Market Mechanics & Betting

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

• 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

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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