华东15选5 Markov Chains — Transition Probabilities
Markov chains analyze which "华东15选5" 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?"
Select a Number for Analysis
Transition Probability Heatmap
| → | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 15 | 10 | 10 | 0 | 5 | 0 | 5 | 0 | 5 | 10 | 10 | 10 | 10 | 10 |
| 2 | 3 | 13 | 5 | 13 | 5 | 5 | 0 | 10 | 5 | 8 | 5 | 3 | 10 | 5 | 13 |
| 3 | 0 | 3 | 3 | 11 | 9 | 9 | 3 | 6 | 6 | 9 | 11 | 6 | 14 | 3 | 9 |
| 4 | 3 | 5 | 5 | 10 | 3 | 15 | 5 | 8 | 8 | 8 | 10 | 5 | 5 | 3 | 10 |
| 5 | 5 | 10 | 0 | 5 | 5 | 15 | 0 | 10 | 0 | 10 | 5 | 10 | 15 | 5 | 5 |
| 6 | 0 | 11 | 9 | 9 | 6 | 9 | 0 | 3 | 6 | 11 | 6 | 0 | 11 | 11 | 9 |
| 7 | 0 | 7 | 7 | 0 | 7 | 13 | 7 | 0 | 7 | 13 | 13 | 7 | 13 | 7 | 0 |
| 8 | 6 | 9 | 3 | 11 | 3 | 6 | 3 | 9 | 0 | 9 | 9 | 6 | 14 | 6 | 9 |
| 9 | 0 | 5 | 5 | 10 | 10 | 15 | 0 | 5 | 5 | 15 | 5 | 0 | 15 | 10 | 0 |
| 10 | 7 | 4 | 9 | 7 | 9 | 7 | 4 | 7 | 4 | 7 | 9 | 9 | 11 | 0 | 7 |
| 11 | 3 | 10 | 7 | 0 | 3 | 10 | 3 | 7 | 7 | 13 | 7 | 7 | 10 | 10 | 3 |
| 12 | 4 | 12 | 4 | 12 | 4 | 0 | 0 | 8 | 0 | 8 | 4 | 4 | 16 | 12 | 12 |
| 13 | 6 | 10 | 10 | 8 | 4 | 6 | 2 | 10 | 2 | 6 | 6 | 10 | 8 | 2 | 10 |
| 14 | 4 | 12 | 8 | 12 | 8 | 12 | 0 | 8 | 8 | 0 | 8 | 4 | 4 | 0 | 12 |
| 15 | 3 | 5 | 8 | 18 | 5 | 8 | 3 | 10 | 5 | 10 | 5 | 0 | 8 | 5 | 10 |
Summary Table
| Ball added | Ball | Top favorite | Probability, % |
|---|---|---|---|
Add | 4 | 17.5 | |
Add | 13 | 16 | |
Add | 2 | 15 | |
Add | 6 | 15 | |
Add | 6 | 15 | |
Add | 6 | 15 | |
Add | 13 | 14.29 | |
Add | 13 | 14.29 | |
Add | 6 | 13.33 | |
Add | 10 | 13.33 | |
Add | 2 | 12.5 | |
Add | 2 | 12 | |
Add | 2 | 11.43 | |
Add | 13 | 11.11 | |
Add | 2 | 10 |
Generator by Markov Chains
How to Use Markov Chains for 华东15选5
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
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%.