Understanding Cash4Life Chances

You may have read on the main game page that the chances of winning the Cash4Life top prize are 1 in 21,846,048 or that you have an overall chance of 1 in 8 to win a prize on each ticket. But how exactly are those chances of winning a prize determined?

Cash4Life is a split-matrix type lotto game similar in game set-up as other split-matrix games such as Powerball or Mega Millions. Split-matrix actually means there are two matrices rather than just one as in a simple lotto game. In the first matrix, you select FIVE numbers out of a field of 60 (numbers 1 to 60) and then the second matrix, you select ONE number out of a field of 4 (numbers 1 to 4) – this number is called the Cash Ball in this game. Like other split-matrix games, these two drawings are independent events played simultaneously. In order to figure the chances for winning, we must consider both events so the chances for each event are multiplied in order to determine the chances for winning one of the prize levels.

The formula for figuring matching possibilities out of a set field of numbers is based on probability theory. It is the mathematical description of how many five number combinations can be made out of the field of 60 numbers which is then multiplied by the number of one digit combinations out of a field of 4. It is important to remember that the formula has to account for the numbers not drawn as well as the numbers drawn. The formula used for this calculation is virtually the same one used for most lotto-type jackpot games, it uses sampling without replacement so when a number is drawn, the next sample size is one smaller – you don’t replace the number. There is a relationship of the total number of ways to select 5 numbers out of the set of 60 to the number of successful choices and number of failed choices. So your first number has a 1 in 60 chance of being drawn and then your second number has a 1 in 59 chance, and so on and can be written as “1/60 x 1/59 x 1/58 x 1/57 x 1/56” which can be expressed as a “binomial coefficient” (this is also a combination function). The basic formula for a binomial coefficient uses what mathematicians call “factorials” and are depicted as x! or a number followed by an exclamation point. A factorial is a number multiplied progressively by all other smaller numbers to find probabilities. Let's use 5 as an example: 5! would be calculated as 5 x 4 x 3 x 2 x 1 = 120.

This type of formula is referred to as a “hypergeometric distribution”. If you have Microsoft Excel, there is a HYPGEOM.DIST function that can calculate these chances easily. The equations below show how the math behind this function works.

Chances for Winning the Top Prize (5 of 5 plus 1 of 1 Cash Ball):

So, 5,461,512 x 4 = 21,846,048. The odds of matching five out of five numbers plus the Cash Ball to win the top prize is 1 in 21,846,048.

Overall Chances:

To determine the overall chances in a game, all of the chances for each winning level are added together. The overall chances of winning Cash4Life are 1 in 8. The formula for the overall chances is:

1 / ((1/30,821,472) + (1/1,813,027.76) + (1/143,355.68) + (1/8,432.69) + (1/3,413.23) + (1/200.78) + (1/249.75) + (1/14.69) + (1/49.95) + (1/32.02)) = 7.77

General Rules That Apply to All Draw Games

1. It is the player's responsibility to check their 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.

Pick 3 Game Rules

For each Pick 3 play, select three numbers from 0 to 9, except when playing Front Pair or Back Pair (two numbers selections). Select the wager amount (50 cents or $1), the type of play (play types specified below) and drawing time (Midday, Evening or Both). Wild Ball (doubles the cost of the play) and EZ Match (additional $1 per play) are both available as optional add-on features. Each playslip allows a player to play up to 5 plays for up to 14 consecutive drawings.

Game selections can be made by 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. Pick 3 is drawn twice daily, seven days a week, at approximately 12:45 p.m. and 8:59 p.m. each day. Depending on the play type chosen (play types specified below), a player must match all three numbers in the Exact Order drawn or in Any Order drawn to win.

How to play Pick 3 using a paper playslip

1. The playslip has five play boards ("Play A" through "Play E"), each containing three rows of numbers from 0 through 9. You may play from one to five boards. To play your numbers for more than one drawing at a time, mark the appropriate box on the top of the playslip next to "MULTI-DRAW." This will play only your selections in "Play A" through "Play E" for that number of drawings. Pick 3 can be played for 1, 2, 3, 4, 5, 6, 7 or 14 consecutive drawings.
2. Select the wager amount ($.50 or $1). Note: $.50 plays are not available for Straight/Box play types.
3. Select one option for the play type. Play types include the following options:
   
   1. Straight (Exact Order)
   2. Box (Any Order)
   3. Straight/Box (Exact Order or Any Order – must be $1 wager)
   4. Front Pair
   5. Back Pair
   6. Combo (Gives all possible three-number combinations of the chosen numbers for an Exact-Order prize - costs between $1.50 and $6, depending on the selected wager amount and numbers chosen.)
4. Based on the play type, select one number (0 to 9) from each of the appropriate rows, or mark the "QP" (Quick Pick) box. You may select the same number multiple times, but Box, Straight/Box and Combo play types require at least two different digits.
5. Pick 3 can be played for the Midday drawing, Evening drawing or Both by selecting the appropriate box on the left side of the playslip. If no selection is made, your selections will be played for the next available Pick 3 drawing.
6. Optional features of Wild Ball and/or EZ Match are available, if desired. Wild Ball creates more possible winning number combinations and doubles the cost of the Pick 3 play (see Wild Ball rules below). EZ Match is an instant-win feature that costs an additional $1 per play (see EZ Match rules below). You may select one, both or neither of these features for your Pick 3 play.
7. If you make a mistake, mark the "Void" box on that board and select your numbers on the next board.
8. Prize payouts for 50-cent plays will be half of the amount of a $1 play.
9. The cost for a Combo wager can be from $1.50 to $6, depending on the wager amount and the numbers played.
10. Use only a blue or black pen or use a pencil for marking selections; red ink will not be accepted by the terminal.

How to play Pick 3 using a digital playslip with the mobile app

1. Select how many drawings you'd like to play. Pick 3 can be played for 1, 2, 3, 4, 5, 6, 7 or 14 consecutive drawings.
2. Select your drawing time. Pick 3 can be played for the Midday drawing, evening Drawing or Both.
3. Select your play type. Options include:
   
   1. Straight (Exact Order)
   2. Box (Any Order)
   3. Straight/Box (Exact Order or Any Order - must be $1 wager)
   4. Front Pair 
   5. Back Pair
   6. Combo (Gives all possible three-number combinations of the chosen numbers for an Exact-Order prize - costs between $1.50 and $6, depending on the selected wager amount and numbers chosen.)
4. Select the amount you'd like to play. Pick 3 can be played for 50 cents or $1, except for the Straight/Box play type, which must be $1 plays. Prize payouts for 50-cent plays are half the payouts for $1 plays. Combo play types cost between $1.50 and $6, depending on the selected wager amount and numbers chosen.
5. Choose whether to add Wild Ball by selecting "Yes" or "No." Wild Ball is a game option that creates more possible winning combinations and doubles the cost of the Pick 3 play. See Wild Ball rules below.
6. Choose whether to add EZ Match by selecting "Yes" or "No." EZ Match is an instant-win feature that costs an additional $1 per play. See EZ Match rules below.
7. Select the numbers you want to play. Select three numbers from 0 to 9, shake your phone/press the Quick Pick button to have the app select your numbers for you. You may choose the same number multiple times, but Box, Straight/Box and Combo play types require at least two different digits.
8. Review your digital playslip, then tap "Save Digital Playslip." Present the QR code at retail to use your digital playslip.

How to play Pick 3 verbally

At the discretion of the retailer, Pick 3 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 numbers to be played – either player-selected or "Quick Pick"
2. The dollar amount to be played - either 50 cents or $1
3. The wager type - Straight, Box, Straight/Box, Front Pair, Back Pair or Combo
4. The number of draws to be played
5. The drawing to be played: Midday, Evening or Both
6. The addition of Wild Ball, if desired
7. The addition of EZ Match, if desired

Wild Ball^™

Wild Ball^™ is an optional add-on feature that replaces any of the winning Pick 3 numbers with the Wild Ball number drawn for that game - creating more winning combinations and more ways to win!

• The Pick 3 Wild Ball number is drawn immediately following the Pick 3 drawing.
• Players can win multiple Wild Ball prizes on the same play, in addition to any wins on the base game.
• Wild Ball DOUBLES the cost of the base Pick 3 play.

EZ Match

EZ Match is an instant-win feature that costs $1 per play, in addition to the cost of the Pick 3 ticket. A player selecting EZ Match for Pick 3 will receive three (3) EZ Match numbers printed below the Pick 3 numbers on the ticket. If any of the randomly-generated EZ Match numbers match the player's Pick 3 numbers, regardless of order, they will instantly win the corresponding EZ Match prize.

• If two (2) or more of the same Pick 3 game numbers match an EZ Match number, the player wins the EZ Match prize amount printed next to the matched EZ Match number one (1) time.
• Players may play EZ Match by marking the applicable EZ Match box on the Pick 3 playslip or by requesting the add-on from the retailer.
• Each board played with EZ Match will be printed on a separate ticket. Pick 3 tickets with the added EZ Match option will print with the Pick 3/EZ Match logo at the top of the ticket; the EZ Match logo will also be within the body of the ticket with the EZ Match numbers, and the amount of the prizes will be printed below the EZ Match logo. Draw Games tickets printed without these elements are not EZ Match tickets and are not eligible to win EZ Match prizes.
• Pick 3 tickets with EZ Match cannot be canceled.
• A winning EZ Match play can be cashed at any Missouri Lottery retail location either before or after the host game drawing. If the EZ Match play is cashed prior to the host game drawing, an exchange ticket will print for the upcoming drawing, just like when a multi-draw winning ticket is cashed before all the drawings have occurred. If a winning EZ Match play is cashed after the host game drawing has occurred, and wins on both the EZ Match wager and the host game drawing, the prizes will be added together and paid in one lump sum.
• EZ Match prizes can be claimed up to 180 days from the host game draw date on which the EZ Match wager was originally purchased.

Pick 3 tickets with EZ Match cannot be canceled.

Pick 3 Liability Limit

Two Missouri Lottery games - Pick 3 and Pick 4 - have liability limits, meaning players may be denied the purchase of numbers when a certain number of tickets with a particular combination have been sold. Liability limits have been placed on these games to keep the Lottery from selling more winning tickets than it can pay. The liability limit is $1.5 million for Pick 3 and $1.5 million for Pick 4. Setting liability limits is standard in the Lottery industry on games with fixed payouts.

On rare occasions, popular Pick 3 and Pick 4 numbers may "sell out" and cannot be purchased. Liability limits are reached when a large number of people have chosen a certain number combination, such as the Pick 4 combination 2-0-0-0, which was popular on Jan. 1, 2000, to mark the new millennium.

There is no need for liability limits on Lotto and Powerball numbers, since jackpots are pari-mutuel, meaning the jackpot prize is divided equally among all its winners.

The Missouri Lottery has an obligation to raise as much money as possible for public education programs, while also ensuring that we have funds available to pay winners. To accomplish this, we must be able to limit our potential payout to an amount that we expect to reasonably pay based on the sales we generate for this game. 

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:

Understanding Pick 3 Chances

You may already know that the chance of winning the top Pick 3 prize of $600 is 1 in 1,000. But you might wonder how those odds are determined.

Pick 3 winning numbers are the result of three separate and independent drawings. In each drawing, one winning number is selected from 10 possible outcomes, 0 through 9. Each selection is completely separate and has no effect on the other two drawings.

So the chance of any number being drawn in each of the three drawings that select the winning numbers for Pick 3 is 1 out of a possible 10 or 1 chance in 10. To get the top prize of $600, a player must correctly pick all three separate winning numbers, meaning they have a 1 in 10 chance of correctly selecting the winner in each of the three draws that make up the Pick 3 winning numbers selected twice daily.

To get the overall probability of choosing all three correctly, we multiply the probabilities of selecting the correct outcome in each separate selection:

The player has one chance to correctly choose the winning outcome out of 1,000 possible outcomes (1,000 different combinations) each time a Pick 3 drawing is conducted. That means there are 1,000 different ways the numbers could be drawn, and the player has one of those possible outcomes as his/her numbers.

We hope this helps to better explain the chances of winning the top prize in Pick 3.