By Prof. Daniel Abreu Macedo | April 2026
Key Takeaways:
- Market makers earn revenue primarily through the bid-ask spread, which is mathematically equivalent to a transaction cost paid by both sides of a trade.
- Commission on a betting exchange is a percentage fee extracted from net winnings, and its effective cost depends on the win probability of the position taken.
- Implied probabilities derived from quoted odds almost always sum to more than one, and that excess is known as the overround or vigorish.
- Expected value calculations must incorporate both the spread and the commission to reflect the true break-even point of any position.
Market making is one of the oldest applications of applied probability theory.
Whenever two parties disagree about the likelihood of a future event, an intermediary can stand between them, quote a price at which it will sell one side and a slightly lower price at which it will buy the other, and earn a small margin for absorbing the risk of imbalance.
The practice predates modern exchanges by centuries, but its mathematical structure is best illustrated through the clean framework of a betting exchange, where every position can be priced as an explicit probability statement. This set of notes walks through the algebra of spreads, overrounds, and commissions, using examples that a student of statistics or finance will find familiar.
From Probability to Price
Every wager can be restated as a probability.
If a market quotes decimal odds of 2.00 on an outcome, it is asserting an implied probability of 1 divided by 2.00, or 0.50.
If the odds are 4.00, the implied probability is 0.25. In general, for decimal odds d, the implied probability p equals 1 over d. This transformation is the central bridge between the language of gambling and the language of statistics.
A fair market, in the theoretical sense, is one where the sum of implied probabilities across all mutually exclusive outcomes equals exactly one. In a two-horse race, if one runner is quoted at 2.00 and the other at 2.00, the implied probabilities sum to 1.00 and the book is said to be balanced. In practice, markets are never quite fair, and the gap between the sum of implied probabilities and unity is the first source of profit for the intermediary.
The Overround and Why It Exists
Suppose a bookmaker posts odds of 1.90 on each side of a coin toss. The implied probability on each side is 1 divided by 1.90, approximately 0.5263. The sum is 1.0526. The 5.26 percent excess is the overround, and it represents the bookmaker's theoretical margin if the book is perfectly balanced across customers.
On a peer-to-peer exchange the mechanism is different. There is no house setting the price. Instead, two users, one backing the outcome and one laying it, agree on a single price. If the agreed odds are 2.00 on both sides, the implied probabilities sum to exactly 1.00 and no overround exists. The exchange does not profit from the spread. It profits from a commission applied after the event settles.
Commission as a Percentage of Net Winnings
A commission is a fee applied to the winning party's net profit. If a user stakes 100 at odds of 2.00 and wins, the gross profit is 100. A commission of 5 percent extracts 5 from this profit, leaving 95. From the loser's perspective, the 100 stake is forfeited in full and no commission applies.
The expected value of a position under this structure can be written in words as: the probability of winning times the net profit after commission, minus the probability of losing times the stake. For a user with a true edge, the commission reduces the theoretical return but does not eliminate it, provided the edge is larger than the commission rate weighted by win probability.
Real-world examples of this arithmetic are abundant. A detailed walkthrough of one such case, including tiered rate reductions for high-volume users, is available in this resource on Betfair commission explained, which breaks down how the headline five percent rate translates into a much higher effective cost for short-priced favorites.
Worked Example: The Short-Priced Favorite Problem
Consider a user backing a strong favorite at decimal odds of 1.20. The implied probability is 1 divided by 1.20, approximately 0.833. A 100 stake wins 20 in gross profit. A 5 percent commission removes 1 from that profit, leaving 19.
The effective commission, expressed as a fraction of the stake, is 1 percent. But expressed as a fraction of the gross profit, it remains 5 percent. Expressed as a reduction in the effective odds, the return is now 1.19 rather than 1.20, a shift that looks small but compounds dramatically over many wagers.
A user placing a thousand such wagers sees an expected commission bill of 833 units across the winning trades, not counting any volume discount. For a user placing the same thousand wagers at odds of 5.00, where the win probability is only 0.20, the expected commission bill is 200 units across the winners, because there are fewer winners to tax. Commission cost, then, is not a fixed percentage of activity. It scales with win frequency.
The Spread as an Implicit Commission
On any exchange, the back price and the lay price differ. A user wishing to back the outcome pays the higher price, and a user wishing to lay it accepts the lower price. The gap between the two is the spread, and it functions as an implicit transaction cost. A market quoting back at 2.04 and lay at 2.00 has a spread of four ticks, equivalent to roughly 2 percent of the mid-price.
Crossing the spread once, to enter a position, and crossing it again, to exit before settlement, costs the trader twice this amount. In liquid markets the spread may narrow to a single tick, making round-trip trading viable. In thin markets the spread can exceed the explicit commission rate, meaning that the cost of entry and exit dominates the economics of any strategy.
Break-Even Edge Calculation
A practical question for any quantitative bettor is: what edge do I need to break even? The answer depends on the commission rate c, the win probability p, and the quoted odds d. The break-even condition is satisfied when the expected value after commission equals zero. Rearranged, the minimum true probability required to break even on a position quoted at odds d with commission c is given by the inverse of d multiplied by a factor that accounts for the commission on the win.
For a 5 percent commission and odds of 2.00, the required true probability is approximately 0.5128. The user must be right more than 51.28 percent of the time simply to avoid losses. At odds of 3.00 the required true probability is approximately 0.3509, against an implied probability of 0.333. At odds of 10.00 the required true probability is approximately 0.1053. The edge requirement compresses at longer odds because the commission is charged on a larger net profit.
Applying the Theory
Practical tools exist for students and analysts who wish to model these dynamics without building spreadsheets from scratch. The SharkBetting platform hosts calculators and reference pages that make the arithmetic above explicit, letting a user enter stake, odds, and commission rate and returning the net return, effective commission, and required break-even edge. For a classroom exercise, the most instructive approach is to build the formulas once by hand and then verify them against such a calculator.
Closing Notes
The mathematics of market making reduces to a handful of identities: implied probability is the reciprocal of decimal odds, overround is the sum of implied probabilities minus one, commission is a proportional tax on net winnings, and the spread is a pair of transaction costs paid on entry and exit. From these four building blocks, a student can derive the expected value, break-even edge, and variance of any position on any exchange. The algebra is not difficult. What is difficult is applying it consistently, with discipline, across hundreds of small decisions. That is the quiet truth behind every successful market maker, and it is the reason the theory is worth studying carefully before placing a single trade.
