Your bankroll is the total capital you dedicate exclusively to betting—completely segregated from rent, bills, savings, and any personal finances. This separation is not merely organizational; it's fundamental to mathematical survival. Professional bettors treat their bankroll as investment capital in a financial market, subject to the same principles of risk management that govern any serious trading operation.

The segregation serves three critical functions. First, it creates a psychological barrier that prevents the most destructive behavior: reloading accounts during losing streaks. Second, it enables precise performance tracking. Third, it facilitates compounding, the engine that transforms small edges into substantial long-term wealth.

Consider the mathematics of compounding with a $10,000 starting bankroll, betting 1% units with a 54% win rate at standard -110 odds. Over 100 bets, expected bankroll grows to approximately $10,450. After 1,000 bets with disciplined reinvestment: roughly $14,500. The key insight: every withdrawal interrupts this compounding engine.

A unit is your standardized bet size, expressed as a fixed percentage of total bankroll. If your bankroll is $10,000 and you use 1% units, every bet risks $100 regardless of how "confident" you feel. This systematic approach is mathematically superior to variable sizing in every measurable way.

Why fixed units rather than variable "confidence-based" sizing? Overconfidence bias systematically destroys expected value. When people rate themselves as "90% confident," they're actually correct only about 70% of the time. This systematic miscalibration means your largest bets—the ones you're "most confident" about—are statistically your worst bets.

Expected Value (EV) is the single most important concept in betting mathematics. It answers one question: if you could place this exact bet infinite times, what would be your average profit or loss per bet?

Small edges compound dramatically over volume. A 3% edge over 500 bets translates to a 55.38% win rate versus the 52.38% breakeven rate. This demonstrates why professionals focus on volume with consistent small edges rather than seeking rare large scores.

The Law of Large Numbers states that as the number of trials increases, the average of results converges to the expected value. In betting terms: over 10 bets, results are mostly random; over 100 bets, your edge begins emerging; over 300-1,000+ bets, mathematical advantage becomes statistically evident.

With a true 55% win rate over 100 bets, actual results could reasonably range from 45-65 wins. A 45-55 record (losing money) is well within normal variance for a winning strategy. After 1,000 bets, the same strategy would produce 520-580 wins, and your edge becomes statistically visible.

A drawdown is the decline from a peak bankroll to a subsequent trough. Drawdowns are mathematically inevitable even with strong positive EV. Simulation data demonstrates that with a 55% win rate, there's a 43% probability of experiencing a 10-unit drawdown over 1,000 bets—despite finishing profitable.

Loss aversion means losses feel approximately twice as painful as equivalent gains feel good. A 20% drawdown creates emotional pressure equivalent to needing a 40% gain. This pressure triggers predictable destructive behaviors: increasing bet sizes to "recover" losses, betting outside normal criteria, or abandoning proven strategies.

The Kelly Criterion, developed by John L. Kelly Jr. at Bell Labs in 1956, mathematically determines optimal bet size. The intuitive insight: edge determines bet size, not confidence or intuition.

However, full Kelly produces extreme volatility that is psychologically unbearable. Professional bettors use Fractional Kelly—betting a fraction of the full Kelly recommendation.

Half Kelly delivers approximately 75% of full Kelly's growth rate while dramatically reducing volatility and drawdown magnitude. This sacrifice of 25% theoretical growth for substantial risk reduction is the universally accepted professional standard.