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The Composed Market / The limits
Twelve legs, 4,096 states, and the price at which a market stops being offered

The three ceilings that decide how far a combination can go

A combination is not limited by courage or by the size of the payout alone. Three separate numbers decide: how many legs may be joined, how long a price the operator will accept, and how much money may be placed against it. None of the three appears in the same place, and each answers a different question.

Desk spec
legs
2 to 12
payable price
500.0
maximum stake
250.00
payout ceiling
25,000.00
the composed priceThe number returned for a set of outcomes the customer named. It is not the product of the legs: on the samples 5.60 multiplies and 4.80 is offered, because the legs happen together more often than independence implies.
the requestA customer asking an operator to invent a market. 500 arrived in the sample month, 218 produced a price, 131 could not be priced at all, and the median answer took 3 hours 40 minutes.
the void legA leg that never happens, repaired by re-pricing the combination from its remaining legs. Dividing the price by the void leg gives 4.50 where the real three-leg price is 4.80 - a 6.7% error.
Direct answer

A composed market is bounded by three separate numbers: 2 to 12 legs, a payable price of 500.0, and a maximum stake of 250.00 behind a payout ceiling of 25,000.00. Twelve legs at 1.70 each already multiply to 582.6, above the payable price, so a request can be within the leg limit and still be refused.

Why three limits and not one

The leg count is the model's limit: 12 legs means 4,096 joint states and 66 pairwise relationships to resolve, and past that point the answer stops being about a market anyone is asking for. The payable price is the arithmetic's limit: a combination can multiply past the point where the return, not the risk, is the problem, and the operator refuses rather than caps. The stake is the liability's limit, and it is the only one of the three that also appears on markets the operator published rather than composed.

They interact in a way that is easy to get backwards. A price of 500.0 is not generous: it is the highest combination the operator will accept, and at that price a 250.00 stake would pay 125,000.00, five times the payout ceiling. So the third limit bites first, and the maximum stake is a function of the price rather than a fixed number.

What the samples show

Sample E - three limits, and what each one stops
LimitValueWhat it preventsWhere it is stated
Legs in one combination2 to 12A market the model cannot resolve18 of 40 terms pages
Payable price500.0A return the book will not hold7 of 40 terms pages
Maximum stake250.00A liability beyond the payout ceiling4 of 40 terms pages
Payout ceiling behind all three25,000.00A single settled combination paying more11 of 40 terms pages
sample E - the leg limit, and the price limit beside it legs = 2 to 12 joint states the model resolves = 2^12 = 4,096 pairs to estimate = C(12,2) = 66 twelve legs at 1.50 each = 1.50^12 = 129.7 twelve legs at 1.70 each = 1.70^12 = 582.6 payable price accepted = 500.0 so 582.6 is refused although it is only twelve legs: the leg limit and the price limit are independent, and the second can refuse a combination the first allows.
sample E - the limit that actually bites payout ceiling = 25,000.00 maximum stake = 250.00 at a composed price of 4.80: 250.00 x 4.80 = 1,200.00 -> under the ceiling at a composed price of 100.0: 250.00 x 100.0 = 25,000.00 -> exactly the ceiling above a price of 100.0 the stake is capped by the ceiling, not by 250.00: at 129.7 maximum stake = 25,000.00 / 129.7 = 192.75 at 500.0 maximum stake = 25,000.00 / 500.0 = 50.00 so the longest combination the operator will price can only be staked at a fifth of the normal maximum.

The limit nobody publishes

Four of the forty terms pages in sample F state the maximum stake on a composed market, and the same four are the only ones where a reader could work out that the payout ceiling binds before the stake limit. The practical version for a reader is this: the number printed next to the stake box is not the amount that will be accepted on a long combination, and the only way to know the real maximum is to price the combination and divide the payout ceiling by the price.

Five limits to look for before composing
  • The minimum and maximum number of legs, and whether a leg may be added after the combination is priced.
  • Whether the operator caps the price or refuses above it - on the samples it refuses, which is different.
  • The maximum stake stated in the account, and whether it is lower on a composed market than on a published one.
  • The payout ceiling, and whether it applies per combination, per account and day, or per market.
  • Whether a combination that is refused at one stake may be accepted at a smaller one, which is what the price limit implies.

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