# Texas Two Step: Lottery Odds & Payout

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

Texas Two Step is a lotto draw game offered in the state of Texas. Tickets cost \$1 for a single play and jackpots start of \$200,000. If the jackpot is not won in a particular drawing, the unclaimed amount is added to the next jackpot of the next drawing. This means the grand prize can grow very large if there is a streak of no-win drawings. Since 2001 when the game was introduced, the largest ever Texas Two Step jackpot was \$2.9 million, in April of 2006.

Compared to Powerball, Mega Millions, and Lotto Texas, the Texas Two Step lottery offers higher probabilities of winning the main prize and lower-tier prizes for partial matches.

## How to Play

To make a number selection for Texas Two Step, you first select four distinct numbers from 1 to 35, and then you pick a fifth number independently from 1 to 35 -- called the "Bonus Ball". This fifth number may be equal to one of the other four. It's a two-step process, hence the name of the lottery.

Structurally and mathematically, this method of number selection is different from a system in which you pick 5 distinct numbers from 1 to 35.

Nor is it equivalent to a system in which you pick 5 numbers from 1 to 35 where up to two numbers can match. In such a system, the order of the 5 numbers would not matter. However, with Texas Two Step the order does matter for the Bonus Ball number, which must be last.

## Texas Two Step Odds

The probability of winning Texas Two Step lottery is the reciprocal of the number of possible lottery ticket number selections. The number of possible tickets is

(35 C 4)*35

where (35 C 4) is "35 choose 4," the combination function. This is multiplied by 35 because there are 35 ways to pick the bonus ball number. The expression works out to

(35 C 4)*35
= [35*34*33*32/(4*3*2*1)]]*35
= 1,832,600

Therefore, the probability of winning the jackpot prize is 1/1832600 = 0.00000054567, or 0.000054567%. In other words, the odds are 1 in 1,832,600.

The probability of matching 4 out of 4 regular numbers without the bonus ball is equal to the number of ways to get all four regular numbers correct with a mismatching bonus ball, divided by the total number of different ticket combinations. The number of ways to get 4/4 without the bonus ball is 34, therefore the probability is

34/1832600
= 1/53900
= 0.00001855287
= 0.001855287%
= odds of 1 in 53,900

The probability of matching 3 out of 4 regular numbers plus the bonus ball is

(4 C 3)*31/1832600
= 31/458150
= 0.000067663
= 0.0067663%
= odds of 1 in 14,779.03

Here are the odds and prizes for the perfect and partial matches in the Texas Two Step lottery.

Match
Odds
Prize
4/4 + bonus
1 in 1,832,600
your share of jackpot
4/4
1 in 53,900
~ \$1,500
3/4 + bonus
1 in 14,779
~ \$50
3/4
1 in 435
~ \$20
2/4 + bonus
1 in 657
~ \$20
1/4 + bonus
1 in 102
\$7
only bonus
1 in 58
\$5

The prize for matching only the bonus ball number is guaranteed at \$5, while the prize for matching 1 out of 4 numbers plus the bonus is guaranteed at \$7.

The other prizes are paid out on a pari-mutuel basis, meaning they fluctuate based on size of the prize fund and the number of winners at each level. The values in the table are estimates based on averages of previous games. Your actual prize may be higher or lower than the amount stated in the table.

## Other Probabilities in Texas Two Step Lottery

The probability that the bonus ball number matches the other four numbers is 4/35 = 11.43%, a little more than 1 out of 9 times. That means you can expect about 1 out of 9 Texas Two Step drawings to feature a winning combo in which the bonus ball matches one of the four regular balls.

Yet for some reason, lottery ticket buyers are skeptical about picking a set of numbers in which the bonus ball is not distinct from the other four numbers. In the historical list of winning numbers you can see that when the bonus ball matches one of the other four numbers, the jackpot almost always rolls over, much more often than when the five numbers are all different. This means that players tend to avoid this pattern.

The probability that the numbers drawn are all even or all odd (same parity) is given by

(17 C 4)*17/1832600 + (18 C 4)*18/1832600
= 281/5390
= 5.21%
= odds of 1 in 19.18

3

2

5

38

10

## Comments

0 of 8192 characters used

No comments yet.

Click to Rate This Article