!)
Example: C(49,6) = 13,983,816 for Lotto 6/49
Permutations (Order Matters)
Used when sequence is important, like PINs or passwords
Formula: P(n,k) = n! / (n-k)!
Example: P(10,4) = 5,040 for a 4-digit PIN
💡 Common Probability Misconceptions
❌ Gambler's Fallacy
Believing that past results affect future outcomes in independent events. If a coin lands heads 10 times in a row, the next flip is still 50/50!
❌ Hot and Cold Numbers
No lottery number is "due" to be drawn. Each combination has exactly the same chance every draw.
❌ Quick Pick vs Self-Pick
Computer-generated numbers have the exact same odds as numbers you choose yourself.
Interactive Probability Calculator
🎯 Practical Applications
Risk Assessment
- Insurance calculations
- Investment portfolios
- Medical testing accuracy
- Weather forecasting
Gaming & Sports
- Poker hand probabilities
- Sports betting odds
- Casino game analysis
- Fantasy sports strategy
Business Decisions
- Market research analysis
- Quality control testing
- Project success rates
- Customer behavior prediction