Powerball

Last data update: 2024-07-10

Winning Frequency

Consider:
What will be the next? as it appeared the more? Or would it be this time?

We find out by finding winning counts of each number.

White Balls

Top
NumberWin Count
61 100
36 95
21 94
32 92
63 92
69 92
27 91
Bottom
NumberWin Count
13 55
49 61
34 63
29 64
46 64
26 65

Powerball

Top
NumberWin Count
4 54
18 51
21 50
24 50
14 47
5 45
Bottom
NumberWin Count
15 32
12 33
16 33
17 33
22 33
20 35
23 37
2 38
7 38

The number of days since the last win

Consider:
What will be the next? Will it be since it was drawn recently? Or will it see as it has not appeared for a long time?

We calculate the number of days since a number's last draw.

White Balls

Top
NumberDraws AgoLast Drawn
63 54 2024-03-09
25 48 2024-03-23
13 45 2024-03-30
65 43 2024-04-03
40 39 2024-04-13
Bottom
NumberDraws AgoLast Drawn
7 1 2024-07-10
11 1 2024-07-10
12 1 2024-07-10
27 1 2024-07-10
46 1 2024-07-10
20 2 2024-07-08
22 2 2024-07-08
31 2 2024-07-08
33 2 2024-07-08
45 2 2024-07-08
5 3 2024-07-06
32 3 2024-07-06
35 3 2024-07-06
39 3 2024-07-06
49 3 2024-07-06
2 4 2024-07-03
26 4 2024-07-03
55 4 2024-07-03
57 4 2024-07-03
9 5 2024-07-01

Powerball

Top
NumberDraws AgoLast Drawn
20 92 2023-12-11
13 81 2024-01-06
11 79 2024-01-10
18 64 2024-02-14
17 62 2024-02-19
Bottom
NumberDraws AgoLast Drawn
26 1 2024-07-10
1 2 2024-07-08
21 3 2024-07-06
22 4 2024-07-03
9 5 2024-07-01

Periodicity of each number: The days since the last win

Consider:
What will be the next? Won't it be since it was periodicially appearing with interval 1 but it didn't for a while?

This is quite similar to the number of days since the last win, but this one is a bit more formal. Assuming that each number usually appears at regular interval, we can estimate how unlikely a ball's inapperance is as well as if now is the avg time for a number to appear.

More formally, we assume that each ball’s occurrence interval follows a Gaussian distribution (a bell curve). We then calculate the p-value of the time since the ball’s last appearance. If it's close to 0.0, a ball didn't win weirdly long time, e.g., as did. If the p-value is around 0.5, a number is supposed to be drawn now if it's appearing at the usual interval.

See the diagram to understand the meaning of the p-value:

White Balls

Bottom
Numberp-value
63 0.000
65 0.009
25 0.014
21 0.030
40 0.037
Near 0.5
Numberp-value
52 0.476
19 0.485
29 0.489
10 0.491
8 0.499

Powerball

Bottom
Numberp-value
11 0.003
20 0.010
18 0.016
13 0.024
3 0.130
Near 0.5
Numberp-value
23 0.430
24 0.492
5 0.506
6 0.510
19 0.556

Periodicity of all numbers: The days since the last win

This is similar to Periodicity of each number: The days since the last win, but this time we assume that all numbers share a single distribution in their average time between wins. After that, it's determined if a number isn't winning for a long time or if a number is supposed to be drawn now if it's appearing at the usual interval (of all numbers).

This diagram shows the case of using separate distributions for each number:

This shows the case of using a single distribution for all numbers:

White Balls

Bottom
Numberp-value
63 0.001
25 0.004
13 0.008
65 0.012
40 0.026
Near 0.5
Numberp-value
8 0.458
3 0.488
10 0.488
59 0.488
19 0.519

Powerball

Bottom
Numberp-value
20 0.004
13 0.014
11 0.018
18 0.065
17 0.075
Near 0.5
Numberp-value
6 0.504
19 0.520
5 0.536
4 0.551
24 0.567

Periodicity of each number: The very recent interval change

Consider:
What will be the next? We see winning interval shift of as it started appear frequently, i.e., became . To the contrary, took longer time to appear in the last wins.

As in the previous section, we assume that each number has a fixed interval between wins. From the distribution, we detect if the most recent winning interval of a number has shown any shift from the usual by computing the p-value.

If the last interval was shorter than usual, it has larger p-value, while longer interval has smaller.

White Balls

Top
Numberp-value
29 0.835
57 0.831
20 0.831
37 0.828
10 0.825
Bottom
Numberp-value
45 0.000
58 0.004
33 0.015
49 0.029
39 0.071

Powerball

Top
Numberp-value
1 0.855
3 0.843
22 0.817
21 0.793
12 0.793
Bottom
Numberp-value
11 0.036
4 0.037
24 0.039
7 0.078
14 0.256

Periodicity of all numbers: The very recent interval change

["This is similar to the previous very recent interval change, but this time we assume that all numbers share a single distribution in their average time until win. After that, p-value of the each number's last winning interval is calculated."]

White Balls

Top
Numberp-value
21 0.833
29 0.833
34 0.833
56 0.833
57 0.833
10 0.813
25 0.813
37 0.813
38 0.813
40 0.813
59 0.813
3 0.792
19 0.792
20 0.792
23 0.792
31 0.792
35 0.792
48 0.792
62 0.792
4 0.769
17 0.769
30 0.769
50 0.769
66 0.769
5 0.745
14 0.745
16 0.745
53 0.745
61 0.745
64 0.745
Bottom
Numberp-value
45 0.000
58 0.001
49 0.008
33 0.037
43 0.080

Powerball

Top
Numberp-value
1 0.829
12 0.829
21 0.829
3 0.809
22 0.787
6 0.751
2 0.726
13 0.726
Bottom
Numberp-value
7 0.065
11 0.087
15 0.107
24 0.130
4 0.157

Conditional Probability

Consider:
What will be the next? Conditional probability estimates how likely is an event given the previous. In the example, appeared 2 times after , while appeared 3 times. Thus, given the last , is more likely to appear.

More formally, we calculate conditional probabililty and then estimate prob(next|prev) where prev is the numbers that appeared in the last draw. To avoid overfit, we adopt add 1 smoothing.

White Balls

Top
NumberProb.
37 0.199
67 0.199
40 0.195
36 0.190
6 0.190

Powerball

Top
NumberProb.
4 0.073
9 0.042
17 0.042
1 0.031
2 0.031
3 0.031
5 0.031
7 0.031
12 0.031
13 0.031
18 0.031
22 0.031
24 0.031
6 0.021
8 0.021
10 0.021
11 0.021
14 0.021
15 0.021
16 0.021
19 0.021
20 0.021
23 0.021
26 0.021
21 0.010
25 0.010

Hidden Markov Model (HMM)

Consider:
What will be the next? Do you see 3 different probability patterns in it? Let's split the sequence into 3 parts of / / , and name first and the last as state A, and the middle as state B. State A has 50% probability of emiting and , while state B has 100% probability of .

Hidden Markov Model (HMM) assumes that the state of the system is hidden and only the output is observed. To apply it to the lottery, we need to 1) determine the # of state, 2) determine when a state starts and ends just given the winning numbers, and 3) estimate the probability of winning numbers in each state.

When using HMM, state corresponds to the lottery machine configuration and we're assuming that the machine is switching to different states over time.

Below is the output of HMM algorithm. It shows numbers and their winning probability (Prob.) from the predicted machine state.

White Balls

Top
NumberProb.
61 0.091
69 0.086
3 0.069
64 0.052
54 0.049

Powerball

Top
NumberProb.
26 0.094
14 0.078
2 0.069
15 0.068
1 0.068