▌ 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.

UK bookmaker-specific rules

Each UK bookmaker publishes its own multi-bet bonus structure. William Hill pays a 12% bonus on Lucky 15 returns when all four selections win as a seven-fold accumulator. Paddy Power pays 30% when all four selections in a Lucky 15 win. 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

• · 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
• · IRS Publication 525, Taxable and Nontaxable Income — Gambling Winnings section. irs.gov/publications/p525
• · IRS Form W-2G triggers — Certain Gambling Winnings. irs.gov/forms-pubs/about-form-w-2-g
• · UK Gambling Commission — affiliates and third parties guidance. gamblingcommission.gov.uk · affiliates
• · William Hill, Paddy Power, Coral, Ladbrokes, Sky Bet — bookmaker-specific bonus rule books (each operator's published terms; reviewed quarterly per editorial standards).