From the ring to the fixed-odds board

Betting on a contest is older than any organised market for it, and for most of its history it required no third party at all. Two people disagreed about an outcome, staked money on the disagreement and settled afterwards. What distinguishes the last two centuries is the arrival of an intermediary who will take one side of that bet with anybody, at a price they set, and who makes a living from the prices rather than from the opinions.

That intermediary appeared in the racing world in the early nineteenth century. Instead of matching two backers, a bookmaker priced every runner in a field and stood ready to accept bets on any of them. The essential trick has nothing to do with predicting winners: if the prices are set so that the implied probabilities across the field add up to more than one, and the money arrives in roughly those proportions, the book returns a profit regardless of which horse wins. The excess over one is the margin, and it is the same idea as a pay table set below true odds.

The pool is a genuinely different mechanism, introduced later in the century as an alternative to the ring. All stakes on a race go into one fund, a fixed percentage is deducted, and what remains is divided among the winning tickets. The operator carries no position at all and cannot lose on a result: the deduction is guaranteed and the price of any runner is not known until betting closes. A bookmaker sells certainty of price and takes on risk; a pool sells no certainty and takes none.

Fixed-odds betting away from the track followed the same commercial logic on a much wider range of events. Prices are posted in advance, accepted on demand, and the intermediary's exposure is managed by moving the prices as money arrives, and by laying off risk elsewhere. Whether the subject is a race, a football match or a coin-toss novelty, the mathematics is the arithmetic of the index on this site: a price is quoted below the true odds, and the gap is the business.

The most consequential change of the last fifty years was neither a new bet nor a new price but a new speed. Betting shops, and later telephone and online accounts, dissolved the limit that attendance at an event used to impose. When the number of decisions available per hour rises sharply, a margin that looked negligible per bet becomes a substantial rate per hour, without any change to the margin itself. That is a point about the law of large numbers rather than about any particular market.