version: "1.0.1" 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
• Quick Reference
• Resource Files

Interactive Menu

What would you like to do?

Core Workflows

1. [Calculate Edge](#1-calculate-edge) - Determine if you have an advantage 2. [Optimize Bet Size (Kelly Criterion)](#2-optimize-bet-size-kelly-criterion) - How much to bet 3. [Extremize Aggregated Forecasts](#3-extremize-aggregated-forecasts) - Adjust crowd wisdom 4. [Optimize Brier Score](#4-optimize-brier-score) - Improve forecast scoring 5. [Hedge and Portfolio Betting](#5-hedge-and-portfolio-betting) - Manage multiple bets 6. [Learn the Framework](#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:

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:

1. Define dedicated betting bankroll (money you can afford to lose)
2. Minimum bet size (market minimums)
3. Maximum bet size (market/liquidity limits)
4. Round to practical amounts

Step 5: Execute bet

Final check:

• [ ] Confirmed edge > minimum threshold
• [ ] Calculated Kelly size
• [ ] Applied fractional Kelly (1/4 to 1/2)
• [ ] Checked bankroll constraints
• [ ] Verified odds haven't changed

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:

Default: Use 1.3 if unsure.

Step 5: Validate and finalize

Sanity checks:

1. Bounded [0%, 100%]: Cap at 99%/1% if needed
2. Reasonableness: Does result "feel" right?
3. 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:

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:

1. Probability changed: Lock in profit when beliefs shift
2. Lock in profit: Event moved in your favor, odds improved
3. 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](resources/betting-theory.md)

• Expected value framework, variance and risk, bankroll management, market efficiency

📄 [Kelly Criterion Deep Dive](resources/kelly-criterion.md)

• Mathematical derivation, proof of optimality, extensions and variations, common mistakes

📄 [Scoring Rules and Calibration](resources/scoring-rules.md)

• Brier score deep dive, log score, calibration curves, resolution analysis, proper scoring rules

Next: Return to menu

Quick Reference

The Market Mechanics Commandments

1. Edge > Threshold - Don't bet small edges (5%+ minimum)
2. Use Fractional Kelly - Never full Kelly (use 1/4 to 1/2)
3. Extremize aggregates - Push away from 50% when combining forecasts
4. Minimize Brier honestly - Be accurate, not safe
5. Watch correlations - Portfolio risk > sum of individual risks
6. Hedge strategically - When probabilities change or lock profit
7. 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/

• betting-theory.md - Fundamentals and framework
• kelly-criterion.md - Optimal bet sizing
• scoring-rules.md - Calibration and accuracy measurement

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