What is a bookie (bookmaker)?
– A bookie—short for bookmaker—is a person or firm that takes bets on events (most often sporting contests), determines the prices (odds), accepts wagers, and pays winners. Bookmakers usually earn money by charging a commission on bets rather than by gambling themselves.
Key definitions (first use)
– Vig (vigorish): the commission a bookie charges on wagers.
– Money line: an odds format that shows which side is favored and how much you must risk or can win.
– Point spread: an odds format that handicaps the favorite by a set number of points to even betting interest.
– Book (or books): the collection of active bets a bookmaker manages.
– Handle: the total amount wagered.
How bookies make money (basic mechanics)
1. Set odds for each possible outcome, expressed as money lines, spreads, or decimals.
2. Try to attract roughly equal amounts of money on each side of an event. When balanced, the bookmaker’s exposure (risk of net loss) is low.
3. Collect the vig on losing bets and pay winners from the pooled stakes. If the book is balanced, the vig represents the bookmaker’s profit.
Vigorish (the vig, or juice)
– Definition: the commission a bookmaker charges on bets; effectively the built‑in margin that makes the book profitable when action is balanced.
– How to compute (basic):
– For decimal odds (d): implied probability = 1/d. Book margin (overround) = sum(implied probabilities) − 1.
– For American odds:
– If odds are positive (+150): implied prob = 100 / (
100 + odds). For negative American odds (e.g., −150): implied probability = −odds / (−odds + 100). These give the same implied probabilities as converting to decimal odds first.
Worked example — two‑way market
– Market quotes: Team A −120, Team B +110.
1) Convert to implied probabilities (American → decimal → prob, or use formulas):
– Team A (−120): implied prob = 120 / (120 + 100) = 120 / 220 = 0.5455 (54.55%).
– Team B (+110): implied prob = 100 / (110 + 100) = 100 / 210 = 0.4762 (47.62%).
2) Sum implied probabilities = 0.5455 + 0.4762 = 1.0217 (102.17%).
– Overround (book margin as probability) = sum − 1 = 0.0217 (2.17 percentage points).
3) Interpret:
– If action were perfectly balanced, the bookmaker’s expected gross profit ≈ 2.17% of stakes (the vig), before operating costs and losses from imperfect balancing.
4) Remove the vig to estimate “true” (fair) probabilities:
– Fair prob Team A = 0.5455 / 1.0217 = 0.5339 (53.39%).
– Fair prob Team B = 0.4762 / 1.0217 = 0.4661 (46.61%).
5) Convert back to fair (vig‑free) decimal odds: decimal = 1 / fair prob.
– Team A fair decimal ≈ 1 / 0.5339 = 1.873 → American ≈ −116.
– Team B fair decimal ≈ 1 / 0.4661 = 2.145 → American ≈ +115.
Step‑by‑step checklist to compute vig and fair odds
1. Obtain quoted odds (American, decimal, or fractional).
2. Convert to implied probabilities:
– Decimal d → prob = 1 / d.
– American +X → prob = 100 / (X + 100).
– American −Y → prob = Y / (Y + 100).
3. Sum implied probabilities; overround = sum − 1.
4. Book vig ≈ overround (as a fraction of total stakes if book is balanced).
5. To strip vig: normalize each implied prob by dividing by the sum of implied probs.
6. Convert normalized probs back to your preferred odds format for vig‑free quotes.
Notes, assumptions and limitations
– This math assumes a two‑outcome (or mutually exclusive, collectively exhaustive) market and no pushes/ties. Multi‑outcome markets (e.g., three‑way soccer: home/draw/away) are handled the same way but typically show larger overrounds.
– “Balanced” book means liabilities (amounts paid out if either side wins) are arranged so the bookmaker’s net result is the vig. In practice stakes are not perfectly balanced, and bookmakers hedge, limit bets, or adjust prices.
– The overround gives an estimate of the margin offered at the quoted prices; the bookmaker’s realized profit can differ due to betting volume imbalance, hedging, or edge in setting true probabilities.
– Converting fair probabilities back to American odds requires rounding; small arithmetic/rounding differences are normal.
Practical tips for traders and students
– Use decimals for arithmetic (conversion is straightforward); convert to American only for display.
– Check multiple books to estimate market consensus and identify poor value (books with larger overrounds typically offer worse value).
– For strategy or modeling, always document whether you use quoted (vig‑included) or implied (vig‑free) probabilities.
– Remember that lower overrounds generally indicate more efficient/liquid markets.
Reputable sources for further reading
– Investopedia — Bookmaker: https://www.investopedia.com/terms/b/book
— Pinnacle — What Is Overround (margin)?: https://www.pinnacle.com/en/betting-articles/educational/what-is-overround-margin/1YF5ZB7ZK5RZCXZK
— UK Gambling Commission — Guidance and research on gambling markets: https://www.gamblingcommission.gov.uk/
— Sportsbook Review — What is vigorish (the “vig” or house edge)?: https://www.sportsbookreview.com/betting-articles/what-is-vigorish/
— Khan Academy — Probability and basic probability rules (useful background): https://www.khanacademy.org/math/statistics-probability
Quick checklist for traders and students
– Use decimal odds for all arithmetic; convert to American only for display. Decimal odds are total return per unit staked (including stake).
– Always compute implied probabilities as 1/decimal_odds.
– Sum implied probabilities to measure the overround (sum > 1 implies bookmaker margin).
– Remove the overround to get vig‑free (fair) probabilities by dividing each implied probability by the overround (the sum).
– Document clearly whether models use quoted (vig‑included) or implied (vig‑free) probabilities.
– Compare multiple books to assess market consensus and spot large overrounds (poorer value).
– Round final displayed odds sensibly; keep stored values as unrounded decimals for calculations.
Worked example — converting a two‑outcome market and removing vig
Assume the market shows two decimal odds:
– Outcome A: 1.80
– Outcome B: 2.20
Step 1 — implied probabilities
– pA = 1 / 1.80 = 0.5556 (55.56%)
– pB = 1 / 2.20 = 0.4545 (45.45%)
– overround = pA + pB = 1.0101 (101.01%)
Step 2 — remove overround to get fair probabilities
– fair_pA = pA / overround = 0.5556 / 1.0101 = 0.5491 (54.91%)
– fair_pB = pB / overround = 0.4545 / 1.0101 = 0.4509 (45.09%)
Step 3 — convert fair probabilities back to decimal odds
– fair_decimal_A = 1 / 0.5491 = 1.821
– fair_decimal_B = 1 / 0.4509 = 2.218
Step 4 — (optional) convert to American odds for display
– For decimal >= 2.00: American = +100 × (decimal − 1)
– For decimal < 2.00: American = −100 / (decimal − 1)
– fair_decimal_A = 1.821 → American ≈ −122 (−100 / 0.821 ≈ −121.