A binary board makes "a full set is $1" obvious. Plenty of boards have a dozen mutually exclusive outcomes — which city is hottest, who wins, which temperature band. Those use a mechanism called NegRisk to hold the same rule: all outcome prices sum to $1. Here is what it adds, and what it costs.
A complementary set is every mutually exclusive outcome of an event. It has to satisfy two conditions:
| Condition | Means | If violated |
|---|---|---|
| Exclusive | no two can both be true | a set could be worth $2; the rule breaks |
| Exhaustive | one of them must be true | all could zero; a set is worth $0 |
With both satisfied, exactly one token in the set pays $1 whatever happens — so "a set = $1" survives intact, just with eleven or twenty pieces instead of two.
Holding some outcomes of an N-outcome event means your worst case has a floor, because the remaining outcomes exist. The mechanism's core capability is conversion: swap "NO on outcome A" for "YES on every other outcome", and back — because those two things are logically identical (A does not happen ⇔ one of the others does).
| Hold | Equivalent to |
|---|---|
| 1 × NO on outcome A | 1 × YES on each of B, C, D … |
One position, two expressions — and the market frequently prices the two differently. That gap is where opportunity on these boards is supposed to live.
A common belief is that conversion routes around the taker fee. It does not. Conversion is a chain action; it cannot unwind fees that were already paid when you built the legs.
What it genuinely changes is capital efficiency: you can realise part of a position without waiting for settlement, so the money recycles sooner. Real value — but it is time value, not a fee discount.
Modelling "conversion saves fees" produces a systematically optimistic result.
Split, merge and redeem are standard and nearly every client has them. Conversion is NegRisk-specific and often absent.
I hit this directly: the SDK I had installed offered split, merge and redeem and no conversion entry point at all — meaning that even if the data showed an opportunity, the execution layer could not perform the action.
General rule, not specific to this feature: an opportunity found in research must be checked against what the execution layer can actually do, or the whole line produces nothing.
Verifying costs one minimum-size trade. Not verifying costs the entire research effort.
| Difficulty | Why |
|---|---|
| N books to watch | a binary needs two sides; eleven bands need eleven, with wildly different depth |
| Naked-leg risk multiplies | a set needs N fills; one missing leg and the set does not exist |
| Cold bands are unbuyable | the near-zero-probability bands often have no quotes — and you must have them |
| Fees on every leg | N legs, N taker fees, not one |
The third row is the usual cause of death: the sum shows 0.96, four cents sit there, and those four cents live precisely in the band you cannot buy. Quotes and executable size are different quantities; a backtest using quotes without depth will invent opportunities that never existed — see walking the book.
"Buy the whole set when it sums under $1" is the most obvious arbitrage on the venue. I ran a full census: live executable inventory was zero.
Not surprising — it is purely mechanical, requires no judgement, and pays a certain amount, which makes it the first thing to be fully automated. The kill file entry is here.
The value to an ordinary reader is twofold: you can safely read the sum as $1, and any opportunity that requires no judgement should be assumed already taken — if you can still see it, that is usually because it cannot be executed, not because nobody noticed.
With more than two outcomes the rule is unchanged: all prices sum to $1. What changes is execution — N legs, N fees, N books that can fail to fill. The distance between the spread on paper and the spread you can collect is exactly those things.