gh-lyndonkl-claude/skills/market-mechanics-betting/resources/betting-theory.md

Betting Theory Fundamentals

This resource explains the core theoretical foundations of rational betting, expected value, variance management, and market efficiency.

Foundation for: All betting and forecasting decisions

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Why Learn Betting Theory

Core insight: Betting theory separates decision quality from outcome quality. Make +EV decisions repeatedly and survive variance.

Enables:

• Think probabilistically (convert beliefs to quantifiable edges)
• Manage risk rationally (distinguish bad decisions from bad outcomes)
• Avoid costly mistakes (identify predictable failure modes)
• Optimize long-term growth (balance aggression with preservation)

Research foundation: Kelly (1956), Samuelson (1963), Thorp (1969), behavioral economics (Kahneman & Tversky), market efficiency (Fama).

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1. Expected Value Framework

Definition and Formula

Expected Value (EV): Probability-weighted average of all possible outcomes.

EV = Σ(Probability × Outcome)

Binary bet:
EV = (P_win × Amount_won) - (P_lose × Amount_lost)

Example:

Bet $100 on 60% event at even odds (+100)
EV = (0.60 × $100) - (0.40 × $100) = $20
EV% = +20% per $100 wagered

Positive vs Negative EV

Decision Framework:

• EV > +5%: Strong bet (after fees/uncertainty)
• EV = 0% to +5%: Marginal (consider passing)
• EV < 0%: Never bet (unless hedging)

Critical Rule: Judge decisions by EV, not outcomes. Good decisions lose sometimes; bad decisions win sometimes. Process matters in small samples, results matter over 100+ trials.

Converting Market Odds to EV

Step 1: Implied probability

Decimal odds: P = 1 / Odds
  Example: 1.67 → 60%

American (+): P = 100 / (Odds + 100)
  Example: +150 → 40%

American (-): P = |Odds| / (|Odds| + 100)
  Example: -150 → 60%

Step 2: Calculate edge

Your probability: 70%
Market probability: 60%
Edge = 70% - 60% = +10%

Step 3: Calculate EV

Bet $100 at 1.67 odds:
EV = (0.70 × $67) - (0.30 × $100) = +$16.90 = +16.9%

Law of Large Numbers

Key principle: Observed frequency converges to true probability as sample size increases.

Practical thresholds:

• 10 bets: High variance, might be down despite +EV
• 100 bets: Convergence starting, likely near EV
• 1000 bets: Results tightly centered around EV

Application: Don't judge strategy on <30 trials. Variance dominates small samples.

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2. Variance and Risk

Standard Deviation

Measures outcome dispersion around EV.

Formula:

σ = √(P_win×(Win-EV)² + P_lose×(Loss-EV)²)

Example ($100 bet, 60% win, even odds):

EV = $20
σ = √(0.60×(100-20)² + 0.40×(-100-20)²)
σ = √9600 = $98

Coefficient of Variation: σ/EV = $98/$20 = 4.9

Interpretation: Standard deviation ($98) is 5× the EV ($20). Variance dominates signal.

Volatility Categories

Coefficient of Variation (CV = σ/EV):

• CV < 1: Low volatility (10-30 trials to see EV)
• CV = 1-3: Moderate (30-50 trials)
• CV = 3-10: High (50-100 trials)
• CV > 10: Extreme (100+ trials)

Higher CV requires: Larger bankroll, more patience, stronger discipline.

Risk of Ruin

Probability of losing entire bankroll before profit.

Practical Guidelines:

Bet Size	Risk of Ruin	Assessment
50% of bankroll	~40%	Reckless
25% of bankroll	~20%	Aggressive
10% of bankroll	~5%	Moderate
5% of bankroll	~1%	Conservative
2% of bankroll	~0.1%	Very conservative

Kelly Criterion naturally manages risk of ruin. Never bet >10% of bankroll on single bet.

Managing Volatility

1. Fractional Kelly (Primary Tool):

• Full Kelly: 100% variance, 40%+ drawdowns
• Half Kelly: 25% variance, ~20% drawdowns
• Quarter Kelly: 6% variance, ~10% drawdowns

2. Diversification:

• Multiple uncorrelated +EV bets
• Requires independence (correlation < 0.3)

3. Expected Drawdown:

• Even optimal betting experiences 20-40% drawdowns
• Mentally prepare for temporary losses
• Don't confuse drawdown with -EV strategy

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3. Bankroll Management

Defining Your Bankroll

Valid: Money you can afford to lose entirely, separate from emergency fund, investment portfolio, daily expenses. Starting: $500-$5000 recreational, $10,000+ serious.

NOT valid: Money needed for bills, emergency fund, retirement, money you'd be devastated to lose.

Separation Principle

Why: Prevents scared money and revenge betting. Clear accounting, tax clarity, risk containment.

Implementation: Separate betting account, never add money mid-downswing, withdraw profits periodically, stop if bankroll → $0.

Growth vs Preservation

Preservation (Default): 1/4 to 1/2 Kelly, for most bettors and bankrolls <$5000 Growth (Advanced): 1/2 to full Kelly, for large bankrolls and high variance tolerance (requires 2+ years track record)

Dynamic Sizing

Bet size scales with bankroll. Example: $1000 bankroll at 5% = $50. After wins → $1500 → bet $75. After losses → $600 → bet $30.

Recalculate: Daily if >20% change, weekly (active), monthly (casual).

Withdrawal Strategy

Recommended: When bankroll doubles, withdraw original amount, continue with profit (break-even if lose profit). Conservative: 50% profit monthly. Aggressive: Never withdraw (full compounding).

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4. Market Efficiency

Efficient Market Hypothesis

Core claim: Prices reflect all available information. Reality: Semi-strong efficient in liquid, mature markets.

Market knows: Published polls/news, historical base rates, expert commentary, obvious statistical patterns.

Where Edges Exist

1. Information Asymmetry: Local knowledge, domain expertise 2. Model Superiority: Better statistical model, proper extremizing 3. Lower Transaction Costs: Market 5% fee vs your 0-1% 4. Behavioral Biases: Recency bias, base rate neglect, narrative following 5. Market Immaturity: Low liquidity, niche topics, few informed traders

Before betting, ask: "What information or model do I have that the market doesn't?"

• Nothing → Pass | Vague → Pass | Specific → Investigate

Trust vs Question Market

Trust: Liquid, mature, objective outcome, many informed participants, low emotion Question: Illiquid, new, subjective outcome, few informed participants, high emotion (politics, fandom)

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5. Common Betting Mistakes

Chasing Losses

What: Increasing bet size after losses. Why: Loss aversion, emotional arousal. Fix: Never increase bet size after loss, use bankroll %, take break after 2+ losses.

Tilt (Emotional Betting)

Triggers: Bad beat, streaks, external stress. Symptoms: No analysis, ignoring Kelly, revenge betting. Fix: Pre-commit no bets when tilted. Checklist: Calm? Calculate EV? Kelly sizing? Betting for +EV not revenge?

Overconfidence Bias

What: Overestimating probability accuracy (90% when true is 70%). Fix: Track calibration, log predictions + outcomes, calculate curve quarterly. Do 70% predictions happen 70%?

Ignoring Variance

What: Judging strategy on <30 trials. Example: "Down 15% after 20 bets, strategy sucks" (normal variance). Fix: Require 50+ bets minimum, 100+ preferred, 200+ for high confidence.

Outcome Bias

What: Judging by results not process. +15% EV lost = good decision (bad outcome). -10% EV won = bad decision (lucky). Fix: Checklist: EV correct? Edge > threshold? Kelly fraction? Followed system? YES = good decision regardless of outcome.

Hindsight Bias

What: After outcome, "I knew it would happen." Fix: Pre-commit logging, write probability before event, don't revise after, accept 40% events happen 40%.

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6. Integration with Kelly Criterion

EV Drives Kelly

Kelly derives from: Expected value (edge), odds received, bankroll optimization (maximize log wealth).

Key relationship: f* = (bp - q) / b. Edge drives bet size: 10% edge → ~10% Kelly, 5% edge → ~5% Kelly, 0% edge → 0% bet.

Variance Tolerance

Fraction	Variance	Growth	Drawdown
Full (1.0)	100%	100%	~40%
Half (0.5)	25%	75%	~20%
Quarter (0.25)	6%	50%	~10%

Bankruptcy Protection

Kelly never bets 100%: prevents ruin, keeps capital for next bet, scales down as bankroll shrinks. Practical: Stop if bankroll drops 80-90%.

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7. Practical Examples for Forecasters

Example 1: Election Prediction Market

Scenario: Market 55%, your forecast 65%, bankroll $2000

Step 1: Edge

Edge = 65% - 55% = +10%
Threshold: 5%
Decision: +10% > 5% → Proceed

Step 2: EV

Bet $100 at 1.82 odds → Win $82
EV = (0.65 × $82) - (0.35 × $100) = +$18.30 = +18.3%

Step 3: Kelly

Full Kelly: 22.3%
Half Kelly: 11.2%
Bet: $2000 × 11.2% = $224

Example 2: Brier Score Tracking

50 forecasts, goal: Brier < 0.15

Forecast	Your P	Outcome	(P-O)²
Event A	80%	YES (1)	0.04
Event B	30%	NO (0)	0.09
Event C	90%	YES (1)	0.01
Event D	60%	NO (0)	0.36
Event E	70%	YES (1)	0.09

Brier: 0.59 / 5 = 0.118 (Excellent)

Analysis: Event D large error normal (40% events happen). Don't game metric by avoiding 60% predictions.

Example 3: Extremizing

Forecasts: You 72%, A 68%, B 75%, C 70%, Market 71% Average: 71.2%

Extremize:

Factor: 1.3 (moderate)
Extremized = 50% + (71.2% - 50%) × 1.3 = 77.6% ≈ 78%

Edge: 78% - 71% = +7%
Half Kelly ≈ 3.5% of $5000 = $175 bet

Example 4: Correlated Portfolio

Scenario: Democrats House (60% yours, 55% market) + Senate (55% yours, 50% market) Correlation: 0.7 (high)

Naive (WRONG):

Bet A: 5% × $10k = $500
Bet B: 5% × $10k = $500
Total: $1000 (10%)

Correct:

Adjust for correlation: 1 - (0.7 × 0.5) = 0.65
Bet A: $500 × 0.65 = $325
Bet B: $500 × 0.65 = $325
Total: $650 (6.5%)

Reasoning: Positive correlation amplifies risk. Reduce sizing to maintain tolerance.

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Key Takeaways

The 10 Commandments

1. Expected Value is King - Judge decisions by EV, not outcomes
2. Variance is Inevitable - Embrace it; don't fight it
3. Bankroll is Sacred - Protect it above all else
4. Kelly is Your Guide - But use fractional (1/4 to 1/2)
5. Market is Usually Right - You need edge to beat it
6. Discipline Over Impulse - System beats emotion
7. Sample Size Matters - 50+ bets before judgment
8. Calibration is Honesty - Track it religiously
9. Correlations Kill - Adjust for portfolio risk
10. Survival Enables Profit - Can't win if bankrupt

Mental Models

Betting = Business

• Bankroll = Working capital
• EV = Profit margin
• Variance = Market volatility
• Kelly = Capital allocation

Decision Quality ≠ Outcome Quality

• Good decisions lose sometimes (variance)
• Bad decisions win sometimes (luck)
• Process > Results (small samples)
• Results > Process (large samples 100+)

Integration Workflow

Before betting:

1. Make forecast (Bayesian, reference class)
2. Calculate edge vs market
3. Check edge > threshold (5%+)
4. Use Kelly for sizing
5. Execute and log

After betting:

1. Track outcome
2. Update calibration
3. Calculate Brier score
4. Don't judge single bet
5. Evaluate after 50+ bets

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