| name | market-mechanics-betting |
| description | Translates beliefs (probabilities) into optimal actions (bet/pass/hedge) using quantitative frameworks including edge calculation, Kelly Criterion bet sizing, forecast extremizing, and Brier score optimization. Use when converting probabilities into decisions, calculating edge against market odds, sizing bets optimally, extremizing aggregated forecasts, improving Brier scores, or when user mentions betting strategy, Kelly Criterion, edge calculation, Brier score, extremizing, or translating belief into action. |
Market Mechanics & Betting
Table of Contents
Interactive Menu
What would you like to do?
Core Workflows
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
1. Calculate Edge
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
Step 1: Identify market probability
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%
Step 2: State your probability
After running your forecasting process, state: Your probability: ___%
Step 3: Calculate edge
Edge = Your Probability - Market Probability
Interpretation:
- Positive edge: More bullish than market → Consider betting YES
- Negative edge: More bearish than market → Consider betting NO
- Zero edge: Agree with market → Pass
Step 4: Apply minimum threshold
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 |
Step 5: Make bet/pass decision
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
2. Optimize Bet Size (Kelly Criterion)
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
Step 1: Understand Kelly formula
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).
Step 2: Calculate full Kelly
Example:
- Your probability: 70% win
- Market odds: 1.67 (decimal) → Net odds (b): 0.67
- p = 0.70, q = 0.30
f* = (0.67 × 0.70 - 0.30) / 0.67 = 0.252 = 25.2%
Full Kelly says: Bet 25.2% of bankroll
Step 3: Apply fractional Kelly
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.
Step 4: Consider bankroll constraints
Practical considerations:
- Define dedicated betting bankroll (money you can afford to lose)
- Minimum bet size (market minimums)
- Maximum bet size (market/liquidity limits)
- Round to practical amounts
Step 5: Execute bet
Final check:
Place bet.
Next: Return to menu
3. Extremize Aggregated Forecasts
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
Step 1: Understand why extremizing works
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.
Step 2: Collect individual forecasts
Gather predictions from multiple sources. Ensure forecasts are independent, forecasters used good process, and have similar information available.
Step 3: Calculate simple average
Average = Sum of forecasts / Number of forecasts
Step 4: Apply extremizing formula
Extremized = 50% + (Average - 50%) × Factor
Where Factor typically ranges from 1.2 to 1.5
Example:
- Average: 77.6%
- Factor: 1.3
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.
Step 5: Validate and finalize
Sanity checks:
- Bounded [0%, 100%]: Cap at 99%/1% if needed
- Reasonableness: Does result "feel" right?
- Compare to best individual: Extremized should be close to best forecaster
Next: Return to menu
4. Optimize Brier Score
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
Step 1: Understand Brier score formula
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.
Step 2: Calculate your Brier score
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
Step 3: Decompose into calibration and resolution
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)
Step 4: Identify improvement strategies
Strategy 1: Fix Calibration
- If overconfident: Widen confidence intervals, be less extreme
- If underconfident: Be more extreme when you have strong evidence
- Tool: Calibration plot (X: predicted probability, Y: actual frequency)
Strategy 2: Improve Resolution
- Avoid being stuck at 50%
- Differentiate between easy and hard forecasts
- Be bold when evidence is strong
Strategy 3: Gather Better Information
- Do more research, use reference classes, decompose with Fermi, update with Bayes
Step 5: Avoid gaming the metric
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
5. Hedge and Portfolio Betting
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
Step 1: Identify correlations between bets
The problem: If bets are correlated, true exposure is higher than sum of individual bets.
Correlation examples:
- Positive: "Democrats win House" + "Democrats win Senate"
- Negative: "Team A wins" + "Team B wins" (playing each other)
- Uncorrelated: "Rain tomorrow" + "Bitcoin price doubles"
Step 2: Calculate portfolio Kelly
Simplified heuristic:
- If correlation > 0.5: Reduce each bet size by 30-50%
- If correlation < -0.5: Can increase total exposure slightly (partial hedge)
Step 3: Assess hedging opportunities
When to hedge:
- Probability changed: Lock in profit when beliefs shift
- Lock in profit: Event moved in your favor, odds improved
- Reduce exposure: Too much capital on one outcome
Hedging example:
- Bet $100 on A at 60% (1.67 odds) → Payout: $167
- Odds change: A now 70%, B now 30% (3.33 odds)
- Hedge: Bet $50 on B at 3.33 → Payout if B wins: $167
- Result: Guaranteed $17 profit regardless of outcome
Step 4: Optimize across all positions
View portfolio holistically. Reduce correlated bets, maintain independence where possible.
Step 5: Monitor and rebalance
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
6. Learn the Framework
Deep dive into the methodology.
Resource Files
📄 Betting Theory Fundamentals
- Expected value framework, variance and risk, bankroll management, market efficiency
📄 Kelly Criterion Deep Dive
- Mathematical derivation, proof of optimality, extensions and variations, common mistakes
📄 Scoring Rules and Calibration
- Brier score deep dive, log score, calibration curves, resolution analysis, proper scoring rules
Next: Return to menu
Quick Reference
The Market Mechanics Commandments
- Edge > Threshold - Don't bet small edges (5%+ minimum)
- Use Fractional Kelly - Never full Kelly (use 1/4 to 1/2)
- Extremize aggregates - Push away from 50% when combining forecasts
- Minimize Brier honestly - Be accurate, not safe
- Watch correlations - Portfolio risk > sum of individual risks
- Hedge strategically - When probabilities change or lock profit
- Track calibration - Your 70% should happen 70% of the time
One-Sentence Summary
Convert beliefs into optimal decisions using edge calculation, Kelly sizing, extremizing, and proper scoring.
Integration with Other Skills
- Before: Use after completing forecast (have probability, need action)
- Companion: Works with
bayesian-reasoning-calibration for probability updates
- Feeds into: Portfolio management and adaptive betting strategies
Resource Files
📁 resources/
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