What is a Markov chain?

A Markov chain is a mathematical model where the probability of a future state depends only on the current one. For lotteries, this means: the probability of number Y appearing in the next draw depends on which numbers appeared in the current draw.

How is the transition matrix built?

For each pair of consecutive draws, it counts which numbers from draw N+1 appeared after each number from draw N. These counts are normalized into probabilities (percentages).

Are transition probabilities accurate?

Probabilities are calculated based on historical data. The more draws in the archive, the more stable the estimates. For lotteries with short archives, probabilities may fluctuate significantly.

Can the next draw be predicted?

No, Markov chains show historical transition statistics but do not predict the future. Each lottery draw is an independent random event, and past results do not determine future ones.

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China: 双色球

双色球 Markov Chains — Transition Probabilities

双色球: which numbers most often follow certain ones? The transition matrix will show

Markov chains analyze which "双色球" lottery numbers most often follow others. For each number, a transition probability vector is built: "if number X was drawn in draw N, what is the probability that number Y will be drawn in draw N+1?"

Analysis based on 20 draws from 04/09/2026, 01:15 PM to 05/24/2026, 01:15 PM

Select a Number for Analysis

Click a number to see its "favorites" — numbers that most often appear in the next draw

Select a number above

Click a number to see its favorites

Transition Probability Heatmap

NxN matrix: rows — current numbers, columns — next numbers

Hide values below: 0%

→	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33
1	9	11	6	9	0	0	3	3	0	0	3	0	6	6	9	0	3	3	0	6	3	0	0	3	3	0	0	0	6	9	0	0	3
2	0	5	2	4	0	4	5	0	4	2	4	2	5	2	4	5	2	0	2	4	2	0	0	7	9	0	4	2	4	9	2	4	5
3	3	11	6	0	0	3	0	6	6	6	0	0	9	6	3	3	3	0	3	3	0	0	0	3	6	0	3	3	6	9	0	0	3
4	0	9	3	0	3	3	0	6	6	11	0	0	6	0	0	3	6	0	9	0	3	3	0	9	3	0	3	3	0	3	6	0	6
5	7	0	7	14	0	0	7	0	0	7	0	0	0	7	0	0	0	0	0	0	0	14	7	7	0	0	0	7	0	7	0	0	7
6	7	7	0	0	0	0	0	0	7	7	0	0	0	14	7	7	7	7	0	0	0	7	0	0	0	0	0	0	7	14	0	0	0
7	14	0	0	4	0	4	4	0	11	0	0	0	0	4	7	7	0	7	0	0	4	0	0	7	4	0	0	7	4	4	0	4	7
8	0	10	5	10	0	0	5	0	0	5	0	5	5	5	0	0	0	0	5	5	0	5	5	5	5	0	0	0	5	5	5	0	10
9	6	6	6	3	0	0	6	0	3	3	6	0	0	9	6	6	3	6	0	3	3	6	0	3	0	3	3	0	3	9	3	0	0
10	10	2	2	2	0	2	12	0	2	5	5	2	0	2	0	7	0	0	2	0	5	5	0	7	2	2	2	2	2	7	5	2	0
11	7	18	7	0	4	0	0	7	4	7	0	0	7	7	0	4	0	0	4	0	4	4	0	4	0	0	0	0	0	0	7	0	7
12	0	0	0	0	0	14	0	0	14	0	0	0	0	14	0	29	0	0	0	0	0	0	0	0	14	0	0	0	0	0	0	14	0
13	0	7	0	4	4	0	4	0	0	7	4	4	7	0	0	0	0	0	7	4	4	4	0	7	7	0	0	0	4	4	7	4	11
14	5	7	5	2	0	2	0	2	2	2	7	0	5	2	5	0	7	2	2	2	0	5	0	5	5	2	2	2	2	10	2	0	2
15	3	9	9	3	0	3	0	0	9	6	6	0	0	3	3	6	0	3	0	3	0	3	0	6	3	3	3	3	0	3	9	0	6
16	11	6	3	0	0	0	6	0	3	0	6	0	0	6	3	3	6	9	0	0	3	9	0	6	0	3	3	3	0	9	3	0	3
17	0	7	4	11	0	0	4	0	4	7	4	4	0	4	7	4	4	0	4	0	0	4	4	11	0	0	0	0	0	4	7	0	7
18	0	4	11	14	0	4	0	0	4	0	4	0	0	7	11	0	4	4	0	4	0	4	4	4	4	0	4	4	0	7	0	0	4
19	5	5	0	0	0	5	10	0	5	10	0	5	0	5	0	10	0	0	5	0	0	5	0	10	5	0	0	5	0	5	5	5	0
20	0	0	7	7	0	7	0	0	7	0	7	0	7	0	0	0	0	0	0	0	0	0	0	7	14	0	7	7	0	7	0	7	7
21	10	0	5	10	0	0	5	0	5	5	0	0	0	5	5	0	0	5	0	0	0	10	5	10	0	0	0	10	0	5	0	0	10
22	11	9	3	6	0	0	6	6	0	6	3	0	6	3	6	0	6	0	3	0	3	3	0	9	0	0	0	3	3	9	0	0	0
23	0	14	0	0	0	0	0	14	0	14	0	0	14	0	0	0	14	0	14	0	0	0	0	14	0	0	0	0	0	0	0	0	0
24	5	5	2	4	2	2	7	0	5	5	0	2	0	4	4	7	0	4	4	2	5	2	0	7	2	0	2	2	2	4	5	2	5
25	3	3	3	9	3	0	0	0	3	6	3	0	3	9	3	3	3	3	3	0	3	9	3	3	3	0	0	0	3	6	3	3	9
26	14	29	14	0	0	0	0	14	0	0	0	0	14	14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
27	7	0	0	0	0	0	0	0	14	7	0	0	0	7	14	7	0	7	0	0	0	0	0	7	0	0	0	7	7	7	0	0	7
28	10	5	5	10	0	0	5	0	5	5	0	0	0	10	10	5	0	5	0	5	5	0	0	0	0	0	0	0	10	10	0	0	0
29	7	0	7	7	0	0	0	0	0	0	21	0	7	0	0	0	0	0	0	0	0	7	0	7	7	7	0	0	0	0	7	7	7
30	7	2	4	9	0	0	2	0	5	4	7	0	2	4	7	4	2	2	0	0	2	4	2	7	2	2	0	2	4	5	4	2	7
31	7	7	4	0	0	4	11	4	4	4	0	0	4	7	0	11	0	0	0	0	4	4	0	7	4	0	4	4	0	7	0	4	0
32	7	7	0	0	7	0	0	0	0	7	0	0	0	7	0	0	7	7	7	0	7	14	0	0	0	0	0	0	0	7	7	0	7
33	2	5	2	5	2	0	7	2	0	7	2	0	5	2	2	2	2	2	5	2	5	5	0	10	2	0	2	2	0	5	2	2	5

Summary Table

For each number — its top favorite and probability

Added to generator 0 / 33

Selected 0

Ball added	Top favorite	Probability, %
Add	16	28.57
Add	2	28.57
Add	11	21.43
Add	2	17.86
Add	4	14.29
Add	14	14.29
Add	1	14.29
Add	4	14.29
Add	25	14.29
Add	2	14.29
Add	9	14.29
Add	22	14.29
Add	7	11.9
Add	2	11.43
Add	2	11.43
Add	10	11.43
Add	1	11.43
Add	1	11.43
Add	33	10.71
Add	4	10.71
Add	7	10.71
Add	2	9.52
Add	30	9.52
Add	7	9.52
Add	1	9.52
Add	1	9.52
Add	24	9.52
Add	25	8.93
Add	4	8.93
Add	14	8.57
Add	2	8.57
Add	4	8.57
Add	7	7.14

Generator by Markov Chains

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How to Use Markov Chains for 双色球

Step-by-step guide to analyzing transition probabilities for 双色球 lottery

Select a number for analysis

Click a number in the ball grid. For multi-drum lotteries, first select the desired field.

Study the favorites

You'll see the top numbers that most frequently appear after the selected one. The percentage shows the historical transition probability.

Analyze the heatmap

If the drum is small (up to 20 numbers), a heatmap is available — the full transition probability matrix. Bright cells indicate strong connections.

Use the summary table and generator

The table shows the top favorite for each number. Mark interesting numbers and generate combinations through the generator.

About Markov Chains

Mathematical foundations

A Markov chain is a stochastic model where the probability of transitioning to the next state depends only on the current state, not on previous ones. In the lottery context: if number X was drawn, what is the probability that number Y will be drawn next?

Transition Matrix

P[i,j] — the probability that number j follows number i. Built from all pairs of consecutive draws in the archive. Each row of the matrix sums to 100%.

Usage Tips

Recommendations for effective application of Markov chains

Use the latest draw results as input: select each drawn number and note its favorites.

The larger the draw archive, the more accurate the transition probabilities. For small samples, results may be unstable.

Markov chains work well in combination with frequency analysis — check favorites against overall draw frequency.

The heatmap is only available for drums with up to 20 numbers — for larger ranges, use the table.

Frequently Asked Questions about 双色球

Answers to common questions about Markov chains in lotteries for 双色球