Multiple bets: the payout multiplies and so does the margin

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Leave a line empty and that leg simply does not exist. The margin is a field because it changes with the house, the sport and the market; the value the page starts with is what a pair priced at minus one hundred and ten on both sides works out to.

Nothing here recommends betting, and nothing here says a multiple is a good idea. The page puts a price on a ticket somebody has already decided to build.

Results

The prize multiplies and so does the margin, and only one of those is advertised. Each leg carries the house cut, and stringing the legs together charges that cut once per leg on the same money: the whole ticket costs one plus the margin, raised to the number of legs, minus one.

What the same margin does as legs pile up

Read that column downwards. A cut of four point seven six on a single bet is the ordinary price of doing business, and nobody argues with it. The same cut on a five leg ticket is twenty six, and on eight legs it is forty five, which no one would accept if it were quoted that way at the counter.

This is also why the ticket that pays the most is the one that costs the most. The payout grows because unlikely things are being multiplied together, and the price of being wrong grows with it in exactly the same motion; the two are the same arithmetic seen from opposite ends.

The other number worth staring at is the implied chance. Three legs that each looked comfortable, at two, one point eight and one point five, come to eighteen and a half out of a hundred for the ticket. Every leg felt likely and the ticket is not, because likelihoods multiply and intuition adds.

None of this says the legs are wrong. It says the ticket is priced worse than the sum of its parts, by an amount that grows every time another leg is added, and that the growth is the point rather than a detail.