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How Does the "Pick 3" Lottery Work?

Updated on October 07, 2016
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TR Smith is a product designer and former teacher who uses math in her work every day.

"Pick 3," sometimes called "Daily 3," "Cash 3," or "the numbers game," is the simplest and most common organized lotto game in the US. It has a longer and more colorful history than fancier modern games with big payouts, such as Powerball and Mega Millions. The numbers game is usually associated with poor people, strung out gamblers, and the elderly because it runs every day (twice a day in some states), costs as little as $0.50, and offers a higher probability of winning. And yet, the old-school Pick 3 numbers game it is still a favorite among players from all walks of life.

Organized Crime Roots of Pick 3, aka Numbers Racket

These days, every state in the US that operates lotteries runs its own version of Pick 3. But before Pick 3 became a state-run lottery, the game was known as the numbers racket or numbers game and was managed by independent bookies and crime organizations in big cities around the country. It was played among residents of the neighborhoods crime bosses considered their turf in the late 1800s and early 1900s.

Illegal lottery organizers needed to sell enough tickets or take enough bets to make running the game worthwhile, but of course most people with common sense didn't trust their local gangs to conduct truly fair and random drawings, and were naturally loathe to participate. The lottery organizers faced the challenge of finding a completely independent way to generate sequences of three random digits to reassure their customers. Eventually, some genius realized that the last three digits of the daily US Treasury balance effectively worked like a random number generator because these least significant digits were unpredictable. These balances were regularly published in the newspapers, making it very easy to conduct fair "drawings" this way. Other organizers of numbers rackets used the final digits of the win, place, and show bets posted at the local race track, which were also unpredictable.

The US government starting cracking down hard on illegal gambling and lottery operations starting in the Prohibition Era and continuing after WWII, diminishing them to the point where only the poor and people with criminal connections bothered to play. The neighborhood numbers game effectively disappeared when states started administering state-wide lotteries with bigger payouts.

A numbers racket slip from 1937 and a Pick 3 slip from 2015.
A numbers racket slip from 1937 and a Pick 3 slip from 2015.

How to Play Pick 3

Pick 3 is the easiest lottery game to play, you simply pick a three-digit number from 000 to 999. The order of the digits matters when playing the basic game, aka straight bet or exact match. For example, if you pick "075" and the winning number is "507" you won't win anything if your ticket is marked as a straight bet or exact match bet. The odds of winning with a straight bet are 1 in 1000, since there are 1000 different three-digit combinations. Typically, the prize for getting all three digits in the correct order is $500 for a $1 bet. Most states let players bet as little as $0.50 for a top prize of $250.

Straight, Box, Front Pair, Back Pair, Split Pair, and Sum

Lotteries offer several ways to increase the odds of winning Pick 3, though the drawback is a smaller prize if you do win. The most popular way to increase your odds is the "box" option. This option lets you win a prize if you have the right numbers but in the wrong order. For instance, if the winning number is "507", then everybody who played "570," "750," "705," "075," and "057" with the box option will also win a prize.

If you play three different digits, then the box option covers six different possibilities, effectively increasing your odds of winning by a factor of six. If you play a set of digits where two are the same and one is different, then there are three different ways of ordering them, so your odds of winning will increase by a factor of three.

Because the odds are improved with the box option, the lottery decreases the prize amount proportionally. Winning the box with three different digits pays about $500 ÷ 6 = $83. Winning the box with two same and one different digit pays about $500 ÷ 3 = $166. Here are some other options your state lottery may offer with Pick 3:

Front Pair: With this option you win if the first two digits of your ticket match the number drawn. For example, if the winning number is "507" then everyone who played "500," "501," "502," "503," "504," "505," "506," "508," or "509" with the front pair option will also win a prize. Because this increases your odds of winning by a factor of 10, the prize is decreased by a factor of 10, thus it pays about $50.

Back Pair: With this option you win if the last two digits of your ticket match the last two digits of the winning number. If the winning number is "507" then any ticket with a number of the form "X07" will also win. Like the front pair option, this option also gives you a 10 times better chance of winning.

Split Pair: With this option you win if the first and last digits of your ticket match the first and last digits of the winning number. As with front pair and back pair, with odds that are 10 times better you get a prize that is 1/10 the size of the straight prize.

Sum: Some Pick 3 lottery games have an option to guess the sum of the winning numbers. For example, if you pick "129" and the winning number is "507" you will get a lower tier prize because 1 + 2 + 9 = 12 and 5 + 0 + 7 = 12. The Texas Lottery sells this game option under the name "Sum it up!" The increase in the probability of winning and the prize depend on the sum. For instance, there are 73 different three-digit tickets whose numbers sum to 12, thus, the probability of winning with a sum of 12 is 73 times better than winning with a straight bet.

Split Bet: The split bet option splits your bet between the exact match and box option. If your numbers match the winning number in exact order, you win half of the straight prize plus half of the box prize. If your numbers match in the wrong order, you win half of the box prize only.

Only six states have no lottery: Alabama, Alaska, Hawai'i, Mississippi, Nevada and Utah.
Only six states have no lottery: Alabama, Alaska, Hawai'i, Mississippi, Nevada and Utah.

Fun Facts about Pick 3 Lottery

  • There are 720 three-digit numbers with three distinct digits, 270 three-digit numbers with two equal digits, and 10 three-digit numbers with all three equal digits. Thus, in a fair lottery the probability of the winning number having all three digits disctinct is 72%, the probability of the winning number having two equal digits is 27%, and the probability of the winning number having three equal digits is 10%.
  • Suppose you choose your ticket number randomly and the lottery chooses the winning number randomly as well. The probability that none of your ticket's digits match any of the winning number's digits (in right or wrong position) is 0.4581. In other words, if you choose the "Quick Pick" (letting the lottery computer randomly select your ticket numbers) then there is a 45.81% chance that you won't get a single digit correct. There's a 54.19% chance you will match at least one digit, possibly in the wrong position.
  • Lottery players tend to be superstitious and gravitate toward numbers with special meanings. Some of the most frequently played numbers are 911, 666, and other the other triples. At the convenience store chain Seven-Eleven, retailers report an high number of players picking "711."
  • Lottery players also like to pick the three-digit number corresponding to the current day's date in month-date format. For instance, on August 6, 2016 the winning number for the California Lottery Daily 3 evening drawing was "806" and the number of winning tickets sold was 1,139. The average number of winning tickets sold for a Daily 3 drawing in California is roughly 500, so they had more than twice the usual number of winners because the winning number was the current date.


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