Dividend shapes: win, place, exotics and multi-leg

§1The win pool: one denominator

The simplest pool pays on one condition: a named selection wins. Its dividend is the net pool divided by the money staked on that selection, and the whole of the answer follows from the two numbers in that division. Nothing about the selection's merit, its previous form or the opinion of anybody who priced it enters the calculation, which is the point and also the trap: the pool is a census, not an assessment.

What is worth noticing is how the win pool's dividend behaves as a distribution. If the money is spread evenly across twelve runners, an equal share of the net pool divided by one twelfth of the gross pool gives a dividend close to 12 × 0.825 = 9.90 on an illustrative 17.5 per cent take. If one runner takes a third of the pool instead, the same pool pays about 2.48. The take is identical in both cases; only the census changed.

§2The place pool: capital comes back before profit is shared

A place pool pays on a different condition — a selection finishing within the paying positions — and it is usually worked on a principle that trips people up when they first meet it. Backers of a placed selection do not receive the whole net pool divided by their money. They receive their own capital back, and then a share of the profit that remains after all placed capital has been returned.

The illustrative arithmetic below shows why a placed favourite often returns barely more than the stake. The pool is 120,000 with an illustrative 16 per cent take, three places are paid, and the three placed selections carried 30,000, 22,000 and 14,000.

Each paying position receives one part of that profit, distributed among the tickets that hold it in proportion to their stakes. So the holders of each placed selection receive their capital plus one third of 34,800, which is 11,600, spread across that selection's tickets:

Two features stand out, and both are consequences of the same structure. First, a place pool pays a return on the stake rather than a price on a chance, so a heavily supported placed selection returns only slightly more than its capital. Second, the profit share is fixed per paying position before it is divided, so the dividend on a lightly supported placed selection is larger — not because it was a better bet, but because fewer tickets were sharing the same slice.

§3Exotic pools: the denominator becomes a combination

An exotic pool does not pay on a runner. It pays on a combination: two named runners in a named order, or three, or four. That single change is the whole economics of the market, because the number of possible combinations grows far faster than the number of runners.

With twelve runners there are twelve possible win outcomes, 132 ordered pairs (twelve multiplied by eleven) and 1,320 ordered triples. The money in an exotic pool is spread across that many possibilities rather than twelve, so the money on the winning combination is usually a small fraction of the pool, and the dividend is correspondingly large. The take on these pools is normally higher than on a win pool, and the pool itself is normally smaller.

The naming is a trap of its own, and worth stating plainly because it differs by jurisdiction. Two runners in exact order are an exacta in some places and a straight forecast in others; two runners in either order are a quinella, or both-order forecast, or reverse; three runners in exact order are a trifecta or a tricast. The name on the ticket is the operator's, and the rules under that name are the ones that apply.

§4Multi-leg tickets: one leg can end it

A multi-leg pool — a double, a treble, a pick-three or a pick-six — is a single pool over several races or events, paid only to tickets that name the correct outcome in every leg. The arithmetic of the pool is the same as any other; what changes is the conditional structure of a ticket.

Because every leg must be correct, a ticket dies with its first wrong leg, and a single non-runner in a single leg is enough to raise a question the rules have to answer: whether the ticket receives a substitute selection (commonly the favourite or the favourite's tote equivalent), whether the stake for that leg is refunded while the rest of the ticket stands, or whether the ticket is void as a whole. Those three treatments produce completely different outcomes on the same ticket, and which one applies is a matter for the rules.

Multi-leg pools also carry the possibility that nobody holds the winning combination, which is when a pool has to decide what happens to its money. That is the subject of the page on guaranteed and carried-over pools.

§5What a dividend of 214.00 actually means

A large dividend looks like a market being generous. Decomposed, it is almost always a pool being thin. Take the trifecta on the front board: a gross pool of 38,000, an illustrative take of 25 per cent, so 28,500 to be paid, and a dividend of 214.00 per unit on the winning combination. Work backwards and the division tells you what the winning combination was carrying:

About 133 units out of 38,000 — roughly one third of one per cent of the pool — was on the combination that came in. The dividend is large because almost nobody held it, not because the pool was rewarding a good judgement. Every ticket that held a different order of the same three runners lost everything, and among those tickets were many that had identified the three most likely runners in the race.

§6A big dividend is not the same as a good bet

The single most common confusion in pool betting is reading the size of a dividend as evidence about the quality of the bet that received it. The dividend is a census result: it reports how few tickets stood on the winning combination. It contains no information about whether staking on that combination was wise before the event.

This matters most in exotics, where the combination count makes large dividends routine. A large dividend is compatible with a terrible bet — one combination out of hundreds, staked without any reason — and a small dividend is compatible with an excellent one. The dividend is what you were paid. It is not a measure of what you did.