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▌ Methodology · BettorStack

Methodology

Every calculator on BettorStack is derived from a primary source. The catalog of formulas in use, with citations and short derivations. Any bettor can verify the math against the original.

Kelly criterion

The Kelly stake fraction f* = (bp − q) / b, where b is decimal odds minus 1, p is the bettor's win probability, and q = 1 − p.

Source: Kelly Jr., J.L. (1956). "A New Interpretation of Information Rate." Bell System Technical Journal, 35(4): 917-926. DOI: 10.1002/j.1538-7305.1956.tb03809.x

Vigorish (vig / juice)

For a 2-way market with American odds A and B, vig is computed as vig = (1 / dec(A) + 1 / dec(B)) − 1, where dec(·) converts American odds to decimal.

Standard derivation from sports-betting market theory.

Implied probability vs implied odds

Implied probability is straightforward: P = 1 / dec(odds). Implied odds is a poker-theory concept — the additional money you expect to win on later betting rounds, conditional on hitting your draw. Two different concepts, two separate calculators.

Parlay payout

A parlay pays only if every leg wins, so the combined decimal odds are the product of each leg's decimal odds: D = D₁ × D₂ × … × Dₙ. Payout is stake × D. The break-even hit rate is 1 / D, and it includes the bookmaker's margin on every leg.

Two assumptions are worth stating. First, a pushed or voided leg is removed and counts as 1.00, which is how most US sportsbooks reprice the remaining legs; promotional tickets and some bet types settle differently, so the sportsbook's house rules take precedence. Second, the product formula treats legs as independent. Same-game parlays are correlated, and sportsbooks price that correlation, so the betslip price can be shorter than the product. A profit boost is applied to winnings only, never to the stake. See the parlay calculator.

Round robin

A round robin turns n picks into every parlay of a chosen size k. The number of parlays is n! / (k! × (n − k)!), and the total cost is the stake per parlay multiplied by that count. Each parlay is priced and settled on its own, using the parlay formula above.

A lost pick settles only the parlays that contain it. A pushed or voided pick is removed from each parlay it sits in, and the parlay is repriced on the remaining picks; if every pick in a parlay pushes, the stake comes back. The combination counts were checked against a published sportsbook guide (for example 4 picks by 2s is 6 parlays, 5 picks by 3s is 10). Pricing a round robin does not remove the margin on the individual legs. See the round robin calculator.

UK bookmaker-specific rules

Each UK bookmaker publishes its own multi-bet bonus structure. William Hill pays a 10% bonus on Lucky 15 total returns when all four selections win. Paddy Power pays the same 10% on the same outcome. Coral, Ladbrokes, Sky Bet each have their own rule books.

The UK calculators encode every published rule book including Rule 4 deductions for non-runners on horse-racing markets.

Per-state US tax math

US gambling winnings face 24% federal withholding above thresholds. State withholding varies widely — NY 8.82%, NJ 3%, CA exempt-but-reportable, FL none, TN none. The payout calculator lets you set your state and shows the post-tax net.

When we update

Bookmaker rules change. State tax tables update annually. Both are tracked, with change notes on each calculator's "Last updated" timestamp. Full process documented at /editorial-standards/.

Primary sources

Found an error in a derivation or citation?

Contact us — material errors fixed within 24 hours per /editorial-standards/.