Lottery Odds and Probability Calculator

Use this calculator to know your risk and make optimal decisions based on your risk tolerance. Stop guessing, make calculated choices. For more details on lottery format and the difference between odds and probability, please check the explanations below.

NOTE: If you're a mobile or tablet user, kindly switch to a desktop computer to use this module efficiently.

RESULTS:

Understanding Lottery Format

This calculator is designed to handle five different lottery formats. We group lottery games into five formats:

• Simple Game – In this game, the rule is straightforward: you pick x numbers from a set of y balls. For example, in a simple 6/49 game, you pick 6 numbers from a pool of 49. Another example is Gimme 5 where you pick 5 numbers from 39.
• Lottery Game with One Extra Ball from a Separate Drum – An example of this format is Powerball, where you pick 5 numbers from 59 and 1 additional number from a separate set of 26. In total, you choose 6 numbers drawn from two different drums.
• Game with Two Extra Numbers from a Separate Drum – Examples include EuroMillions and EuroJackpot. In this format, you pick 5 numbers from 50, plus 2 additional numbers from a separate drum containing 12. This is a seven-number game with numbers drawn from two different drums.
• Lottery Game with One Supplementary Number from the Same Drum – This game is similar to the simple type, except that it draws one additional number from the same drum. An example is the Irish Lotto, where 6 numbers are drawn from 47, and a seventh number is drawn from the same drum.
• Game with Two Supplementary Numbers from the Same Drum – Also similar to the simple type, but with two extra balls drawn from the same drum. One example of this game is the Australia Saturday Lotto where it picks 8 numbers and you match the first 6 numbers to win the jackpot.

Knowing the Difference Between Simple and Extra-Ball Lottery Games

Lottery games are not the same. If you're actually going to buy a ticket, you should know what you're actually committing to. Lottery games are classified into three types:

1. Simple Lottery Game (No Extra Balls) - This is the simplest structure. You choose a fixed number of balls (e.g., 6 out of 49), and that is it. The drawn winning numbers come from the one shared pool. You match all 6 winning numbers and that is it. The prize levels tend to be fewer. You can win on matching 3, 4, or 5 numbers with no complex mechanics. Why it matters? The jackpot odds are easier to calculate and less confusing.

2. Lottery with Extra Ball(s) from a Separate Drum - When a draw is divided among two drums in a game, you might win lesser sums for matching only the additional ball, or 3 numbers and the additional ball, and so on. But there's something. Topping the jackpot become tougher because now you're not only matching 5 numbers, you need to match the two sets of numbers, which increases the complexity. More prize levels, more thrill, but more difficult jackpot odds.

3. Lottery Games with Supplementary Numbers - When the main numbers and supplementary are pulled from the same drum, the primary numbers alone are relevant for the jackpot. Supplementary numbers only exist to provide additional smaller prizes. The jackpot odds remain the same as in a basic game—because they do not rely on the supplementary number. In short, you have more opportunities to win lesser prizes without making the jackpot more challenging.

The Key Takeaway:

If you're hoping for the jackpot, use the simple games or supplementary numbers. These games maintain your odds in simple form.

Understanding Lottery Odds and Probability

The lottery can be a thrilling thing to play. You choose a few numbers, purchase a ticket, and begin fantasizing about being an instant millionaire. But first, let your dreams be tempered with an understanding of how the lottery actually works, specifically what your odds and probability of winning are.

Take note that probability and odds are two related terms, but they employ different equations and describe likelihood in different contexts.

What is probability in the lottery?

Probability is a number between 0 and 1. If something has a probability of 0, it is impossible, and if it has a probability of 1, then it is certain to occur. For instance, a probability of 0.5 is a 50/50 chance of something happening.

In the lottery context, a 50/50 chance to win only occurs when you purchase half of all combinations. Let's take an example of a 6/49 lottery game. There are about 14 million combinations. If you purchase 7 million different tickets, your chances of winning will be 0.5 or 50%. In reality though, purchasing seven million tickets isn't a financially viable option.

Typically, we only purchase one or two tickets at a time. Here's another example: if you are playing Mega Millions, your opportunity to win the jackpot with a single ticket is 0.0000000034. That's immensely low since it is almost zero.

Lucky for you, as long as you have a ticket, you're in the game. And that's what counts in the lottery. You have to be in it to win it.

What do odds mean in the lottery?

Odds in favor indicate the proportion of favorable outcomes to unfavorable outcomes. In a game of the lottery, this lets you know how often you are likely to win in relation to how often you are likely to lose.

For instance, when playing the UK Lotto, there are 45,057,474 combinations. When you play one ticket, you have only one way to win and 45,057,473 ways to lose. Therefore, your odds in favor of winning the jackpot are 1:45,057,473. This implies that for each winning way there are more than 45 million losing ways.

But odds are scalable. Suppose you purchase 10 tickets. Your favorable outcomes are now 10, and your unfavorable outcomes are 45,057,464 (45,057,474 - 10). Your odds in favor are now 10:45,057,464. We can simplify this per ticket to approximately 1:4,505,746. It implies that on average, you have just one favorable outcome per 4.5 million tickets.

We can apply the same method of calculation for winning smaller prizes. For instance, in a 6/49 lottery, the odds in favor of getting exactly 3 numbers correct is 1:55.65. Meaning that on average, you have one chance for every 56 tickets.

In short, the lottery is fun, but winning is extremely difficult. Do you want to enhance the fun and play the lottery more intelligently? Read How to Win the Lottery: The Math No One Talks About (No Hype) .

Lottery games are based on chance, and no tool can alter the odds. Play for fun.