# New Jersey Pick-6 Lotto Odds & Payouts

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

The New Jersey Pick-6 lotto is a popular game in one of the most populous US states and costs just \$1 to play. Jackpots start at a guaranteed \$2 million, and frequently reach the tens of millions of dollars since New Jersey has a lot of potential ticket buyers both inside state lines and throughout the surrounding major metropolitan areas.

This number draw lottery is played by selecting 6 distinct numbers from 1 to 49. In structure it is identical to Canada's 6/49 lottery and Ohio's Classic Lotto. The jackpot and lesser prizes are paid out on a pari-mutuel basis, meaning they are not fixed amounts, but vary depending on the number of winners for each prize level and the size of the pool (ticket sales and rollover) from which funds are distributed. The only exception is the lowest prize level, which pays out a fixed \$3 when you match exactly 3 out of 6 balls.

## Probability of Winning NJ Pick-6 Jackpot

If players much select 6 distinct numbers from between 1 and 49, then there are 13,983,816 different combinations of lottery ticket numbers. This means the probability of matching all 6 out of 6 numbers and winning (a share of) the jackpot is

1/13983816
= 0.000000071511
= 0.0000071511%

The way this is computed is with the combination formula

(49 C 6)
= (49*48*47*46*45*44)/(6*5*4*3*2*1)
= 13983816

## Probability of Making a Partial Match

The likelihood of matching n out of 6 is the number of ways to match n out of 6 divided by 13983816.

5 of 6:

(6 C 5)*(43 C 1)/13983816
= 6*43/13983816
= 0.00001844989
= 0.001844989%
≈ odds of 1 in 54201

## More Lottery Guides

4 of 6:

(6 C 4)(43 C 2)/13983816
= 15*903/13983816
= 0.00096861972
= 0.096861972%
≈ odds of 1 in 1032

3 of 6:

(6 C 3)*(43 C 3)/13983816
= 20*12341/13983816
= 0.01765040386
= 1.765040386%
≈ odds of 1 in 57

## Prize Amounts

For matching exactly 5 of 6 numbers in Pick-6 your approximate winnings on average are \$2700. This figure is taken from the average of pari-mutuel payouts from past games. Historically, most payouts for matching 5 of 6 have been in the range of \$1500 to \$4000, but occasionally they have reached even \$9000 and \$10000.

For matching 4 of 6 numbers, the average winnings are \$56. Most payments for this prize level are in the range of \$45 to \$77. Less frequently the prizes are lower or higher than this range.

Matching 3 of 6 earns you exactly \$3, the only fixed prize level.

Because the prizes are variable here, it's hard to compare the expected return of New Jersey Pick-6 and the identical game Ohio Classic Lotto.

## Previous Winning Numbers

The New Jersey state lottery website has a list of previous winning number combinations from the past year. The table below shows the frequency of the numbers 1 through 49 as they occur in winning lottery combinations between December 24, 2012 and December 23, 2013.

Num.
Freq.
Num.
Freq.
Num.
Freq.
Num.
Freq.
01
13
14
15
27
12
40
10
02
14
15
14
28
13
41
7
03
10
16
16
29
13
42
5
04
9
17
17
30
16
43
11
05
11
18
11
31
13
44
11
06
15
19
13
32
14
45
17
07
19
20
7
33
10
46
15
08
14
21
14
34
10
47
15
09
10
22
11
35
17
48
10
10
14
23
17
36
10
49
21
11
12
24
12
37
14

12
14
25
10
38
17

13
8
26
14
39
15

There were 105 lottery drawings for Pick-6 between these dates, and with 6 numbers selected per drawing, there are 105*6 = 630 data points represented in the table. The expected frequency of each number is 630/49 = 12.857.

As you can see from the table, the most frequently drawn number was 49, which occurred 21 times. The next runner-up was 7, which occurred 19 times. The least frequently drawn number was 42, followed closely by 20 and 41.

## How to Win New Jersey Pick 6

How do you increase your chances of winning a prize in Pick 6 Lotto? The only mathematical way to increase the probability of winning a prize is simply to buy more lottery tickets. There are no secrets for picking winning numbers since every combination has an equal change of winning or losing. But holding two tickets instead of one makes it twice as likely that you will win, and holding three lottery tickets instead of one makes it thrice as likely.

Unfortunately, buying multiple tickets does not increase your expected winnings. On average, you will lose the same amount of money whether you buy one ticket per week for a year, or 52 tickets for a single lottery drawing once a year.

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