Markov Chain Monte Carlo MCMC Analysis (BETA)
MCMC Lottery Prediction
Loading…
What Is MCMC?
MCMC stands for Markov Chain Monte Carlo, a powerful simulation method used in data science to explore probabilities of future outcomes. It works by walking through possible states (lottery numbers), updating beliefs based on historical transitions. This technique is widely used in fields like machine learning, Bayesian statistics, and financial modeling. Here, it helps predict numbers with the highest likelihood based on draw history and weighted patterns.
Advanced Settings Explained
This section allows you to fine-tune the behavior of the MCMC algorithm. Even if you're not familiar with MCMC, don’t worry — we’ll walk you through each setting with simple explanations.
Understanding MCMC Settings
Each of the five settings below controls how the Markov Chain Monte Carlo algorithm explores past lottery draws and produces predictions. Adjusting them changes both the speed of computation and the stability (variance vs. bias) of results. Use the “Fast” configuration for quick tests, and the “Thorough” configuration when you need the most reliable output.
1. Simulations (Number of MCMC Walks)
Range: 100 to 20 000
Effect: Number of independent random walks.
More walks → more samples → lower variance in the final visit‐frequency estimates, but slower runtime.
Fewer walks → very fast but unstable/noisy results.
2. Burn-In (Discard Initial Steps)
Range: 0 to 500
Effect: Number of steps at the start of each walk that are ignored.
A larger burn-in ensures the chain has “mixed” and reached its steady state before counting visits.
A small burn-in (even 0) keeps all early transient steps, which can bias results if the chain has not stabilized.
3. Laplace K (Smoothing Constant)
Range: 0.1 (or 0) to 10 (or higher if you type it manually)
Effect: Adds a small constant to every possible transition count to avoid zero‐probability edges.
A higher K → heavier smoothing → prevents impossible transitions but can flatten real differences.
A smaller K → minimal smoothing → “spikier” transition probabilities.
4. Recency Decay (Weight Recent Draws)
Range: 0.001 to 1.0
Effect: Controls how much more influence the newest draws have compared to older draws.
A higher decay value (closer to 1.0) → very heavy weighting on the most recent draw steps → older history quickly becomes negligible.
A lower decay (0.001–0.01) → relatively uniform weighting → all historical draws more evenly influence transition probabilities.
5. Chain Length (Steps per Walk)
Range: 100 to 5 000
Effect: Number of transitions each walk makes after burn-in.
A longer chain → deeper exploration of the state graph → better steady‐state approximation but slower per-walk cost.
A shorter chain → faster but may not fully explore all transitions in each walk.
Quick Comparison Table
| Setting | Minimum (Fast) | Maximum (Thorough) | Impact |
|---|---|---|---|
| Simulations (Walks) | 100 (very fast, unstable) | 20 000 (very slow, stable) | Controls sampling variance – more walks = smoother results. |
| Burn-In | 0 (use all early steps) | 500 (discard more transient) | Ensures chain is in steady-state before counting. |
| Laplace K | 0.1 (minimal smoothing) | 10 (heavy smoothing) | Prevents zero-count transitions; higher K flattens differences. |
| Recency Decay | 0.001 (almost uniform weight) | 1.0 (max weight on newest) | Biases towards recent draws; higher values emphasize latest data. |
| Chain Length | 100 (very short walk) | 5 000 (very long walk) | Depth of exploration per walk; longer = better mixing but costlier. |
Tip: If you want a quick preview of how these choices affect results, start with
Walks = 500, Burn-In = 50, K = 1.0, Decay = 0.005, Chain Length = 1 000.
That combination usually balances speed vs. stability quite well.
Simulations (Number of MCMC Walks)
This tells the system how many different “random paths” to simulate using your lottery history. More paths = more stable predictions, but more work.
Burn-In (Discard Initial Steps)
Removes the first few steps so we only use the more stable part of each walk.
Laplace K (Smoothing Constant)
Gives every possible transition a small base count to avoid zero‐probability issues.
Recency Decay (Weight Recent Draws More)
Controls how much more influence newer draws have versus older ones.
Chain Length (Steps per Walk)
How many transitions to make in each random walk. More steps = deeper exploration, but slower.
⚙️ Optimizer (Exhaustive Grid Search)
Grid Search Optimizer (Experimental)
Try every combination of settings in the ranges below to find the best-performing configuration based on historical draw results.
Note: This optimizer does a true brute-force MCMC over every combination in your specified ranges. Depending on how wide those ranges are, it can take anywhere from a few minutes up to several days to finish. Because it’s such an exhaustive search, you only need to run it once to discover the “best” settings, then save those as your favorite (feature coming soon). It’s not intended to be re-run on every analysis—use it sparingly, then reuse its result.
Live Leaderboard (Top 5 Combos)
Score Heatmap (ChainLen vs Decay at K=2,B=50)
How to Read This Heatmap:
- Dark red = Highest matches (best combination)
- Dark blue = Lowest matches (worst combination)
- Grey = No data (not tested for that combo)
Each square represents a combination of Chain Length (Y-axis) and Recency Decay (X-axis) tested during optimization. The redder the cell, the higher the total number of historical “matches” that run would have produced.
Progress Log
Run Prediction
Use the settings above to run a full MCMC simulation and generate predicted numbers based on statistical transition behavior from historical draws.
0%