How a pool forms, and how a dividend is struck from it

§1A pool is a ledger of stakes, not a book of prices

When a pool opens, the operator has published no price for anything in it. What exists is a ledger: for each selection in the pool, the total amount staked on it. That ledger is the entire state of the market. Every number that will eventually be paid out is derived from it.

This means the operator has two jobs and no third one. It records stakes correctly, and it removes the percentage it is entitled to. It does not have to decide what any selection is worth, it does not have to take a view on the event, and it does not carry the risk that a price it published turns out to be wrong. In a book, a badly priced market is the operator's loss. In a pool, a badly priced market is simply a dividend that nobody would have offered as a price — and the pool pays it anyway.

The trade the operator has made is therefore a simple one: it has given up the margin and the risk of pricing, and taken in exchange a fixed percentage of everything staked and the certainty of that percentage regardless of the result.

§2What a stake actually buys

A stake in a pool buys one thing: a claim on a share of the net pool, conditional on the selection winning. The share is not a fixed amount and it is not a price. It is a fraction, and the fraction is the money you staked on that selection divided by all the money staked on that selection.

Put as a single expression, the dividend one unit receives on the winning selection is:

Two features of that expression decide almost every practical question in pool betting. The first is that the numerator is the whole pool: money staked on losing selections is not returned to its owners, it is the prize fund. The second is that the denominator is the money on your own selection: if you win, you are sharing the net pool with everyone who agreed with you, in proportion to how much each of you put in.

Notice also that your own stake appears in the denominator. It is not a fee you pay to enter the pool; it is part of the winning money that the net pool gets divided by. This is why a stake large relative to its own selection reduces the dividend on that very ticket, a point worked through on the page on late money and dilution.

§3The number on the board is a running estimate

Boards, screens and apps show dividends during the betting period. They are computed from the ledger as it stands at that moment. Because the ledger keeps changing until the pool closes, the number on the board is a reading of an open pool, not a quotation anybody has committed to.

The distinction matters in two ways. First, a pool that closes in the last seconds before an event can move a long way after the moment you look at it, because late money does not arrive evenly: those who stake late tend to concentrate on fewer selections than the crowd that staked early. Second, the last dividend shown is sometimes a settled dividend from a previous round rather than a live estimate, which is a different number with a different meaning. Whichever it is, the number you will actually be paid is struck once, at the close, from the final ledger.

§4Three distributions, one pool

The same gross pool pays three very different dividends depending on how concentrated the money is. Below, the gross pool is 250,000 and the illustrative take is 17.5 per cent throughout; only the money on the winning selection changes. This is the single most useful table on the site, because it shows that pool size and dividend size are not the same thing.

Read down the last column and then across to the dividend: as the winning selection takes a larger share of the pool, the dividend collapses, even though the pool is identical and the number of runners is identical. A book would have priced all three cases into its odds in advance. A pool pays whatever the crowd did, and the crowd's distribution is the price.

§5The pool's own margin, expressed as a book margin

Because the take is a percentage of the pool and the dividend is what remains, the equivalent margin is larger than the take. Formally, if every selection in the pool is priced at the pool's own implied break-even, the implied probabilities sum to the gross pool divided by the net pool, which is one over one minus the take. So the equivalent overround of the pool is take divided by one minus take.

This is worth internalising because it stops an error in the other direction. A 17.5 per cent take sounds mild next to margins quoted for some markets; it is the equivalent of a book that adds 21.2 per cent across its book. The two ways of charging are different in shape — a book margin can be shopped and varies by market, a take is uniform and unavoidable — but they are comparable in size, and the take is larger than the percentage suggests.

§6Where the money sits, and what that means

Every stake in a pool is paid to the operator and held there until settlement. Nothing is matched between bettors at the moment of staking; the matching is statistical, and it happens at settlement when the net pool is divided. That has two consequences.

The first is favourable and worth stating plainly: you are not exposed to any single counterparty's failure to pay in the way an unmatched order on an exchange is exposed. What you are exposed to is whether the operator itself pays, and the pool being co-mingled means the operator is a custodian of everyone's stakes at once.

The second is that a ticket is not an asset you own in the way a matched position is. There is no counterparty to sell it to and normally no mechanism to transfer it; the only exit offered is whatever the operator itself chooses to offer, on its own terms and at its own price, if it offers one at all. A ticket bought at the start of a long pool is committed for the life of the pool.