Lottery Odds Calculator

Calculate the exact odds of winning any lottery game

Formula:Odds = C(n,r) × C(b,p)

Lottery Configuration

Enter the lottery format

Main Numbers

Bonus Ball (Optional)

Odds Results

Your lottery odds breakdown

Jackpot Odds
1 in 292.2M
292,201,338 total combinations
Probability: 0.34 in 1M

Main Combinations

11,238,513

Bonus Combinations

26

Est. Any Prize

1 in 5.8M

Prize Tier Odds

Match 5 + Bonus
1 in 292.2M
Match 5 only
1 in 11.7M
Match 4 + Bonus
1 in 913.1K
Match 4 only
1 in 36.5K
Match 3 + Bonus
1 in 14.5K
Match 3 only
1 in 580
Match 2 + Bonus
1 in 701
Match 2 only
1 in 28
Important: Lottery games have a significant house edge (typically 40-50%). The expected value of a ticket is usually negative. Play responsibly and only with money you can afford to lose.

Popular Lottery Formats

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Combinations Formula

How lottery odds are calculated

C(n,r) = n! / (r! × (n-r)!)
n = Total balls in the pool
r = Numbers you pick
! = Factorial (e.g., 5! = 5×4×3×2×1)
C(n,r) = Total possible combinations

Quick Answer

TL;DR summary

Lottery odds are calculated using combinations: C(n,r) = n! / (r!(n-r)!). For Powerball (5/69 + 1/26): C(69,5) × C(26,1) = 11,238,513 × 26 = 292,201,338. Your chance of winning the jackpot is 1 in 292.2 million - you're more likely to be struck by lightning twice.

Key Facts About Lottery Odds

Important things to know

  • Powerball jackpot odds: 1 in 292,201,338 (matching 5 white + 1 red)
  • Mega Millions jackpot odds: 1 in 302,575,350 (matching 5 white + 1 gold)
  • Overall odds of winning ANY Powerball prize: 1 in 24.87
  • Adding a bonus ball multiplies the total combinations significantly
  • Buying 100 tickets only changes odds from 1:292M to 100:292M (still negligible)
  • Lottery expected value is typically -40% to -50% (house edge)
  • State lotteries are mathematically worse than most casino games

Frequently Asked Questions

Common lottery odds questions

How are lottery odds calculated?

Lottery odds use the combinations formula: C(n,r) = n! / (r!(n-r)!). For a game where you pick r numbers from n total numbers, this formula calculates all possible combinations. For games with bonus balls, multiply the main combinations by the bonus ball combinations.

Why are lottery odds so bad?

Lotteries need to fund prizes, operating costs, and state revenue - typically only 50-60% of ticket sales go to prizes. The large jackpot odds are necessary to create exciting prize pools. The mathematical expected value of a lottery ticket is usually -40% to -50%, worse than almost any casino game.

Does buying more tickets improve my odds significantly?

Mathematically yes, but practically no. Buying 100 Powerball tickets changes your odds from 1 in 292 million to 100 in 292 million (still 0.000034%). You would need to buy millions of tickets to have meaningful odds, which would cost more than most jackpots.

What are the odds of matching some numbers but not all?

Partial match odds are much better. In Powerball: matching 5 numbers (no Powerball) is 1 in 11.7 million, matching 4 + Powerball is 1 in 913,000, and matching just the Powerball is 1 in 38. These tiers make up the majority of winners.

Are some number combinations luckier than others?

No. Every combination has exactly the same probability of being drawn. "1-2-3-4-5-6" has the same odds as any other combination. However, popular numbers (birthdays, patterns) mean more people might share your jackpot if you win.