WagerFormula
Probability
Combinations in Gambling: How to Count Hands (nCr)
Learn how combinations (nCr) count card hands and lottery tickets, with the formula, worked examples and a quick-reference table of probabilities.
Gambler’s Fallacy: Why Past Spins Don’t Change the Odds
The gambler’s fallacy is the belief that past results change the next outcome. See the math with roulette, coin and dice examples,…
Expected Value
Expected Value in Sports Betting: Formula and Examples
Learn how to calculate expected value for a sports bet with the EV formula, worked -110 and +150 examples, a probability table…
Expected Loss Per Hour: How to Estimate Gambling Cost
Expected loss per hour = bets per hour × average bet × house edge. See the formula with worked roulette examples, comparison…
Expected Value Formula for Gambling: Worked Examples
The expected value formula for gambling, with worked roulette and betting examples, a table of EV by bet, and how EV becomes…
WagerFormula in Numbers
- Active Monthly Users Around the World
- 1M+
- Guides and Reviews
- 150+
- Topics
- 7
- Authors
- 2
House Edge
Baccarat House Edge: Banker, Player and Tie Calculated
Learn how the baccarat house edge is calculated for Banker, Player and Tie bets from outcome probabilities, with worked examples and expected…
Craps House Edge: How Each Bet’s Edge Is Calculated
How the craps house edge is calculated for the Pass Line, Don’t Pass, Field, Any 7 and Place bets, with every step…
Roulette House Edge: Formula and Calculation
How the roulette house edge is calculated from true odds and payout odds, with worked examples and a table of European, American…
Variance
Risk of Ruin in Gambling: The Formula With Examples
Risk of ruin is the probability that a bankroll hits zero before it reaches a chosen goal. Learn the gambler’s ruin formulas…
Law of Large Numbers in Gambling: What It Really Means
What the law of large numbers says about gambling: averages settle on the house edge while totals swing wider, with roulette and…
Variance in Gambling: Standard Deviation and Swings
How variance and standard deviation measure gambling swings, with roulette examples, the square-root-of-n rule and a table of session ranges.
Odds & Payouts
Gambling Mathematics
Fibonacci and D’Alembert Betting Systems: The Math
Fibonacci and D’Alembert only choose stake sizes. See the streak formulas, a worked example and an exact 100-bet comparison on American roulette…
Kelly Criterion Formula: How It Works and Its Limits
The Kelly criterion formula explained with hypothetical worked examples, and why it gives a zero stake on every standard casino bet.
The Martingale System: Why the Math Doesn’t Work
The Martingale system doubles stakes after losses. See the formulas, losing-streak odds and why its expected value stays negative.
