Lotto Texas: Odds, Prizes, and How to Win

TR Smith is a product designer and former teacher who uses math in her work every day.

A quick-pick ticket for Lotto Texas with two number selections.

Lotto Texas is a fun, multi-million dollar random number draw game offered by the Texas Lottery Commission. Lotto Texas offers a higher probability of winning than other big-jackpot lotteries such as Powerball and Mega Millions, with a grand prize that starts at \$5 million. The jackpot prize and lower-tier prizes rollover to the same tier on the drawing if there are no winners for that level. In May 2010, the jackpot reached a record-high of \$100 million (estimated) when the jackpot rolled over continuously for six months straight!

Tickets cost \$1 for a single play. For \$1 more you can purchase the Extra option, which increase the amounts of the non-jackpot prizes if you happen to win such a prize. Lotto Texas prizes are paid out on a pari-mutuel basis, meaning they vary according to the number of winners at each level and how much money is available to allocate to each award level. Knowing the odds of winning can help you make more responsible decisions with your money.

Other state lotteries:

How to Play

To play Lotto Texas, select 6 distinct numbers from 1 to 54 on your play slip. You can buy as many selections as you want for \$1 each. There are no bonus balls or randomly drawn multipliers. If you want a chance to increase your lower-tier prize amounts, you can can pay \$1 more for the extra option, which increases the lesser prizes by a fixed amount.

Odds of Winning Lotto Texas

The probability of making a perfect 6/6 match and winning the grand prize is

6! * 48! / 54!
= (6*5*4*3*2*1)/(54*53*52*51*50*49)
= 1 / 25827165
= 0.000000038719
= odds of 1 in 25,827,165

The odds of winning the Lotto Texas jackpot are 10 times better than that of winning the Mega Millions jackpot, and about 7 times better than that of winning the Powerball jackpot. However, in comparison to the other multi-state lottery game Hot Lotto, the odds are about equal. (Hot Lotto is currently not available in Texas.)

The odds of making a partial match of 5/6 are

6 * 48 / 25827165
= 32 / 2869685
= 0.000011151
= odds of 1 in 89,677.7

The probability of matching exactly 4 out of 6 numbers is

(6 C 4)(48 C 2)/25827165
= 376 / 573937
= 0.00065512
= odds of 1 in 1,526.4

The probability of matching 3 out of 6 is

(6 C 3)(48 C 3)/25827165
= 69184 / 5165433
= 0.013394
= odds of 1 in 74.7

The expression (x C y) is "x choose y," the combination function. Here are the odds for all prize levels, along with the approximate prizes, for the regular \$1 ticket and the \$2 ticket with Extra.

Match
Odds
Regular Prize
w/ Extra
6/6
1 in 25,827,165
same
5/6
1 in 89,678
~ \$1,000 - \$3,000
4/6
1 in 1,526
~ \$50
3/6
1 in 75
\$3
\$13
2/6
1 in 9
\$0
free ticket

The prizes for matching 5/6 and 4/6 are variable, but most of the time you will win between \$1,000 and \$3,000 for matching 5 of 6 numbers. If you match 4 of 6 numbers, your prize will be around \$50. If you purchase the Extra option and match 5/6 or 4/6, your prize will be increased by \$10,000 and \$100 respectively.

The prize for matching 3/6 is fixed at \$3, or \$13 if you have the Extra option. Matching 2/6 will win you a free ticket if you have the Extra option, otherwise it earns nothing.

Logo of Texas Lottery and Lotto Texas.

Expected Return

To calculate the expected return on a regular \$1 play, we multiply each prize by its probability (or divide by the odds) and then add the results. Assuming a jackpot value of \$5 million, and average award of \$2,000 for matching 5/6, and an average award of \$50 for matching 4/5 this gives us an estimated expected return of \$0.29 per \$1 wagered.

To calculate the expected return on a Lotto Texas ticket with Extra, we follow the same procedure using the increased prize amounts, and the divide the resulting number by 2 since the ticket costs \$2. This gives us an estimated expected return of \$0.30 per \$1 wagered. So both games are about equal in terms of expected return.

Probability Curiosities

The probability that the winning numbers will consist of only odds or only evens is given by the expression

2*(27 C 6)/25827165

which works out to

1012 / 44149
= 0.022922
= 1 in 43.6

The chances of a winning ticket consisting of all prime numbers is

(16 C 6)/25827165
= 88 / 283815
= 0.00031
= 1 in 3,225.2

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