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From thinking-frameworks-skills
Converts probabilities into betting decisions using edge calculation, Kelly Criterion sizing, forecast extremizing, and Brier score optimization. Activates when users discuss betting strategy, probabilities, or market odds.
How this skill is triggered — by the user, by Claude, or both
Slash command
/thinking-frameworks-skills:market-mechanics-bettingThe summary Claude sees in its skill listing — used to decide when to auto-load this skill
- [Interactive Menu](#interactive-menu)
What would you like to do?
1. Calculate Edge - Determine if you have an advantage 2. Optimize Bet Size (Kelly Criterion) - How much to bet 3. Extremize Aggregated Forecasts - Adjust crowd wisdom 4. Optimize Brier Score - Improve forecast scoring 5. Hedge and Portfolio Betting - Manage multiple bets 6. Learn the Framework - Deep dive into methodology 7. Exit - Return to main forecasting workflow
Determine if you have a betting advantage.
Edge Calculation Progress:
- [ ] Step 1: Identify market probability
- [ ] Step 2: State your probability
- [ ] Step 3: Calculate edge
- [ ] Step 4: Apply minimum threshold
- [ ] Step 5: Make bet/pass decision
Sources: Prediction markets (Polymarket, Kalshi), betting odds, consensus forecasts, base rates
Converting betting odds to probability:
Decimal odds: Probability = 1 / Odds
American (+150): Probability = 100 / (150 + 100) = 40%
American (-150): Probability = 150 / (150 + 100) = 60%
Fractional (3/1): Probability = 1 / (3 + 1) = 25%
After running your forecasting process, state: Your probability: ___%
Edge = Your Probability - Market Probability
Interpretation:
Minimum Edge Thresholds:
| Context | Minimum Edge | Reasoning |
|---|---|---|
| Prediction markets | 5-10% | Fees ~2-5%, need buffer |
| Sports betting | 3-5% | Efficient markets |
| Private bets | 2-3% | Only model uncertainty |
| High conviction | 8-15% | Substantial edge needed |
If Edge > Minimum Threshold → Calculate bet size (Kelly)
If 0 < Edge < Minimum → Pass (edge too small)
If Edge < 0 → Consider opposite bet or pass
Next: Return to menu or continue to Kelly sizing
Calculate optimal bet size to maximize long-term growth.
Kelly Criterion Progress:
- [ ] Step 1: Understand Kelly formula
- [ ] Step 2: Calculate full Kelly
- [ ] Step 3: Apply fractional Kelly
- [ ] Step 4: Consider bankroll constraints
- [ ] Step 5: Execute bet
f* = (bp - q) / b
Where:
f* = Fraction of bankroll to bet
b = Net odds received (decimal odds - 1)
p = Your probability of winning
q = Your probability of losing (1 - p)
Maximizes expected logarithm of wealth (long-term growth rate).
Example:
f* = (0.67 × 0.70 - 0.30) / 0.67 = 0.252 = 25.2%
Full Kelly says: Bet 25.2% of bankroll
Problem with full Kelly: High variance, model error sensitivity, psychological difficulty
Solution: Fractional Kelly
Actual bet = f* × Fraction
Common fractions:
- 1/2 Kelly: f* / 2
- 1/3 Kelly: f* / 3
- 1/4 Kelly: f* / 4
Recommendation: Use 1/4 to 1/2 Kelly for most bets.
Why: Reduces variance by 50-75%, still captures most growth, more robust to model error.
Practical considerations:
Final check:
Place bet.
Next: Return to menu
Adjust crowd wisdom when aggregating multiple predictions.
Extremizing Progress:
- [ ] Step 1: Understand why extremizing works
- [ ] Step 2: Collect individual forecasts
- [ ] Step 3: Calculate simple average
- [ ] Step 4: Apply extremizing formula
- [ ] Step 5: Validate and finalize
The Problem: When you average forecasts, you get regression to 50%.
The Research: Good Judgment Project found aggregated forecasts are more accurate than individuals BUT systematically too moderate. Extremizing (pushing away from 50%) improves accuracy because multiple forecasters share common information, and simple averaging "overcounts" shared information.
Gather predictions from multiple sources. Ensure forecasts are independent, forecasters used good process, and have similar information available.
Average = Sum of forecasts / Number of forecasts
Extremized = 50% + (Average - 50%) × Factor
Where Factor typically ranges from 1.2 to 1.5
Example:
Extremized = 50% + (77.6% - 50%) × 1.3 = 85.88% ≈ 86%
Choosing the Factor:
| Situation | Factor | Reasoning |
|---|---|---|
| Forecasters highly correlated | 1.1-1.2 | Weak extremizing |
| Moderately independent | 1.3-1.4 | Moderate extremizing |
| Very independent | 1.5+ | Strong extremizing |
| High expertise | 1.4-1.6 | Trust the signal |
Default: Use 1.3 if unsure.
Sanity checks:
Next: Return to menu
Improve forecast accuracy scoring.
Brier Score Optimization Progress:
- [ ] Step 1: Understand Brier score formula
- [ ] Step 2: Calculate your Brier score
- [ ] Step 3: Decompose into calibration and resolution
- [ ] Step 4: Identify improvement strategies
- [ ] Step 5: Avoid gaming the metric
Brier Score = (1/N) × Σ(Probability - Outcome)²
Where:
- Probability = Your forecast (0 to 1)
- Outcome = Actual result (0 or 1)
- N = Number of forecasts
Range: 0 (perfect) to 1 (worst). Lower is better.
Interpretation:
| Brier Score | Quality |
|---|---|
| < 0.10 | Excellent |
| 0.10 - 0.15 | Good |
| 0.15 - 0.20 | Average |
| 0.20 - 0.25 | Below average |
| > 0.25 | Poor |
Baseline: Random guessing (always 50%) gives Brier = 0.25
Brier Score = Calibration Error + Resolution + Uncertainty
Calibration Error: Do your 70% predictions happen 70% of the time? (measures bias) Resolution: How often do you assign different probabilities to different outcomes? (measures discrimination)
Strategy 1: Fix Calibration
Strategy 2: Improve Resolution
Strategy 3: Gather Better Information
Wrong approach: "Never predict below 10% or above 90%" (gaming)
Right approach: Predict your TRUE belief. If that's 5%, say 5%. Accept that you'll occasionally get large Brier penalties. Over many forecasts, honesty wins.
The rule: Minimize Brier score by being accurate, not by being safe.
Next: Return to menu
Manage multiple bets and correlations.
Portfolio Betting Progress:
- [ ] Step 1: Identify correlations between bets
- [ ] Step 2: Calculate portfolio Kelly
- [ ] Step 3: Assess hedging opportunities
- [ ] Step 4: Optimize across all positions
- [ ] Step 5: Monitor and rebalance
The problem: If bets are correlated, true exposure is higher than sum of individual bets.
Correlation examples:
Simplified heuristic:
When to hedge:
Hedging example:
View portfolio holistically. Reduce correlated bets, maintain independence where possible.
Weekly review: Check if probabilities changed, assess hedging opportunities, rebalance if needed After major news: Update probabilities, consider hedging, recalculate Kelly sizes Monthly audit: Portfolio correlation check, bankroll adjustment, performance review
Next: Return to menu
Deep dive into the methodology.
📄 Scoring Rules and Calibration
Next: Return to menu
Convert beliefs into optimal decisions using edge calculation, Kelly sizing, extremizing, and proper scoring.
bayesian-reasoning-calibration for probability updates📁 resources/
Ready to start? Choose a number from the menu above.
npx claudepluginhub lyndonkl/claude --plugin thinking-frameworks-skillsDetermines optimal capital allocation to portfolio positions using Kelly criterion, fractional Kelly, risk budgeting, liquidity sizing, and conviction weighting. For position sizing and bet size queries.
Routes probabilistic thinking to the right skill: base-rate anchoring, confidence calibration, expected value, or scenario weighting. Activates on queries about probability, likelihood, and uncertainty.
Expresses forecasts, estimates, and risks as probability ranges with base-rate anchoring and explicit updates when new evidence arrives.