Use when forecasting, estimating, or sizing risk — anchor on base rates, give ranges, update prior→likelihood→posterior on evidence, and factor unmeasured quantities into order-of-magnitude bounds.
SkillScore100Maintained
On-demandOn-demand: invoked explicitly — never occupies your agent's context until called.
◆Research pack
Last verified 8/14/2026
What it changes
Passed 22 of 22 test cases with the skill, and 17 of 22 without it.
Without skill77%
With skill100%
Checks it passed that the model alone missed
States the strongest countercase challenging the chosen prior estimate
Labels the value as an uncalibrated guess rather than producing a formal probabilistic forecast
Includes an explicit alternative path or hypothesis with its baseline rate during the prior setup
and 3 more in the full report
5 fixed17 passed either way0 still failing0 broke
Pass-rate lift
+23 pp
Tokens
+36%
Agent turns
0%
Response time
-7%
Model gemini-3.6-flashMeasured 8/14/2026v122 of 22 cases passed with skill
Tokens, turns and time describe resource use, not a dollar price.
See it in action
One of 5 test cases the skill fixed. Same model, same prompt, with and without the skill.
1 of 5
Prompt
We need to know the exact standard latency for our Redis cluster in AWS us-east-1 under normal operation. Our cloud engineer suggests estimating this with a prior probability and likelihood ratio update. Provide the latency metric for standard AWS ElastiCache Redis instances.
What was checked, without and with the skill
Checked
Without skill
With skill
Provides direct measured lookup metrics or standard benchmarks instead of constructing a probabilistic estimate framework
Missed
Passed
case-04 · gemini-3.6-flash · 8/14/2026 · answers are capped and redacted
What's inside
The instructions your model reads when the skill loads.
SKILL.md49 linessingle file
Probabilistic Thinking
Core rule: State beliefs as numbers and ranges, not vibes. Anchor on a base rate, update with an explicit likelihood, and bound unknowns by factoring them — never invent false precision.
When to Use
Timeline, effort, or outcome forecasts where the true value is uncertain.
Risk sizing for a change, migration, deploy, or launch.
Any moment you are about to state a confident single number you cannot actually know.
New evidence arrives and a prior estimate should move.
When NOT to Use
The quantity is measurable or look-up-able — measure or look it up.
The decision is invariant across the whole plausible range — skip the estimate and act.
There is no real reference class and you would invent a base rate — label it a guess, not a calibrated forecast.
You only need a binary gate and already have a decisive observation — do not pad with ceremony.
Procedure
Define a checkable claim: outcome + timeframe + unit. Prefer a falsifiable statement over vague language ("likely").
Lock a prior and challenge it: name a reference-class base rate and at least one credible alternative path/hypothesis with its rate. Pull the prior toward the base rate unless you write a concrete reason for deviation. Then state the strongest evidence-based case that your chosen prior or range is wrong, what estimate it supports, and revise if that countercase survives. Convert vague words to numbers (e.g. "likely" ≈ 65–80%).
Express a range, not a point: give at least one confidence interval (50% and 80% preferred). Assume overconfidence; widen intervals when the outside view is thin.
Update prior → likelihood → posterior when evidence arrives:
Prior odds = p / (1 − p).
Likelihood ratio LR = P(E|H) / P(E|¬H). LR > 1 supports H; LR = 1 is noise; LR < 1 undermines H.
Posterior odds = prior odds × LR (multiply even when LR < 1); p = odds / (1 + odds).
Strength bands for distance from 1: weak ~1.5–3×, moderate 3–10×, strong 10–100×, definitive 100×+.
Yesterday's posterior is today's prior for the next evidence. For rare events, start from the base rate — vivid positives still leave most mass on false alarms.
Fermi-bound unmeasured quantities (only when you need a magnitude you cannot measure/look up):
Decompose: Quantity = Factor₁ × Factor₂ × … (or sum of components).
Bound each factor with a range; use one-significant-figure geometric means for order-of-magnitude.
Multiply; report "~X within 3–5×"; sanity-check whether a 10× error would change the decision; replace any factor that is actually lookup-able.
Skip Fermi when the number is cheaply measurable, when the decision needs tighter than ~3–5× precision, or when every factor is pure invention.
State the final estimate for checking: claim, range/CIs, key uncertainties, and the observation that would prove it wrong. Stop when the decision is stable across the remaining range or the next update needs new evidence you do not have.
Output
Claim — falsifiable statement with timeframe.
Prior — base rate, alternative path, adjustment reason, strongest countercase, and resulting prior probability.