Aftermath: Life-Changing Math Intuition Lab

The Base-Rate Fallacy: Even with a 99% accurate test, if a condition affects only 1 in 1,000 people (0.1%), testing positive still means you have only an ~8.3% true positive probability because healthy false alarms drastically outnumber true diseased cases.

Base Rate Prevalence 0.1%

Test Sensitivity (True +) 99.0%

False Positive Rate 1.0%

True Positives

1

False Positives

10

Posterior Probability P(Condition | Positive)

9.09%

Geometric Compounding Drag: A +50% gain followed by a -50% loss does not leave you break-even—it leaves you at -25%. Symmetrical variance systematically erodes terminal wealth compared to arithmetic return averages.

Arithmetic Annual Mean +7.0%

Annual Volatility (σ) 25.0%

Time Horizon 30 Years

Arithmetic Growth

$76,123

Real Geometric (Drag)

$32,410

Estimated Volatility Drag Tax

-3.12% / yr

Order of Magnitude Intuition: By estimating lower and upper bounds of sub-factors on logarithmic scales, independent errors cancel out, yielding surprisingly robust 90% confidence intervals for complex real-world unknowns.

Preset Estimation Chains

Geometric Median

80,000

90% Confidence Span

60k – 110k

Asymmetric Risk & Ruin: Over-betting in positive-expectancy bets inevitably triggers catastrophic gambler's ruin. The Kelly Criterion $f^* = (bp - q) / b$ maximizes the logarithmic growth rate, while Half-Kelly protects against estimation error.

Win Probability (p) 60%

Win / Loss Odds Ratio (b) 1.5 : 1

Your Chosen Bet Size Fraction 33% (Full Kelly)

Optimal Kelly (f*)

33.3%

Simulated Ruin Risk

2.1%