Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add deciqAI/knowledge-skills --skill expected-value-and-kellygit clone --depth 1 https://github.com/deciqAI/knowledge-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/deciqai/knowledge-skills/expected-value-and-kelly)<a href="https://agentmods.dev/skills/deciqai/knowledge-skills/expected-value-and-kelly"><img src="https://agentmods.dev/badge/skills/deciqai/knowledge-skills/expected-value-and-kelly/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/deciqai/knowledge-skills/expected-value-and-kelly"><img src="https://agentmods.dev/badge/skills/deciqai/knowledge-skills/expected-value-and-kelly.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- NVIDIA SkillSpector pass
What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00132 | $0.02543 |
| Opus 5 | $0.00066 | $0.01272 |
| Sonnet 5 | $0.00026 | $0.00509 |
| Haiku 4.5 | $0.00013 | $0.00254 |
Grade A, and why
expected-value-and-kelly scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 7d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 124 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Expected Value and the Kelly Criterion
Overview
Two questions decide most repeated bets: is this bet good? (EV) and how big? (Kelly). Most professional ruin comes from positive-EV bets sized wrong. EV = p · W − q · L. If EV ≤ 0, do not bet. Kelly f* = (bp − q) / b maximizes long-term geometric growth (Kelly, Bell Labs, 1956). Full Kelly requires casino-grade certainty; default to half- or quarter-Kelly for estimated edges.
Neighbors: first-principles · occams-razor · second-order-thinking · inversion · regret-minimization (for non-repeating life decisions).
When to Use
- Decision repeats many times — capital allocation, position sizing, VC portfolio, ad spend, A/B test budget
- How big to bet matters as much as whether to bet; you have a measurable or estimable edge
- Someone says: "expected value," "EV," "Kelly," "optimal bet size," "how much should we put on this?"
- Sizing bets in a boom with power-law payoffs and possible ruin — how much to allocate to AI startups / GPU-compute capex / AI-exposed equities given frothy AI valuations, uncertain AI adoption, and correlated bets
When NOT to use: one-shot life decisions → regret-minimization; negative-EV bets (don't bet); unestimable probabilities; correlated bets without portfolio adjustment.
Coaching Novices (Adaptive Front Door)
Engine mode: user has a concrete repeated bet → run The Process directly. Coach mode: user is unfamiliar → guide step by step.
In Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.
- One-line what-it-is: EV tells you whether the bet is worth taking; Kelly tells you what fraction of bankroll to stake — sized to maximize long-term growth without ruin.
- Check fit against When to Use / When NOT to use. If one-shot life decision, redirect to regret-minimization. If EV is negative, say "don't bet" and stop.
- Elicit their real bet. Ask for a concrete repeated decision with measurable inputs. > [WAIT — do not advance until user responds]
- Walk The Process one step per turn: outcomes → probabilities → payoffs → EV → Kelly → fractional Kelly. > [WAIT — do not advance until user responds]
- Close by naming their sizing rule: "bet f* × bankroll, use half-Kelly given estimation uncertainty" — and the trigger that would change it. > [WAIT — do not advance until user responds]
What ships with it
4 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 7d ago First seen · 124 lines · 132 tokens per session scan A 46dce06f6fd9
expected-value-and-kelly is a skill published in the GitHub repository deciqAI/knowledge-skills (10 stars, last pushed 9d ago), licensed MIT. It adds 132 tokens to every session and 2,543 once invoked, about $0.0007 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-03.
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