Overview
Russian roulette path termination chooses whether to continue a rendering path based on survival probability, and scales surviving paths so expected contribution remains unchanged.
CoreSource checked
Russian Roulette Path Termination
Randomly terminates low-contribution light paths while preserving an unbiased estimator.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Rendering
- Difficulty
- Intermediate
- Family
- Monte Carlo Rendering
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 3
- Code example
- Ready
- Visualization
- Ready
Core Concepts
unbiased estimatorsurvival probabilitypath throughputvariance tradeoff
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(path length)
Average
O(samples * expected path length)
Worst
O(samples * max depth)
Space
O(1)
When to Use
- Use in Monte Carlo path tracing when many long paths contribute very little.
- Use when unbiasedness matters and termination probability can be tied to throughput.
When Not to Use
- Avoid in deterministic preview renderers where random termination noise is unacceptable.
- Avoid when survival probabilities are so low that variance becomes excessive.
What It Does
- Randomly terminates low-contribution light paths while keeping the estimator unbiased
- Uses unbiased estimator and survival probability to guide the work.
- Produces rendered image.
Use Cases
- Real-time graphics
- Offline rendering
- Lighting and visibility effects
Inputs
- Scene geometry
- Materials
- Camera and lighting state
Outputs
- Rendered image
- Visibility or shading buffers
Key Formulas (1)
Survivor weight
throughput = throughput / psurvive
throughput = throughput / p_surviveCompensates surviving paths so the expected contribution remains unchanged.
Pseudocode
- 1.After a minimum depth, compute survival probability p
- 2.Draw a random number r in [0, 1)
- 3.If r >= p, terminate the path
- 4.Otherwise divide path throughput by p
- 5.Continue tracing the surviving path
Canonical Example
- Input
- path throughput 0.25 and survival probability 0.25
- Output
- terminate 75% of such paths; multiply survivors by 4
- Explanation
- The expected contribution remains 0.25 while fewer paths continue.
Implementation Notes
- Delay roulette until a minimum path depth.
- Choose survival probability from path throughput or luminance.
- Scale surviving contribution by 1 / probability.
Common Pitfalls
- Not dividing surviving throughput by survival probability biases the result dark.
- Terminating too early increases variance and can remove important indirect light.
- Probability must be clamped away from zero for numerical safety.
Interactive Mechanism Walkthrough
Spatial Primitive & Sweep-Line CanvasShow rays, samples, buffers, or shading terms that contribute to the final pixel.
Step 1 of 5: After a minimum depth, compute survival probability p
rendering-mechanismNotes
Russian roulette controls work, not noise directly; poor probabilities can increase variance.
Sources (1)
What each reference supports for this entry.
Physically Based Rendering
BookRendering reference for light transport, ray tracing, sampling, BRDFs, acceleration structures, and path termination.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageOften paired withImportance Sampling
Russian roulette and importance sampling are commonly combined to control Monte Carlo rendering cost and variance.
Used byPath Tracing
Path tracing uses Russian roulette to terminate paths without biasing estimates.
Related Algorithms
Tags
GraphicsPath TracingSamplingStochastic