Understanding Lotto Chances

You may already know that the chances of winning the Lotto jackpot are roughly 1 in 3.5 million, or that the overall chances of winning any prize in the Lotto game are about 1 in 20. But many people wonder how those chances of winning are determined.

Lotto is played by selecting six numbers out of 44 possible choices (the numbers from 1 to 44). During each drawing, one by one, the six numbers are randomly selected. Drawings are carefully monitored and are open to the public for viewing.

So, how does one determine what the chances of winning are for correctly matching all six numbers for any Lotto drawing? We start with the math. The formula for calculating the possibilities for matching the numbers drawn out of all the numbers in the machine is based on probability theory. So, how likely is it to get one particular outcome out of all the possible outcomes that could happen? In other words, how many different combinations of six numbers can be made out of 44 numbers?

Let's do the math; it won't be hard. The general math formula for calculating lottery chances will combine three things:

Any calculation of chances for a Lotto game involves three basic elements:

• The total number of numbers you are choosing from, which is called the field or (f);
• The number of numbers the player selects on his\her playslip, which is called the pick or (p); and
• The number of correct matches between the player's picks and the numbers drawn, which is called the match (m).

Here is the formula statisticians use to calculate the probability:

It looks complicated, but let us explain. Remember, f = the 44 numbers, p = the numbers you picked, and m = the number you correctly matched.

So, here we go. The factors or elements depicted as x over y, with ( ) around them are called binomial coefficients, and when filled in with our numbers, are what mathematicians call factorials and are depicted as x!, or a number followed by an exclamation point. What's that all about? Well, simply put, a factorial is a number multiplied progressively by all other smaller numbers until you reach 1. It looks like this:

Let's use 6 as an example; 6! would be figured as 6 x 5 x 4 x 3 x 2 x 1 = 720

In other words, we would multiply 6 times 5 times 4 times 3 times 2 times 1 to get the result. 0! is equal to 1.

So what does that have to do with Lotto? Well, 6! is all the different combinations you can theoretically make out of six numbers. Starting to make sense?

To match all six numbers and win the Lotto jackpot, here are the chances of winning:

(Remember, there are 44 numbers, and you must choose six of those numbers to play and match to win the jackpot.)

Lotto chances of winning the jackpot:

We have one six-number combination (our pick) in a possible 7,059,052 different possible combinations or outcomes. These are your chances of hitting the jackpot with any six numbers played.

But wait! Your chances are actually better than that . . .

. . . on a Lotto playslip, you must choose two sets of six numbers for each draw (two plays for $1). So, if we choose two different sets of six numbers, we actually reduce our chances by having two, not one, of the possible sets of winning combinations. So on any given playslip, if we choose different numbers on our ticket, we actually have a 1 in 3,529,526 chance of having the winning set of numbers (divide above by two).

We hope this helps to better explain the chances of winning the Lotto jackpot.

General Rules That Apply to All Draw Games

1. It is the player's responsibility to check his or her ticket to make sure it represents the correct game, draw date, numbers requested and has a visible bar code or serial number.
2. Winning tickets must be claimed within 180 days of the last winning draw date on the ticket.
3. Purchased tickets are only valid for the dates shown on the ticket.
4. The ticket, not the playslip, is the only valid proof of your number selection, and it is the only valid receipt to claim a prize.
5. All tickets, transactions and winners are subject to the directives of the executive director of the Missouri Lottery, the rules and regulations of the Missouri Lottery and the Missouri Statutes, and tickets are only offered for sale in accordance with the same.
6. Upon purchasing a ticket, the player agrees to abide by the Missouri Statutes and all rules and regulations of the Missouri Lottery.
7. A ticket is a bearer instrument. It is recommended that the ticket be signed at the time of purchase.
8. The Missouri Lottery is not responsible for lost or stolen tickets. Tickets are void and will not be paid if determined stolen, unissued, illegible, mutilated, altered in whole or part, misregistered, defective, incomplete, printed or produced in error, multiply-printed, or if the ticket fails any of the Missouri Lottery's confidential validation tests. Liability for void tickets is limited to replacement of the ticket or refund of sales price.
9. Tickets may not be sold to or redeemed by minors under the age of 18.
10. The holder of a winning ticket may win in only one prize category per play board and shall be paid the prize in the highest category won.

Mega Millions Game Rules

A player must select five numbers between 1 and 70 and then select one number (the Mega Ball) between 1 and 24. The cost for one play is $5. A player may select each set in one of four ways: by verbally communicating the numbers to the retailer, by completing a paper playslip, by completing a digital playslip or by requesting a "Quick Pick." A Quick Pick is a computerized randomly-selected set of numbers available through the Draw Games terminal. Mega Millions is drawn twice a week – Tuesday and Friday – at approximately 9:59 p.m. The more numbers the player matches to those drawn, the more the player wins.

How to play Mega Millions using a paper playslip

1. The playslip has five play boards ("PLAY A" through "PLAY E") with two sections on each board. The top section of each board contains numbers 1 through 70, and the bottom section contains numbers 1 through 24. Select five numbers in the top section and one number (the Mega Ball) in the bottom section of each board. You may play 1, 2, 3, 4 or all 5 boards. Cost per board is $5.
2. Make your selections by placing a heavy mark in the top portion and one number (the Mega Ball) in the bottom section by placing a heavy mark in each circle, beginning with board "PLAY A." To have the terminal select the numbers randomly, mark the "QP" circle for "Quick Pick." If you make a mistake, mark the "VOID" circle on that board and select your numbers on the next board.
3. To play your numbers for more than one drawing at a time, mark the appropriate box on the playslip next to "MULTIDRAW." This will play only your selections in boards "PLAY A" through "PLAY E" for that number of drawings.
4. You can play Mega Millions for 1, 2, 3, 4, 5, 10 or 15 drawings.
5. Use only a blue or black pen or use a pencil for marking selections. The terminal will not accept red ink.

How to play Mega Millions using a digital playslip with the mobile app

1. Select how many drawings you'd like to play. You can play Mega Millions 1, 2, 3, 4, 5, 10 or 15 drawings.
2. Select the numbers you want to play. First, select five white-ball numbers from 1 to 70; shake your phone or tap the Quick Pick button to have the app select your numbers for you. Next, select a Mega Ball number from 1 to 24; shake your phone or tap the Quick Pick button to have the app select your Mega Ball number for you.
3. Review your digital playslip, then tap "Save Digital Playslip." Present the QR code at retail to use your digital playslip.

How to play Mega Millions verbally

At the discretion of the retailer, Mega Millions may be played by making a verbal request for a ticket. The player must provide the clerk with all of the following information:

1. The dollar amount to be played;
2. The numbers to be played - either player-selected or "Quick Pick"
3. The number of draws to be played.

Mega Millions tickets CANNOT be canceled.

Jackpot winners have 60 days from the claiming date to declare whether they would like their payments in CASH (equal to approximately 50 percent of the estimated, advertised jackpot) or ANNUITY (the advertised jackpot amount paid in 30 graduated annuity payments).

The set prize amounts are based on an expected number of winners. In some cases, these prizes may be paid on a pari-mutuel basis, which will be lower than the published prize levels.

Prizes are approximately 50 percent of sales. Overall odds of winning a prize are 1 in 23.07 for each $5 Mega Millions play.

Selling Hours

All Draw Games are available for purchase from 5 a.m. to 2 a.m. (Club Keno until 1:52 a.m.) seven days a week at any Draw Games retailer, except during Draw Breaks.

Draw Breaks

The process of selecting winning numbers for each game is referred to as a "Drawing" or "Draw." A "Draw Break" is when sales are suspended for a particular game so that the wagers for that "Drawing" may be balanced and the winning numbers drawn. The draw breaks for each game are listed below: