Probability Director Lab

Probability Director Lab is the Editor-facing environment for exact event probability, Probability Bias, Bernoulli/Binomial analysis, isolated Monte Carlo, RNG Health, and isolated Lab sampling.

For exact probability concepts and Runtime/API behavior, see Probability.md.

1. Purpose

Use Probability Director Lab to answer questions such as:

What is the exact Base probability?
What does Probability Bias change it to?
What is the exact Bernoulli or Binomial distribution?
How do Monte Carlo results compare with theory?
What is the isolated Lab stream actually producing?
Is a Binomial success-count experiment behaving as configured?
How large is the observed sampling error?
Do simple RNG Health metrics show unexpected behavior?

2. Core Authoring

The approved Probability Director Lab input order is:

Numerator.
Denominator.
Binomial Trial Count.
Binomial K.
Probability Bias (%).

The Lab keeps exact probability authoring separate from empirical sampling.

3. Base Probability

Numerator/Denominator define the exact Base probability.

Example:

Numerator = 1
Denominator = 4

means:

Base Probability = 1/4 = 25%

The exact ratio remains authoritative.

4. Probability Bias in the Lab

Probability Director Lab exposes one symmetric signed:

Probability Bias (%)

field.

Normal authoring range:

-99.999% ... +99.999%

Semantics:

Positive chooses the positive Bias direction.
Negative chooses the negative direction.
Zero is Neutral.

Up to four decimal places are converted through the exact authoring path.

5. Runtime Endpoint vs. Lab Range

The native/Blueprint probability authority supports exact:

±100%

deterministic endpoints.

Probability Director Lab intentionally keeps ordinary tuning at:

±99.999%

Exact certainty/impossibility endpoints remain API capabilities outside normal Lab probabilistic authoring.

6. Base and Configured

At zero Bias:

Blue Base is shown.
No identical Green duplicate is required.

At nonzero Bias:

Blue = Base.
Green = Configured / Probability Bias.

This isolates the effect of Bias.

7. Bernoulli Analysis

Bernoulli represents one success/failure event.

The theoretical outcomes are:

Failure
Success

One actual Runtime Sample Outcome represents one complete Bernoulli event.

8. Binomial Analysis

For:

Trial Count = N

the exact outcome support is:

0 ... N successes

The selected K can be used for exact Binomial probability questions where applicable.

One actual Runtime Sample Outcome is one complete N-trial success-count observation.

It is not one Bernoulli trial.

9. Evaluate

Evaluate computes the current exact theoretical result.

No Runtime Context is required.

Evaluation establishes the valid current:

Base probability/distribution.
Configured Bias distribution.
Exact chart.
Result summary.
Export snapshot.

Lab sampling and Monte Carlo must correspond to that current configuration.

10. Monte Carlo

Probability Director Lab supports isolated Monte Carlo.

The simulation owns a temporary standalone Probability Director context/Stream.

It does not advance the isolated Lab stream.

Random modes:

Fixed Seed.
Secure.

Keyed Monte Carlo is intentionally not a V1 mode.

11. Monte Carlo Trial Bounds

Trial Count:

1 ... 10,000,000

Common presets:

1K.
10K.
100K.
1M.

Runs are chunked and cancellable.

Canceled runs report requested/completed work rather than pretending the requested experiment completed.

12. RNG Health

Probability Director Lab Monte Carlo can show RNG Health diagnostics such as:

Sample Count.
Maximum absolute probability error.
Mean absolute probability error.
Chi-square statistic.
Degrees of freedom.
P-value.
Lag-1 correlation.
Lag-2 correlation.
Lag-3 correlation.
Lag-4 correlation.

These metrics compare observed samples with expected behavior and test simple serial dependence.

They are not proof of perfect or cryptographically secure randomness.

13. Sample Outcome

Sample Outcome executes one experiment against the Lab-owned isolated Sequential stream. It does not use the selected gameplay Probability subsystem or a live registered stream.

For Bernoulli, one action produces one Success/Failure observation. For Binomial, one action produces a complete N-trial success count and contributes one aggregate observation. Evaluation is refreshed before sampling so invalid or stale authored configuration is rejected.

14. Lab Sample Scope

The Lab has no gameplay Runtime Context or live stream selector. Its sample accumulator is local presentation data; clearing it does not clear diagnostics or reset any gameplay stream. A fresh Lab session starts its own ephemeral experiment stream.

15. Isolated Sequential Sampling

Sample Outcome and continuous Lab sampling use the Lab-owned isolated Sequential engine. Repeated Lab samples advance only this experiment engine. They cannot alter future gameplay outcomes or retained gameplay diagnostics.

16. Keyed Operations

The Lab does not execute live Keyed Probability operations. For a deliberate operation against a live Keyed stream, use Probability Director Runtime Controls and review the live-probe warning. Keyed calls do not advance the Sequential cursor, though they execute through the live subsystem and may be recorded in its diagnostics.

17. Continuous Lab Sampling

The Lab can sample at 1–100 samples per second (default 10). Start Continuous and Stop control only the isolated Lab experiment stream. Sampling is scheduled without blocking the Editor. It is independent of the Live Stream Probe gate in Runtime Controls.

23. Binomial Runtime Aggregation

For Binomial, Red outcome buckets are:

0 ... N successes

One Lab sample increments exactly one bucket.

With a stable configuration and enough observations, Red empirical behavior should trend toward the configured theoretical distribution.

24. Runtime Hover Semantics

For a Red Binomial outcome, the hover presentation can identify:

Lab Samples.
Sample Outcome Result.
K successes.
Observed percentage.
Count / Lab sample total.
Configured probability for that success-count outcome.

This keeps the observed result distinct from theoretical Green probability.

25. Chart Colors

Color	Meaning
Blue	Base
Green	Configured / Probability Bias
Orange	Monte Carlo / Empirical
Red	Lab Samples

Where all are present:

Blue -> Green -> Orange -> Red

26. Semantic Chart Titles

Title priority:

Red Lab Samples.
Orange Monte Carlo when no Red exists.
Exact current online.
Exact current offline.

Approved titles:

Runtime:

Probability Analysis - <StreamId>

Monte Carlo:

Monte Carlo Theoretical vs Empirical Distribution - Probability Director Lab

Exact online:

Probability Analysis

Exact offline:

Probability Analysis - Offline

PIE/GameInstance/map identifiers are not placed in the visible title.

27. Orange and Red Coexistence

A completed same-configuration Monte Carlo result can remain visible while actual Lab sampling begins.

Interpretation:

Orange = isolated simulator
Red = isolated Lab stream

If the authored probability configuration changes, both empirical projections are invalidated.

28. Configuration Invalidation

Changing a meaningful authored Probability field:

Stops Continuous.
Clears stale exact chart.
Clears stale Orange Monte Carlo.
Clears stale Red Runtime aggregate.
Clears last sample.
Clears old export snapshot.
Restores the Lab Guide/result-empty presentation.

No Runtime result should be plotted against older theory.

29. Runtime Context / Stream Changes

Changing Runtime Context or Registered Stream resets the Lab’s Runtime presentation session.

It clears stream-specific:

Red samples.
Last result.
Old chart/export session state.

It does not reset or rewind the gameplay Stream itself.

30. Active Job Exclusion

Active Monte Carlo and active Runtime Continuous sampling are mutually exclusive.

The Lab should not run both jobs simultaneously through one UI session.

This keeps progress/cancellation/state semantics clear.

31. Exports

Probability Director Lab supports:

CSV.
Markdown.
PNG.
SVG.
Report bundle.

Runtime aggregate export uses:

ProbabilityLab-RuntimeSamples.csv

The export is aggregate-focused.

It does not emit an unbounded chronological sample log.

32. Export Security

Secure Monte Carlo/Runtime projections do not expose:

Secure root.
Entropy bytes.
Generator key.
Nonce.
Raw generator state.
Byte position.

Fixed Monte Carlo may intentionally include its authored Fixed Seed.

33. Failure Handling

Common visible failures include:

Invalid numerator/denominator.
Invalid exact probability.
Invalid Binomial Trial Count.
Invalid Binomial K.
Invalid Bias input.
Missing Runtime Context.
Missing Registered Stream.
Decision-mode mismatch.
Invalid Decision Key.
Monte Carlo Trial Count out of bounds.
Numerical/sampling failure.

A failed automatic Evaluate prevents Lab sampling against invalid/stale theory.

34. Recommended Workflows

Analyze one probability

Set Numerator / Denominator
-> Evaluate
-> inspect exact Base

Tune Probability Bias

Evaluate Base
-> set Probability Bias
-> Evaluate
-> compare Blue vs Green

Validate empirically

Evaluate
-> choose Fixed or Secure
-> Run Monte Carlo
-> compare Orange
-> inspect RNG Health

Inspect isolated Lab stream

Start PIE
-> select Runtime Context
-> select Registered Stream
-> Sample Outcome / Start Continuous
-> inspect Red

Check a Keyed decision

Select Keyed Stream
-> author/select Decision Key
-> set Occurrence Index
-> Sample Outcome
-> repeat or change occurrence intentionally

35. Common Mistakes

Treating one Binomial sample as one Bernoulli trial

One Binomial Sample Outcome is one complete N-trial success count.

Orange means gameplay output

Orange is isolated Monte Carlo.

Red means Monte Carlo

Red is actual isolated Lab stream sampling.

Lab should author exact ±100% Bias

The Runtime/API supports it; normal Lab authoring intentionally uses ±99.999%.

Clear Lab Samples resets the Stream

It clears only the Lab aggregate.

Keyed Continuous owns a hidden counter

No. Occurrence behavior is explicit.

36. Quick Reference

Evaluate
    = exact theory

Probability Bias
    = Base -> Configured

Monte Carlo
    = isolated repeated experiment

Sample Outcome
    = one isolated Lab stream operation

Bernoulli Sample Outcome
    = one yes/no observation

Binomial Sample Outcome
    = one complete N-trial success count

Blue
    = Base

Green
    = Configured

Orange
    = Monte Carlo

Red
    = Lab Samples