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Betting

Sportsbooks and prediction markets quote prices in different languages—translate them into comparable probabilities and payouts.

Odds formats are conventions; probability is the underlying quantity. These tools help you move between American, decimal, and fractional quotes, combine legs for parlays when independence assumptions hold, estimate hedge stakes to lock outcomes, and explore cash-out approximations. Nothing here predicts winners—use them for bookkeeping, comparison shopping, and understanding what the numbers imply. Always follow local laws and bet responsibly.

Implied probability

Price ↔ chance

Decimal odds imply win probability ≈ 1/odds (ignoring vig). American odds encode profit per stake—convert before comparing lines.

Conditional vs joint

Parlay honesty

Multiplying leg probabilities assumes independence (or uses supplied joint inputs). Correlated legs break naive parlay math.

Hedging

Lock or trim risk

Offsetting stakes across outcomes can stabilize return given updated prices—sizes depend on odds and desired guarantees.

Cash-out

Early settlement

Books offer buyouts blending fair value and margin; calculators help benchmark offers against simple models.

Guides & Articles

View all Betting articles

Formula Quick Reference

Lines move; definitions matter—confirm posted rules with your operator and jurisdiction for anything binding.

FormulaEquationVariablesResult unitCalculator
Implied probability (decimal)p ≈ 1 / ddecimal odds d; ignores vigprobabilityUse calculator →
American → decimal (positive)d = 1 + US/100US > 0decimal oddsUse calculator →
American → decimal (negative)d = 1 + 100/|US|US < 0decimal oddsUse calculator →
Independent parlay (decimal)d_parlay = d₁ × d₂ × …correlation breaks independencedecimal oddsUse calculator →
Complement ruleP(not A) = 1 − P(A)partition of outcomesprobabilityUse calculator →
Conditional probabilityP(A|B) = P(A∩B)/P(B)requires P(B) > 0probabilityUse calculator →
Prediction market pricep ≈ price (in $1 scale)binary contract framingprobabilityUse calculator →

Watch & Learn

Probability foundations—how independence and conditioning relate to odds formats and combined bets.

Probability explained | Independent and dependent events

Foundations for when you can multiply probabilities—and when dependence changes the story.

Khan Academy~8 min

Conditional probability and independence

How new information updates probabilities—directly relevant to correlated betting legs.

Khan Academy~7 min

Independent or dependent probability event?

Worked classification practice—helps spot naive parlay assumptions in the wild.

Khan Academy~4 min

Frequently Asked Questions

Odds formats, independence, and cash-outs—how the calculators fit theory to everyday tickets.