The take: a flat cut of every winning dividend, whoever won

§1The shape of the cut

There are three places a betting operator can take its money, and they are not variations of one idea. It can build a margin into a price: publish 1.90 for a selection it believes is an even-money chance, and be paid for the difference. It can take a commission on winnings, typically charged on the net amount won rather than on the stake. Or it can remove a percentage from a pool, which is this site's subject.

The third shape is unusual because it is charged on the turnover of a pool rather than on a price or on a profit. It is taken before any ticket is valued, from money that belongs to winners and losers alike, so its effect is the same on every winning ticket and it applies whether the dividend turns out to be 1.30 or 130.00.

§2A flat proportional haircut, not a worse price on the outsider

Take the expression for a dividend and rewrite it in two parts:

Two things follow. First, the take does not punish long shots and reward favourites, or vice versa: it is a fixed proportion of whatever the dividend would otherwise have been. If a take reduces a 100.00 dividend by 17.5 per cent, it reduces a 1.20 dividend by exactly the same proportion.

Second, a take is invisible in the same way a margin is invisible but not in the same place. With a book, the margin shows up as slightly worse odds on both sides of a market, and a bettor can compare it across operators. With a pool there is one pool and one take, and the only way to see it is to know what it is and to be able to do the division above with it.

§3The take and the pool it comes from

Because the take and the pool's own overround are related by take divided by one minus take, the last column below is the honest comparison with a bookmaker's prices — a take of 17.5 per cent is not 17.5 per cent of a price, it is the equivalent of a 21.2 per cent book.

The last column is the number worth carrying around. On a pool with a 25 per cent take, a winning ticket that would have returned 4.00 per unit returns 3.00. The 1.00 difference is not a fee charged on the transaction and it will not appear as a line on a statement. It is simply what a winning ticket is worth once the pool has been cut.

§4Breakage and rounding: the part of the cut that is not called a cut

A dividend is rarely a clean number of currency units. The division in the formula produces something like 4.4163, and the rules have to decide what to do with the tail. Some rules round down to a fixed increment and retain the difference — a practice usually called breakage — while others round to the nearest unit, or express the dividend only to a stated number of decimal places.

Two points are worth holding on to. The first is that the increment and the direction of rounding are set by the rules of the pool, not by arithmetic, so they are a thing to read rather than calculate. The second is that breakage is a second, smaller retention sitting on top of the take: it is taken from the dividend after the take has been removed, and like the take it applies uniformly to every winning ticket.

§5Why the shape of the cut compounds faster than the size suggests

A percentage taken off every payout behaves differently from a percentage taken off profit, and the difference grows with activity. Consider an illustrative stake of 100 units at an illustrative payout of 4.00, so that the ticket returns 400 if it wins, of which 300 is profit. Three structures with identical prices and different fee shapes return quite different amounts:

The comparison holds the underlying price identical, which the three structures would not in reality do, so it is a comparison of the fee shapes and not of the markets. What it shows is why a moderate-sounding take is a heavy fee on a winning ticket: a 17.5 per cent cut of a payout is 70 units on this bet, where a 3 per cent commission on the profit is 9. A bettor who wins half of their bets pays the pool's cut on every winning ticket every time, and the total paid is larger than the headline percentage feels.

This is also the reason the take is worth checking before anything else about a pool. Every other question — which selection, which pool type, when to stake — is a question about the numerator and the denominator. This one is a constant multiplier applied to the whole answer.

§6What the take does not depend on

It is worth being exact about this, because a take is often described in ways that imply it varies when it does not.